Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

1

Control of an MR Tuned Vibration Absorber for Wind Turbine Application

Utilising the Refined Force Tracking Algorithm

Paweł Martynowicz

AGH University of Science and Technology Department of Process Control al Mickiewicza

30 30-059 Cracow Poland

e-mail pmartynaghedupl

ABSTRACT

This work covers selected control issues concerning the wind turbine tower-nacelle

laboratory model equipped with a magnetorheological (MR) damper based tuned vibration

absorber (TVA) The objective of the current research is a development and experimental

implementation of the control algorithm that couples a basic adaptive stiffness solution with

refined stock MR damper force tracking concept to obtain a quality tower vibration reduction

system The experiments were conducted assuming monoharmonic horizontal excitation

applied to the assembly modelling the nacelle The frequency range comprised the

neighbourhood of the first bending mode of the tower-nacelle system The results proved the

effectiveness of the adopted algorithm referring to the other high performance solutions

1 INTRODUCTION

The wind energy sector is rapidly growing nowadays Wind turbines are ecological solutions

yet their implementation cost is significant Structural vibrations and their consequences

imply relatively high investment into the construction process which is one of the greatest

contributors to the amount that wind farm implementation costs The aerodynamic load (and

the hydrodynamicice load for offshore structures) that varies in time including wind shear

Karman vortices blade passing effect differences in inflow conditions for each of the blades

as well as rotating turbine elements unbalance and generator operation these are the major

contributors to the structural vibrations of towers and blades [1] The cyclic stress that the

tower is subjected to may decrease reliable operation time due to structure fatigue wear [2]

or even a failure accident These vibrations are generally lightly damped especially

considering low aeroelastic damping for the first tower lateral mode [3456] The lateral

modes are excited due to Karman vortices generator operation sea wave variable load and

rotating machinery unbalance rather than due to direct wind load variations and the blade

passing effect as for longitudinal modes In the current project tower vibration only is being

analysed

The solutions utilised to reduce wind turbines towers vibrations include collective blade

pitch control generator electromagnetic torque control [789] and tuned vibration absorbers

(TVAs) [10111213] In the standard (passive) approach a TVA consists of an additional

moving mass spring and viscous damper which parameters are tuned to the selected (most

often the first) mode of vibration [1014] Passive TVAs work well at the load conditions

characterised with a single frequency to which they are tuned but cannot adapt to a wide

excitation spectrum [15] thus more advanced TVAs are required to changetune the TVA

operating frequency Among them magnetorheological (MR) TVAs are placed [15] as using

an MR damper instead of a viscous one guarantees a wide range of resistance force

millisecond response time high operational robustness including lower sensitivity to

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

2

temperature change and minor energy requirements as compared with active systems

[1617181920212223] Simulations and experiments show that implementation of an MR

damper in the TVA system may lead to further vibration reduction in relation to passive TVA

[24252627]

Within the scope of the current project a specially developed and built tower-nacelle

laboratory model (Fig 1) was made in which all turbine components (a nacelle blades a

hub a shaft a generator and possibly a gearbox) are represented by nacelle concentrated

mass The laboratory test rig of the wind turbine tower-nacelle system makes it possible to

model tower vibrations under various excitation sources as the horizontal concentrated force

generated by the dedicated shaker may model the load applied to the nacelle or to the tower

itself at the arbitrary height Both locations enable to force tower bending modes of vibration

The rig may also be laid down on the horizontally excited platform to model the vibrations of

buoy-floating wind turbine structures or vibrations due to seismic excitation

The problem of wind turbine tower vibration control with an MR TVA utilising an

adaptive stiffness concept with a newly developed force tracking algorithm is presented here

Both the adaptive stiffness and the MR damper force tracking solutions were investigated

previously separately however limited (numerical or hardware in the loop only continuous ndash

with no discontinuities or two-level force current pattern regarded) implementation

scenarios were presented only [2829303132] or the quality of the force follow-up left the

field for further improvements [242526] The MR damper real-time force tracking problem

along with the adaptive stiffness and damping friction was investigated extensively with fair

results in [33343536] Weber in [33] uses a series of BoucndashWen models computed in

parallel to estimate the required control current with no need of force sensor however

presented measured tracking of clipped viscous damping with negative stiffness exhibits slow

force rise after piston velocity sign change The interesting logics is adopted in [34] for a

system tailored MR damper dealing separately with the regions of rapid MR damper force

increase decrease and the transition between these two relations together with the negative

current spikes just before the desired force sign changes However measured real-time

tracking of force patterns exhibiting negative stiffness is again characterised with

insufficiently sharp force rise while tracking of force patterns exhibiting positive stiffness is

characterised with significant force error (overshoot) due to the remanent magnetization

These two problems occurring either if the actual MR damper force should be quickly

increased to a large value or if the force should be rapidly decreased to zero both at the

displacement extreme (and force sign change) are not removed by this approach utilising MR

damper inverse model feed forward and force sensor feedback even using negative current

applied each half cycle [35] Weber in [36] also uses MR damper inverse model combined

with force sensor Again measured real-time tracking of force patterns is characterised with

insufficiently rapid force rise or significant overshoot both after force sign change

The current work covers real-time realisation of the improved (over the previous solutions

[24252629313237]) stock MR damper continuous pattern tracking algorithm coping well

with the discontinuities (rapid value changes) of the force and the magnetic remanence

combining MR damper forward model with force sign change prediction (feed forward)

force sensor feedback and dedicated logics together with a basic adaptive stiffness

implementation resulting in a quality vibration reduction system As a reference passive

solutions with several MR damper constant input current values the adaptive stiffness

concept with previously tested MR damper hyperbolic tangent inverse model and PI-based

force tracking algorithms [24252629313237] along with a modified ground hook control

[2526] results are presented Only the first bending mode of vibration frequency

neighbourhood is analysed here

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

3

The paper is organised as follows In the forthcoming section the wind turbine tower-

nacelle laboratory model is introduced Then a vibration control algorithm is presented and

followed by the experimental analysis results The paper is finished with several conclusions

2 THE WIND TURBINE TOWER-NACELLE LABORATORY MODEL

The model to be analysed (Fig 1) consists of a titanium (Ti Gr5) rod 1 arranged vertically

representing the wind-turbine tower and a stiff body (system of steel plates) 2 fixed rigidly to

the top of the rod representing both nacelle and turbine assemblies The bottom end of the

rod is rigidly mounted to the ground via an adequately stiff steel foundation frame 3 As the

first tower bending mode has dominant modal mass participation (ca fivefold greater than the

next mode) a vibration reduction system (an MR TVA) is located at the top of the rod (at the

nacelle) The MR TVA is an additional stiff body 6 (an absorber) moving horizontally along

linear bearing guides connected with the system representing the nacelle via a spring and

Lord RD 1097-1 MR damper [38] in parallel 7 The absorber mass m2 and the spring stiffness

k2 parameters of the TVA were tuned to the first bending mode of the tower-nacelle system

vibrations on the basis of standard principles of the TVA tuning [10] The RD 1097-1 damper

(which force depends on the current fed to its coil) is an actuator of such vibration reduction

system The MR TVA operates along the same direction as the vibration excitation applied

(assuming small bending angles) Force excitation system comprises The Modal Shop

lightweight electrodynamic force exciter of 2060E series 4 [39] with the drive train assembly

5 of the changeable leverage [4041424344]

The horizontal displacement and velocity of the system modelling the nacelle are

designated by x1 and v1 (respectively) while the horizontal displacement and velocity of the

absorber (the TVA mass) are x2 and v2 Thus x1ndashx2 designates the MR damper relative

displacement (that is measured by LVDT transducer 8) while v1ndashv2 designates the MR

damper relative velocity The MR damper force PMR is measured by the tensometric

transducer 9

Figure 1 The laboratory test rig

1

2 6

3

4

5

6 7 9

8 2

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

4

3 THE CONTROL ALGORITHM

The underlying idea of the implemented control system is presented in Fig 2 Three

measurement input signals are regarded spring MR damper relative displacement x1ndashx2meas

MR damper current iMRmeas and MR damper force PMR

meas The MR Damper Required Force

subsystem corresponds to the real-time calculation of the demanded MR damper force PMRreq

ndash for the purpose of the current analysis the algorithm of the undamped dynamic vibration

absorber [10] that tracks excitation frequency [252628] is emulated using the MR damper

The MR damper should generate positive or negative stiffness force in such a way that the

TVA stiffness 2

reqk in equations (1) and (2) is tuned to the actual operationexcitation

frequency exc rather than to the tower-nacelle system first bending frequency Based on this

assumption the real-time determination of exc is followed by the real-time calculation of the

TVA required stiffness force 2 1 2

req req

stiffP k x x while the damping is assumed to be zero

(for the most efficient vibration mitigation at the frequency of tuning) leading to the MR

damper required force formula

2 2 1 2

req req

MRP k k x x (1)

with

2

2

2

req

exck m (2)

where γ is a correction factor that is present as the MR damper cannot deliver energy to the

system thus the force defined by equation (1) cannot be exactly mapped

Figure 2 The schematic diagram of the control system

When active forces are required zero force is assumed Thus arises a problem of a precise

MR damper force tracking in the case of pattern being discontinuous due to such a switching

A quick timeous (with possible prediction) and sharp force follow-up is needed whereas the

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

5

actuator dynamics exhibits the inertia due to the coil electrical resistance and inductance

magnetic remanence as well as the time lag hysteresis resulting from the MR effect

(particle chains formation) delay MR fluid preyield operation regime These effects cannot

be eliminated by a simple PIPID feedback controller with the sign adjustments

[242526313237] as it can shape the force-velocity relationship only into a linear or a

higher-order polynomial function with the inherent time lag even utilising the adequate

current controller Thus a dedicated MR damper force follow-up PID-based control

algorithm that was specially developed and refined during the current study based on

[252631] is represented by the PID Force Controller with Correction Demagnetisation amp

Sharpening subsystem (see Fig 2) Apart from the demanded MR damper force PMRreq input

the measured actual MR damper force PMRmeas and the modelled MR damper force PMR

modelled

signals are fed to the input of this subsystem PMRmodelled is the real-time calculated force with

the use of the MR damper forward hyperbolic tangent model (the MR Damper Model

subsystem) in the form of

1 2 1 1 2 0 1 2 2 1 2tanh p pmodelled

MR cP P v v x x c v v x x (3)

where Pc = C1iMR + C2 and c0 = C3iMR + C4 are the MR damper current (iMR) dependent

friction force and viscous damping coefficients (respectively) while p1 and p2 are the

scaling parameters The parameters initial values taken from Ref [45] were modified

accordingly for the current analysis frequency and piston travel ranges Additionally p1 and

p2 values were lowered down to be negative to obtain the earlier MR damper response sign

changes serving as PMRmeas sign change prediction The resultant MR damper model

parameters are gathered in the Tab 1 The Kalman Filter subsystem as introduced in [27] is

used for the real-time reproduction of the unmeasured state namely the MR damper relative

velocity v1ndashv2 in a presence of measurement noise that otherwise would be amplified by the

simple differentiating of x1ndashx2

Table 1 The adopted parameters of the MR damper model

Parameter Value

ν 130

p1 -250

p2 -100

C1 202

C2 225

C3 312

C4 467

The PID Force Controller with Correction Demagnetisation amp Sharpening subsystem

representation in Simulink is depicted in Fig 3 Its three main elements are the PID

Controller with Correction the Demagnetisation and the Response Sharpening subsystems

The primary version (V1) of the PID Controller with Correction subsystem is depicted in

Fig 4 It consists of the Abs blocks the Gain block Alpha1 as the scaling factor (Alpha1gt1 is

necessary as |PMRreq|=|PMR

meas| case should not result in zero control) the PID Controller

with Alpha2 Constrained Integration block (Alpha2lt1 multiplier constraints the integral

action when Alpha1|PMRreq|le|PMR

meas|) the multiplying blocks sign relations of

PMRreqampPMR

meas PMRreqampPMR

modelled PMRmeasampPMR

modelled determination conditional (rhombus)

blocks with logical (marked in grey) outputs and the Switch blocks with grey logical inputs

and black switched signals inputs Standard automatic control PID tuning techniques were

used for selection of proportional P integral I and derivative D path gains Additionally the

Saturation block is used with constants idemag=1510ndash2 A (the MR damper magnetic path amp

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

6

MR fluid particles demagnetisation current value) and imax=15 A while the Gain ndash1 is for

negation and the Max block with ndash02imax (ndash03 A) constant input are used to sharpen the

system response when PMRmeas changes sign (while PMR

req sign is maintained) what is

predicted by PMRmodelled signal to set the instantaneous current adequately early to ndash03 A and

moreover obtain minimum MR damper residual force modulus (that is greater due to the

remanent magnetisation) after PMRmeas sign change (see time range of (0315 0350) s in Figs

18 19 and 21 (b) vs Figs 16 and 17) Such constructed MR damper force tracking idea is

insensitive to MR damper dynamics changes due to eg temperature or stroke amplitude

variation during its operation as PMRmodelled sign is considered here instead of PMR

modelled value

Figure 3 Simulink diagram of the PID Force Controller with Correction

Demagnetisation amp Sharpening subsystem

Figure 4 Simulink diagram of the PID Controller with Correction subsystem V1

The second version (V2) of the PID Controller with Correction concept is depicted in

Fig 5 It differs from V1 by an idea of the integrator resetting when PMRmeas and PMR

modelled

have the opposite signs while the integrator initial condition (after the reset) is Alpha3

(Alpha3lt1) times the most recent nonzero integrator state This solution is implemented to

cope with the integrator wind-up problem that may be observed for the V1 concept (see Fig

18 vs Fig 19 starting eg at 005 s) and comes along with possibly enlarged I path gain and

higher integration constraint Alpha2 (Alpha2lt1) in relation to V1 concept

The Demagnetisation subsystem (see Fig 3) is depicted in Fig 6 It produces the

exponentially decaying current pattern (due to the presence of derivative element with first

order inertia and T=0067tperiod where tperiod= 2 exc ) that is switched between positive and

negative values using Rectangle Pulse Generator multiplier block (with two levels ndashidemag

and idemag) when the force should be zero due to the MR damper inability to produce active

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

7

forces (see Fig 21 (b)) The Running Mean subsystem (Fig 7) calculates the difference of the

outputs of two integrator blocks with the level-type reset (integration runs only when the

required value of the control current is ndashidemag ie PMRreq and PMR

meas have opposite signs ndash

see Figs 4 and 5) with the delay time tdelay=0067tperiod between them assuming that the

vibration patterns are characterised by single dominant frequency which is the case in the

most real world wind turbine structures operation scenarios

Figure 5 Simulink diagram of the PID Controller with Correction subsystem V2

Figure 6 Simulink diagram of the Demagnetisation subsystem

Figure 7 Simulink diagram of the Running Mean subsystem

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

8

The Response sharpening subsystem (see Fig 3) is presented in Fig 8 Its aim is to

sharpen the MR damper response at the moment of PMRmeas signal sign change while PMR

req

sign has changed earlier however the MR damper (as a dissipative device) was unable to

produce the active force (see Figs 13 and 14) To fulfil this task the control current is

enlarged by the value of 05 A when PMRmeas modulus is decreasing and is lower than 10 of

PMRmeas running amplitude and PMR

meas sign is consistent within last two sampling periods t0

(see Figs 13 14 and 21 (a) t0=110ndash3 s was assumed) Thanks to such logics the required

value of the control current iMRreq precedes the sign change of PMR

meas thus the control current

that actually flows through the MR damper coil iMRmeas is set at the moment of the PMR

meas

sign change with no delay The Running Amplitude subsystem (Fig 9) calculates the

difference of the outputs of the two integrator blocks with delay of five oscillation periods

between them The input to both integrators is the quantity (PMRmeas) squared (Sqr block) The

resultant difference is multiplied by two and divided by a time of five periods to obtain the

amplitude squared thus finally the Sqrt (square root) block is needed only to obtain

amplitude A(bull) of the input signal (assuming that vibration pattern is characterised by single

dominant frequency)

The parameters imax idemag tdelay Alpha1 Alpha2 Alpha3 values were selected on the

basis of numerical simulations supported by MR damper dynamics experimental testing

Figure 8 Simulink diagram of the Response sharpening subsystem

Figure 9 Simulink diagram of the Running Amplitude subsystem

The system in Fig 2 also includes standard analogue PID Current Controller subsystem

aimed to control MR damper with the use of an electronic board that enforces the MR damper

current via a control voltage uMR based on iMRmeas and iMR

req signals (see Figs 22 (a)(b))

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

9

4 THE EXPERIMENTAL ANALYSIS

For the purpose of the current experimental analysis that is oriented to the development of the

refined MR damper force tracking algorithm the value of γ = 1 was assumed while the

selection of γ was not a scope of the present research The theoretical study of γ determination

for the idealised semiactive device case of negligible response time zero residual force and

zero inherent system damping is presented in [28]

The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic

horizontal excitation applied to the nacelle The frequency range comprised the

neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz

Several system configurations were regarded passive system with the constant control

current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the

newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2

respectively) or with the simple previously tested MR damper hyperbolic tangent inverse

model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm

(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)

that was previously proved to be the best approach [242526] was selected The obtained

output frequency response functions of the tower tip horizontal displacement x1 amplitude are

presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1

the MR damper force PMRreq PMR

meas and the MR damper current iMRreq iMR

meas (adequately

scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-

displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT

PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and

435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most

crucial concerning preferable control solutions (see Fig 10 open loop systems are not of

interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR

meas

and the MR damper current iMRreq iMR

meas (adequately scaled and zoomed) obtained for the

system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current

Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)

25 3 35 4 45 505

1

15

2

25

3

35

4

45

5

55x 10

-3

Frequency [Hz]

Dis

pla

cem

ent A

mplit

ude A

(x1)

[m]

P0 = 61 N

00 A

01 A

02 A

03 A

04 A

05 A

ADPT V1

ADPT V2

ADPT INV

ADPT PI

ModGND

Figure 10 Tower tip displacement amplitude output frequency response functions

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

10

0 01 02 03 04 05 06 07-3

-2

-1

0

1

2

3

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

11

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

12

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops

Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

005 006

-1

0

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

13

0 005 01 015 02 025 03 035 04 045-2

-15

-1

-05

0

05

1

15

2

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops

021 0215 022 0225 023

-14

-12

-1

-08

-06

-04

-02

0

02

04

06

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

0315 032 0325 033 0335 034 0345 035

-03

-02

-01

0

01

02

03

04

05

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

001 x

PMR

req

001 x

PMR

meas

i MR

req

i MR

meas

Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

14

0 001 002 003 004 005-01

0

01

02

03

04

05

06

07

08

09

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

0 001 002 003 004 005-04

-03

-02

-01

0

01

02

03

04

05

06

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

Figure 22 PID current controller operation at

(a) positive (b) negative step change of iMRreq

Table 2 presents values of the quality index Q (best values in bold) being a root-mean-

square of the PMRreqndashPMR

meas difference

2

1

Nreq meas

MR MR

j

Q P j P j

(4)

where j is the time sample number and N is the number of the regarded samples ModGND

solution is omitted here as it is not based on required MR damper force tracking idea

Table 2 Values of the quality index Q (4)

System 295 [Hz] 435 [Hz]

ADPT INV 3002 6531

ADPT PI 2679 6274

ADPT V1 2366 4955

ADPT V2 2273 5374

In Fig 10 two maxima that are typical for TVA operation are apparent for all the

solutions but 02 03 04 and 05 A for which the damping is relatively too high

Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most

favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood

(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)

however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or

some positive damping added may improve the system response (as higher amplitude of

PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR

req ADPT V2

may become a preferred choice as it copes better with the integrator wind-up (by changing

the value of γ either the first maxima is lowered while the second maxima is elevated or the

second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to

the previously introduced [242526313237] ADPT PI and especially to ADPT INV within

the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper

required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz

for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially

considering the time instants immediately following PMRmeas sign changes (all presented time

patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the

difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

15

MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI

and especially for ADPT INV are incomparable to the respective patterns registered for

ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The

same may be concluded concerning PMRreq force tracking quality just before PMR

meas sign

changes although ADPT INV characteristics (Fig 16) could not be even described as

acceptable Concerning the MR damper residual force minimisation both ADPT V1 and

ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted

for the demagnetisation and response sharpening do the job properly The MR damper force-

displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along

with the friction (due to the MR damper residual force) phenomena at 295 Hz and the

positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper

measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not

differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2

however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash

as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated

according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of

nonlinear damping

As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one

may observe iMRreq signal rise at a time instant of 005 s while PMR

meas response modulus rise

is at ca 006 s what makes a real challenge for the follow-up-type-controller operational

quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations

present in Figs 13 and 14

5 CONCLUSION

The conducted experimental analysis proved the effectiveness of the proposed refined MR

damper force tracking algorithm in two versions The obtained output frequency response

function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels

former solutions (designated by ADPT PI and ADPT INV) and is comparable to the

frequency response of the ModGND system that previously demonstrated the best

performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range

while ModGND excels for frequencies higher than 435 Hz and marginally in the (300

320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope

best with the problem of the residual MR damper force magnetic remanence when zero

force is assumed due to the MR damper inability to generate active forces The

implementation of these logics for the ModGND algorithm along with the analysis of the

demanded value of γ for the real-world system with response time residual force and

inherent damping all of which are nonzero shall be a subject of the future research The

minimisation of the residual force negative effects and the quality of positive stiffness

tracking will also be investigated Based on these analyses results and laboratory model

measurements and considering the dynamic similarity study that includes determined time

and length scale factors [41] in combination with force scale factor [44] direct calculation of

the demanded control signal for a real-world full scale vibration reduction system MR TVA

will be possible

Acknowledgment

This work is supported by AGH University of Science and Technology under research

program No 1111130958

References

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

16

[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL

[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech

Struct amp Mach (1996) 24 (2) 155-187

[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering

low structural damping and soil structure interaction European Wind Energy Association

Annual Event (2012) Copenhagen 16-19042012

[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic

damping of operational wind turbine modes from experiments European Wind Energy

Association Annual Event (2012) Copenhagen 16-19042012

[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z

wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)

209-216

[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M

Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European

Wind Energy Association Annual Event (2012) Copenhagen 16-19042012

[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p

harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen

16-19042012

[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor

speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)

Monaco

[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind

turbines on two floating platforms Mechatronics (2011) 21 691-703

[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY

[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation

test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013

[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu

M Wind turbine tower load reduction using passive and semiactive dampers European Wind

Energy Association Annual Event (2011) Brussels

[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace

Exposition (2010) Orlando

[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej

z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198

[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR

damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds

Lisse CRC Press

[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and

experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State

Phenomena (2011) 177 (Control engineering in materials processing) 102-115

[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR

shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)

[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical

and Applied Mechanics (2007) 45 (1) 133-146

[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension

system with MR shock absorbers Computers and Structures (2008) 86 379-385

[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the

Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32

(1+2) 67-80

[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based

vibration reduction system Bulletin Of The Polish Academy Of

Sciences-Technical Sciences (2011) 59 (1) 75-80

[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes

Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

17

Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33

(3) 289-316

[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-

active vibration isolation systems using revised Bingham model Journal of Low Frequency

Noise Vibration and Active Control (2016) 35 (1) 17-24

[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration

absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoring (IACSM) (2014)

Barcelona Spain 15-17072014

[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with

magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi

1011771077546315591445

[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-

nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish

Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359

[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle

model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics

(2016) 54 (4) 1109-1123

[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled

semi-active damper Smart Mater Struct (2014) 23

[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers

for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control

Engineering

[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System

Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

3

The paper is organised as follows In the forthcoming section the wind turbine tower-

nacelle laboratory model is introduced Then a vibration control algorithm is presented and

followed by the experimental analysis results The paper is finished with several conclusions

2 THE WIND TURBINE TOWER-NACELLE LABORATORY MODEL

The model to be analysed (Fig 1) consists of a titanium (Ti Gr5) rod 1 arranged vertically

representing the wind-turbine tower and a stiff body (system of steel plates) 2 fixed rigidly to

the top of the rod representing both nacelle and turbine assemblies The bottom end of the

rod is rigidly mounted to the ground via an adequately stiff steel foundation frame 3 As the

first tower bending mode has dominant modal mass participation (ca fivefold greater than the

next mode) a vibration reduction system (an MR TVA) is located at the top of the rod (at the

nacelle) The MR TVA is an additional stiff body 6 (an absorber) moving horizontally along

linear bearing guides connected with the system representing the nacelle via a spring and

Lord RD 1097-1 MR damper [38] in parallel 7 The absorber mass m2 and the spring stiffness

k2 parameters of the TVA were tuned to the first bending mode of the tower-nacelle system

vibrations on the basis of standard principles of the TVA tuning [10] The RD 1097-1 damper

(which force depends on the current fed to its coil) is an actuator of such vibration reduction

system The MR TVA operates along the same direction as the vibration excitation applied

(assuming small bending angles) Force excitation system comprises The Modal Shop

lightweight electrodynamic force exciter of 2060E series 4 [39] with the drive train assembly

5 of the changeable leverage [4041424344]

The horizontal displacement and velocity of the system modelling the nacelle are

designated by x1 and v1 (respectively) while the horizontal displacement and velocity of the

absorber (the TVA mass) are x2 and v2 Thus x1ndashx2 designates the MR damper relative

displacement (that is measured by LVDT transducer 8) while v1ndashv2 designates the MR

damper relative velocity The MR damper force PMR is measured by the tensometric

transducer 9

Figure 1 The laboratory test rig

1

2 6

3

4

5

6 7 9

8 2

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

4

3 THE CONTROL ALGORITHM

The underlying idea of the implemented control system is presented in Fig 2 Three

measurement input signals are regarded spring MR damper relative displacement x1ndashx2meas

MR damper current iMRmeas and MR damper force PMR

meas The MR Damper Required Force

subsystem corresponds to the real-time calculation of the demanded MR damper force PMRreq

ndash for the purpose of the current analysis the algorithm of the undamped dynamic vibration

absorber [10] that tracks excitation frequency [252628] is emulated using the MR damper

The MR damper should generate positive or negative stiffness force in such a way that the

TVA stiffness 2

reqk in equations (1) and (2) is tuned to the actual operationexcitation

frequency exc rather than to the tower-nacelle system first bending frequency Based on this

assumption the real-time determination of exc is followed by the real-time calculation of the

TVA required stiffness force 2 1 2

req req

stiffP k x x while the damping is assumed to be zero

(for the most efficient vibration mitigation at the frequency of tuning) leading to the MR

damper required force formula

2 2 1 2

req req

MRP k k x x (1)

with

2

2

2

req

exck m (2)

where γ is a correction factor that is present as the MR damper cannot deliver energy to the

system thus the force defined by equation (1) cannot be exactly mapped

Figure 2 The schematic diagram of the control system

When active forces are required zero force is assumed Thus arises a problem of a precise

MR damper force tracking in the case of pattern being discontinuous due to such a switching

A quick timeous (with possible prediction) and sharp force follow-up is needed whereas the

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

5

actuator dynamics exhibits the inertia due to the coil electrical resistance and inductance

magnetic remanence as well as the time lag hysteresis resulting from the MR effect

(particle chains formation) delay MR fluid preyield operation regime These effects cannot

be eliminated by a simple PIPID feedback controller with the sign adjustments

[242526313237] as it can shape the force-velocity relationship only into a linear or a

higher-order polynomial function with the inherent time lag even utilising the adequate

current controller Thus a dedicated MR damper force follow-up PID-based control

algorithm that was specially developed and refined during the current study based on

[252631] is represented by the PID Force Controller with Correction Demagnetisation amp

Sharpening subsystem (see Fig 2) Apart from the demanded MR damper force PMRreq input

the measured actual MR damper force PMRmeas and the modelled MR damper force PMR

modelled

signals are fed to the input of this subsystem PMRmodelled is the real-time calculated force with

the use of the MR damper forward hyperbolic tangent model (the MR Damper Model

subsystem) in the form of

1 2 1 1 2 0 1 2 2 1 2tanh p pmodelled

MR cP P v v x x c v v x x (3)

where Pc = C1iMR + C2 and c0 = C3iMR + C4 are the MR damper current (iMR) dependent

friction force and viscous damping coefficients (respectively) while p1 and p2 are the

scaling parameters The parameters initial values taken from Ref [45] were modified

accordingly for the current analysis frequency and piston travel ranges Additionally p1 and

p2 values were lowered down to be negative to obtain the earlier MR damper response sign

changes serving as PMRmeas sign change prediction The resultant MR damper model

parameters are gathered in the Tab 1 The Kalman Filter subsystem as introduced in [27] is

used for the real-time reproduction of the unmeasured state namely the MR damper relative

velocity v1ndashv2 in a presence of measurement noise that otherwise would be amplified by the

simple differentiating of x1ndashx2

Table 1 The adopted parameters of the MR damper model

Parameter Value

ν 130

p1 -250

p2 -100

C1 202

C2 225

C3 312

C4 467

The PID Force Controller with Correction Demagnetisation amp Sharpening subsystem

representation in Simulink is depicted in Fig 3 Its three main elements are the PID

Controller with Correction the Demagnetisation and the Response Sharpening subsystems

The primary version (V1) of the PID Controller with Correction subsystem is depicted in

Fig 4 It consists of the Abs blocks the Gain block Alpha1 as the scaling factor (Alpha1gt1 is

necessary as |PMRreq|=|PMR

meas| case should not result in zero control) the PID Controller

with Alpha2 Constrained Integration block (Alpha2lt1 multiplier constraints the integral

action when Alpha1|PMRreq|le|PMR

meas|) the multiplying blocks sign relations of

PMRreqampPMR

meas PMRreqampPMR

modelled PMRmeasampPMR

modelled determination conditional (rhombus)

blocks with logical (marked in grey) outputs and the Switch blocks with grey logical inputs

and black switched signals inputs Standard automatic control PID tuning techniques were

used for selection of proportional P integral I and derivative D path gains Additionally the

Saturation block is used with constants idemag=1510ndash2 A (the MR damper magnetic path amp

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

6

MR fluid particles demagnetisation current value) and imax=15 A while the Gain ndash1 is for

negation and the Max block with ndash02imax (ndash03 A) constant input are used to sharpen the

system response when PMRmeas changes sign (while PMR

req sign is maintained) what is

predicted by PMRmodelled signal to set the instantaneous current adequately early to ndash03 A and

moreover obtain minimum MR damper residual force modulus (that is greater due to the

remanent magnetisation) after PMRmeas sign change (see time range of (0315 0350) s in Figs

18 19 and 21 (b) vs Figs 16 and 17) Such constructed MR damper force tracking idea is

insensitive to MR damper dynamics changes due to eg temperature or stroke amplitude

variation during its operation as PMRmodelled sign is considered here instead of PMR

modelled value

Figure 3 Simulink diagram of the PID Force Controller with Correction

Demagnetisation amp Sharpening subsystem

Figure 4 Simulink diagram of the PID Controller with Correction subsystem V1

The second version (V2) of the PID Controller with Correction concept is depicted in

Fig 5 It differs from V1 by an idea of the integrator resetting when PMRmeas and PMR

modelled

have the opposite signs while the integrator initial condition (after the reset) is Alpha3

(Alpha3lt1) times the most recent nonzero integrator state This solution is implemented to

cope with the integrator wind-up problem that may be observed for the V1 concept (see Fig

18 vs Fig 19 starting eg at 005 s) and comes along with possibly enlarged I path gain and

higher integration constraint Alpha2 (Alpha2lt1) in relation to V1 concept

The Demagnetisation subsystem (see Fig 3) is depicted in Fig 6 It produces the

exponentially decaying current pattern (due to the presence of derivative element with first

order inertia and T=0067tperiod where tperiod= 2 exc ) that is switched between positive and

negative values using Rectangle Pulse Generator multiplier block (with two levels ndashidemag

and idemag) when the force should be zero due to the MR damper inability to produce active

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

7

forces (see Fig 21 (b)) The Running Mean subsystem (Fig 7) calculates the difference of the

outputs of two integrator blocks with the level-type reset (integration runs only when the

required value of the control current is ndashidemag ie PMRreq and PMR

meas have opposite signs ndash

see Figs 4 and 5) with the delay time tdelay=0067tperiod between them assuming that the

vibration patterns are characterised by single dominant frequency which is the case in the

most real world wind turbine structures operation scenarios

Figure 5 Simulink diagram of the PID Controller with Correction subsystem V2

Figure 6 Simulink diagram of the Demagnetisation subsystem

Figure 7 Simulink diagram of the Running Mean subsystem

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

8

The Response sharpening subsystem (see Fig 3) is presented in Fig 8 Its aim is to

sharpen the MR damper response at the moment of PMRmeas signal sign change while PMR

req

sign has changed earlier however the MR damper (as a dissipative device) was unable to

produce the active force (see Figs 13 and 14) To fulfil this task the control current is

enlarged by the value of 05 A when PMRmeas modulus is decreasing and is lower than 10 of

PMRmeas running amplitude and PMR

meas sign is consistent within last two sampling periods t0

(see Figs 13 14 and 21 (a) t0=110ndash3 s was assumed) Thanks to such logics the required

value of the control current iMRreq precedes the sign change of PMR

meas thus the control current

that actually flows through the MR damper coil iMRmeas is set at the moment of the PMR

meas

sign change with no delay The Running Amplitude subsystem (Fig 9) calculates the

difference of the outputs of the two integrator blocks with delay of five oscillation periods

between them The input to both integrators is the quantity (PMRmeas) squared (Sqr block) The

resultant difference is multiplied by two and divided by a time of five periods to obtain the

amplitude squared thus finally the Sqrt (square root) block is needed only to obtain

amplitude A(bull) of the input signal (assuming that vibration pattern is characterised by single

dominant frequency)

The parameters imax idemag tdelay Alpha1 Alpha2 Alpha3 values were selected on the

basis of numerical simulations supported by MR damper dynamics experimental testing

Figure 8 Simulink diagram of the Response sharpening subsystem

Figure 9 Simulink diagram of the Running Amplitude subsystem

The system in Fig 2 also includes standard analogue PID Current Controller subsystem

aimed to control MR damper with the use of an electronic board that enforces the MR damper

current via a control voltage uMR based on iMRmeas and iMR

req signals (see Figs 22 (a)(b))

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

9

4 THE EXPERIMENTAL ANALYSIS

For the purpose of the current experimental analysis that is oriented to the development of the

refined MR damper force tracking algorithm the value of γ = 1 was assumed while the

selection of γ was not a scope of the present research The theoretical study of γ determination

for the idealised semiactive device case of negligible response time zero residual force and

zero inherent system damping is presented in [28]

The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic

horizontal excitation applied to the nacelle The frequency range comprised the

neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz

Several system configurations were regarded passive system with the constant control

current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the

newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2

respectively) or with the simple previously tested MR damper hyperbolic tangent inverse

model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm

(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)

that was previously proved to be the best approach [242526] was selected The obtained

output frequency response functions of the tower tip horizontal displacement x1 amplitude are

presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1

the MR damper force PMRreq PMR

meas and the MR damper current iMRreq iMR

meas (adequately

scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-

displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT

PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and

435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most

crucial concerning preferable control solutions (see Fig 10 open loop systems are not of

interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR

meas

and the MR damper current iMRreq iMR

meas (adequately scaled and zoomed) obtained for the

system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current

Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)

25 3 35 4 45 505

1

15

2

25

3

35

4

45

5

55x 10

-3

Frequency [Hz]

Dis

pla

cem

ent A

mplit

ude A

(x1)

[m]

P0 = 61 N

00 A

01 A

02 A

03 A

04 A

05 A

ADPT V1

ADPT V2

ADPT INV

ADPT PI

ModGND

Figure 10 Tower tip displacement amplitude output frequency response functions

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

10

0 01 02 03 04 05 06 07-3

-2

-1

0

1

2

3

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

11

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

12

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops

Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

005 006

-1

0

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

13

0 005 01 015 02 025 03 035 04 045-2

-15

-1

-05

0

05

1

15

2

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops

021 0215 022 0225 023

-14

-12

-1

-08

-06

-04

-02

0

02

04

06

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

0315 032 0325 033 0335 034 0345 035

-03

-02

-01

0

01

02

03

04

05

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

001 x

PMR

req

001 x

PMR

meas

i MR

req

i MR

meas

Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

14

0 001 002 003 004 005-01

0

01

02

03

04

05

06

07

08

09

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

0 001 002 003 004 005-04

-03

-02

-01

0

01

02

03

04

05

06

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

Figure 22 PID current controller operation at

(a) positive (b) negative step change of iMRreq

Table 2 presents values of the quality index Q (best values in bold) being a root-mean-

square of the PMRreqndashPMR

meas difference

2

1

Nreq meas

MR MR

j

Q P j P j

(4)

where j is the time sample number and N is the number of the regarded samples ModGND

solution is omitted here as it is not based on required MR damper force tracking idea

Table 2 Values of the quality index Q (4)

System 295 [Hz] 435 [Hz]

ADPT INV 3002 6531

ADPT PI 2679 6274

ADPT V1 2366 4955

ADPT V2 2273 5374

In Fig 10 two maxima that are typical for TVA operation are apparent for all the

solutions but 02 03 04 and 05 A for which the damping is relatively too high

Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most

favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood

(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)

however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or

some positive damping added may improve the system response (as higher amplitude of

PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR

req ADPT V2

may become a preferred choice as it copes better with the integrator wind-up (by changing

the value of γ either the first maxima is lowered while the second maxima is elevated or the

second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to

the previously introduced [242526313237] ADPT PI and especially to ADPT INV within

the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper

required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz

for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially

considering the time instants immediately following PMRmeas sign changes (all presented time

patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the

difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

15

MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI

and especially for ADPT INV are incomparable to the respective patterns registered for

ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The

same may be concluded concerning PMRreq force tracking quality just before PMR

meas sign

changes although ADPT INV characteristics (Fig 16) could not be even described as

acceptable Concerning the MR damper residual force minimisation both ADPT V1 and

ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted

for the demagnetisation and response sharpening do the job properly The MR damper force-

displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along

with the friction (due to the MR damper residual force) phenomena at 295 Hz and the

positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper

measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not

differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2

however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash

as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated

according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of

nonlinear damping

As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one

may observe iMRreq signal rise at a time instant of 005 s while PMR

meas response modulus rise

is at ca 006 s what makes a real challenge for the follow-up-type-controller operational

quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations

present in Figs 13 and 14

5 CONCLUSION

The conducted experimental analysis proved the effectiveness of the proposed refined MR

damper force tracking algorithm in two versions The obtained output frequency response

function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels

former solutions (designated by ADPT PI and ADPT INV) and is comparable to the

frequency response of the ModGND system that previously demonstrated the best

performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range

while ModGND excels for frequencies higher than 435 Hz and marginally in the (300

320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope

best with the problem of the residual MR damper force magnetic remanence when zero

force is assumed due to the MR damper inability to generate active forces The

implementation of these logics for the ModGND algorithm along with the analysis of the

demanded value of γ for the real-world system with response time residual force and

inherent damping all of which are nonzero shall be a subject of the future research The

minimisation of the residual force negative effects and the quality of positive stiffness

tracking will also be investigated Based on these analyses results and laboratory model

measurements and considering the dynamic similarity study that includes determined time

and length scale factors [41] in combination with force scale factor [44] direct calculation of

the demanded control signal for a real-world full scale vibration reduction system MR TVA

will be possible

Acknowledgment

This work is supported by AGH University of Science and Technology under research

program No 1111130958

References

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

16

[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL

[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech

Struct amp Mach (1996) 24 (2) 155-187

[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering

low structural damping and soil structure interaction European Wind Energy Association

Annual Event (2012) Copenhagen 16-19042012

[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic

damping of operational wind turbine modes from experiments European Wind Energy

Association Annual Event (2012) Copenhagen 16-19042012

[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z

wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)

209-216

[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M

Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European

Wind Energy Association Annual Event (2012) Copenhagen 16-19042012

[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p

harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen

16-19042012

[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor

speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)

Monaco

[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind

turbines on two floating platforms Mechatronics (2011) 21 691-703

[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY

[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation

test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013

[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu

M Wind turbine tower load reduction using passive and semiactive dampers European Wind

Energy Association Annual Event (2011) Brussels

[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace

Exposition (2010) Orlando

[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej

z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198

[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR

damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds

Lisse CRC Press

[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and

experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State

Phenomena (2011) 177 (Control engineering in materials processing) 102-115

[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR

shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)

[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical

and Applied Mechanics (2007) 45 (1) 133-146

[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension

system with MR shock absorbers Computers and Structures (2008) 86 379-385

[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the

Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32

(1+2) 67-80

[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based

vibration reduction system Bulletin Of The Polish Academy Of

Sciences-Technical Sciences (2011) 59 (1) 75-80

[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes

Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

17

Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33

(3) 289-316

[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-

active vibration isolation systems using revised Bingham model Journal of Low Frequency

Noise Vibration and Active Control (2016) 35 (1) 17-24

[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration

absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoring (IACSM) (2014)

Barcelona Spain 15-17072014

[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with

magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi

1011771077546315591445

[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-

nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish

Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359

[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle

model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics

(2016) 54 (4) 1109-1123

[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled

semi-active damper Smart Mater Struct (2014) 23

[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers

for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control

Engineering

[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System

Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

4

3 THE CONTROL ALGORITHM

The underlying idea of the implemented control system is presented in Fig 2 Three

measurement input signals are regarded spring MR damper relative displacement x1ndashx2meas

MR damper current iMRmeas and MR damper force PMR

meas The MR Damper Required Force

subsystem corresponds to the real-time calculation of the demanded MR damper force PMRreq

ndash for the purpose of the current analysis the algorithm of the undamped dynamic vibration

absorber [10] that tracks excitation frequency [252628] is emulated using the MR damper

The MR damper should generate positive or negative stiffness force in such a way that the

TVA stiffness 2

reqk in equations (1) and (2) is tuned to the actual operationexcitation

frequency exc rather than to the tower-nacelle system first bending frequency Based on this

assumption the real-time determination of exc is followed by the real-time calculation of the

TVA required stiffness force 2 1 2

req req

stiffP k x x while the damping is assumed to be zero

(for the most efficient vibration mitigation at the frequency of tuning) leading to the MR

damper required force formula

2 2 1 2

req req

MRP k k x x (1)

with

2

2

2

req

exck m (2)

where γ is a correction factor that is present as the MR damper cannot deliver energy to the

system thus the force defined by equation (1) cannot be exactly mapped

Figure 2 The schematic diagram of the control system

When active forces are required zero force is assumed Thus arises a problem of a precise

MR damper force tracking in the case of pattern being discontinuous due to such a switching

A quick timeous (with possible prediction) and sharp force follow-up is needed whereas the

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

5

actuator dynamics exhibits the inertia due to the coil electrical resistance and inductance

magnetic remanence as well as the time lag hysteresis resulting from the MR effect

(particle chains formation) delay MR fluid preyield operation regime These effects cannot

be eliminated by a simple PIPID feedback controller with the sign adjustments

[242526313237] as it can shape the force-velocity relationship only into a linear or a

higher-order polynomial function with the inherent time lag even utilising the adequate

current controller Thus a dedicated MR damper force follow-up PID-based control

algorithm that was specially developed and refined during the current study based on

[252631] is represented by the PID Force Controller with Correction Demagnetisation amp

Sharpening subsystem (see Fig 2) Apart from the demanded MR damper force PMRreq input

the measured actual MR damper force PMRmeas and the modelled MR damper force PMR

modelled

signals are fed to the input of this subsystem PMRmodelled is the real-time calculated force with

the use of the MR damper forward hyperbolic tangent model (the MR Damper Model

subsystem) in the form of

1 2 1 1 2 0 1 2 2 1 2tanh p pmodelled

MR cP P v v x x c v v x x (3)

where Pc = C1iMR + C2 and c0 = C3iMR + C4 are the MR damper current (iMR) dependent

friction force and viscous damping coefficients (respectively) while p1 and p2 are the

scaling parameters The parameters initial values taken from Ref [45] were modified

accordingly for the current analysis frequency and piston travel ranges Additionally p1 and

p2 values were lowered down to be negative to obtain the earlier MR damper response sign

changes serving as PMRmeas sign change prediction The resultant MR damper model

parameters are gathered in the Tab 1 The Kalman Filter subsystem as introduced in [27] is

used for the real-time reproduction of the unmeasured state namely the MR damper relative

velocity v1ndashv2 in a presence of measurement noise that otherwise would be amplified by the

simple differentiating of x1ndashx2

Table 1 The adopted parameters of the MR damper model

Parameter Value

ν 130

p1 -250

p2 -100

C1 202

C2 225

C3 312

C4 467

The PID Force Controller with Correction Demagnetisation amp Sharpening subsystem

representation in Simulink is depicted in Fig 3 Its three main elements are the PID

Controller with Correction the Demagnetisation and the Response Sharpening subsystems

The primary version (V1) of the PID Controller with Correction subsystem is depicted in

Fig 4 It consists of the Abs blocks the Gain block Alpha1 as the scaling factor (Alpha1gt1 is

necessary as |PMRreq|=|PMR

meas| case should not result in zero control) the PID Controller

with Alpha2 Constrained Integration block (Alpha2lt1 multiplier constraints the integral

action when Alpha1|PMRreq|le|PMR

meas|) the multiplying blocks sign relations of

PMRreqampPMR

meas PMRreqampPMR

modelled PMRmeasampPMR

modelled determination conditional (rhombus)

blocks with logical (marked in grey) outputs and the Switch blocks with grey logical inputs

and black switched signals inputs Standard automatic control PID tuning techniques were

used for selection of proportional P integral I and derivative D path gains Additionally the

Saturation block is used with constants idemag=1510ndash2 A (the MR damper magnetic path amp

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

6

MR fluid particles demagnetisation current value) and imax=15 A while the Gain ndash1 is for

negation and the Max block with ndash02imax (ndash03 A) constant input are used to sharpen the

system response when PMRmeas changes sign (while PMR

req sign is maintained) what is

predicted by PMRmodelled signal to set the instantaneous current adequately early to ndash03 A and

moreover obtain minimum MR damper residual force modulus (that is greater due to the

remanent magnetisation) after PMRmeas sign change (see time range of (0315 0350) s in Figs

18 19 and 21 (b) vs Figs 16 and 17) Such constructed MR damper force tracking idea is

insensitive to MR damper dynamics changes due to eg temperature or stroke amplitude

variation during its operation as PMRmodelled sign is considered here instead of PMR

modelled value

Figure 3 Simulink diagram of the PID Force Controller with Correction

Demagnetisation amp Sharpening subsystem

Figure 4 Simulink diagram of the PID Controller with Correction subsystem V1

The second version (V2) of the PID Controller with Correction concept is depicted in

Fig 5 It differs from V1 by an idea of the integrator resetting when PMRmeas and PMR

modelled

have the opposite signs while the integrator initial condition (after the reset) is Alpha3

(Alpha3lt1) times the most recent nonzero integrator state This solution is implemented to

cope with the integrator wind-up problem that may be observed for the V1 concept (see Fig

18 vs Fig 19 starting eg at 005 s) and comes along with possibly enlarged I path gain and

higher integration constraint Alpha2 (Alpha2lt1) in relation to V1 concept

The Demagnetisation subsystem (see Fig 3) is depicted in Fig 6 It produces the

exponentially decaying current pattern (due to the presence of derivative element with first

order inertia and T=0067tperiod where tperiod= 2 exc ) that is switched between positive and

negative values using Rectangle Pulse Generator multiplier block (with two levels ndashidemag

and idemag) when the force should be zero due to the MR damper inability to produce active

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

7

forces (see Fig 21 (b)) The Running Mean subsystem (Fig 7) calculates the difference of the

outputs of two integrator blocks with the level-type reset (integration runs only when the

required value of the control current is ndashidemag ie PMRreq and PMR

meas have opposite signs ndash

see Figs 4 and 5) with the delay time tdelay=0067tperiod between them assuming that the

vibration patterns are characterised by single dominant frequency which is the case in the

most real world wind turbine structures operation scenarios

Figure 5 Simulink diagram of the PID Controller with Correction subsystem V2

Figure 6 Simulink diagram of the Demagnetisation subsystem

Figure 7 Simulink diagram of the Running Mean subsystem

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

8

The Response sharpening subsystem (see Fig 3) is presented in Fig 8 Its aim is to

sharpen the MR damper response at the moment of PMRmeas signal sign change while PMR

req

sign has changed earlier however the MR damper (as a dissipative device) was unable to

produce the active force (see Figs 13 and 14) To fulfil this task the control current is

enlarged by the value of 05 A when PMRmeas modulus is decreasing and is lower than 10 of

PMRmeas running amplitude and PMR

meas sign is consistent within last two sampling periods t0

(see Figs 13 14 and 21 (a) t0=110ndash3 s was assumed) Thanks to such logics the required

value of the control current iMRreq precedes the sign change of PMR

meas thus the control current

that actually flows through the MR damper coil iMRmeas is set at the moment of the PMR

meas

sign change with no delay The Running Amplitude subsystem (Fig 9) calculates the

difference of the outputs of the two integrator blocks with delay of five oscillation periods

between them The input to both integrators is the quantity (PMRmeas) squared (Sqr block) The

resultant difference is multiplied by two and divided by a time of five periods to obtain the

amplitude squared thus finally the Sqrt (square root) block is needed only to obtain

amplitude A(bull) of the input signal (assuming that vibration pattern is characterised by single

dominant frequency)

The parameters imax idemag tdelay Alpha1 Alpha2 Alpha3 values were selected on the

basis of numerical simulations supported by MR damper dynamics experimental testing

Figure 8 Simulink diagram of the Response sharpening subsystem

Figure 9 Simulink diagram of the Running Amplitude subsystem

The system in Fig 2 also includes standard analogue PID Current Controller subsystem

aimed to control MR damper with the use of an electronic board that enforces the MR damper

current via a control voltage uMR based on iMRmeas and iMR

req signals (see Figs 22 (a)(b))

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

9

4 THE EXPERIMENTAL ANALYSIS

For the purpose of the current experimental analysis that is oriented to the development of the

refined MR damper force tracking algorithm the value of γ = 1 was assumed while the

selection of γ was not a scope of the present research The theoretical study of γ determination

for the idealised semiactive device case of negligible response time zero residual force and

zero inherent system damping is presented in [28]

The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic

horizontal excitation applied to the nacelle The frequency range comprised the

neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz

Several system configurations were regarded passive system with the constant control

current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the

newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2

respectively) or with the simple previously tested MR damper hyperbolic tangent inverse

model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm

(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)

that was previously proved to be the best approach [242526] was selected The obtained

output frequency response functions of the tower tip horizontal displacement x1 amplitude are

presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1

the MR damper force PMRreq PMR

meas and the MR damper current iMRreq iMR

meas (adequately

scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-

displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT

PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and

435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most

crucial concerning preferable control solutions (see Fig 10 open loop systems are not of

interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR

meas

and the MR damper current iMRreq iMR

meas (adequately scaled and zoomed) obtained for the

system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current

Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)

25 3 35 4 45 505

1

15

2

25

3

35

4

45

5

55x 10

-3

Frequency [Hz]

Dis

pla

cem

ent A

mplit

ude A

(x1)

[m]

P0 = 61 N

00 A

01 A

02 A

03 A

04 A

05 A

ADPT V1

ADPT V2

ADPT INV

ADPT PI

ModGND

Figure 10 Tower tip displacement amplitude output frequency response functions

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

10

0 01 02 03 04 05 06 07-3

-2

-1

0

1

2

3

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

11

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

12

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops

Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

005 006

-1

0

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

13

0 005 01 015 02 025 03 035 04 045-2

-15

-1

-05

0

05

1

15

2

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops

021 0215 022 0225 023

-14

-12

-1

-08

-06

-04

-02

0

02

04

06

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

0315 032 0325 033 0335 034 0345 035

-03

-02

-01

0

01

02

03

04

05

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

001 x

PMR

req

001 x

PMR

meas

i MR

req

i MR

meas

Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

14

0 001 002 003 004 005-01

0

01

02

03

04

05

06

07

08

09

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

0 001 002 003 004 005-04

-03

-02

-01

0

01

02

03

04

05

06

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

Figure 22 PID current controller operation at

(a) positive (b) negative step change of iMRreq

Table 2 presents values of the quality index Q (best values in bold) being a root-mean-

square of the PMRreqndashPMR

meas difference

2

1

Nreq meas

MR MR

j

Q P j P j

(4)

where j is the time sample number and N is the number of the regarded samples ModGND

solution is omitted here as it is not based on required MR damper force tracking idea

Table 2 Values of the quality index Q (4)

System 295 [Hz] 435 [Hz]

ADPT INV 3002 6531

ADPT PI 2679 6274

ADPT V1 2366 4955

ADPT V2 2273 5374

In Fig 10 two maxima that are typical for TVA operation are apparent for all the

solutions but 02 03 04 and 05 A for which the damping is relatively too high

Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most

favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood

(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)

however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or

some positive damping added may improve the system response (as higher amplitude of

PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR

req ADPT V2

may become a preferred choice as it copes better with the integrator wind-up (by changing

the value of γ either the first maxima is lowered while the second maxima is elevated or the

second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to

the previously introduced [242526313237] ADPT PI and especially to ADPT INV within

the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper

required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz

for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially

considering the time instants immediately following PMRmeas sign changes (all presented time

patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the

difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

15

MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI

and especially for ADPT INV are incomparable to the respective patterns registered for

ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The

same may be concluded concerning PMRreq force tracking quality just before PMR

meas sign

changes although ADPT INV characteristics (Fig 16) could not be even described as

acceptable Concerning the MR damper residual force minimisation both ADPT V1 and

ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted

for the demagnetisation and response sharpening do the job properly The MR damper force-

displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along

with the friction (due to the MR damper residual force) phenomena at 295 Hz and the

positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper

measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not

differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2

however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash

as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated

according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of

nonlinear damping

As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one

may observe iMRreq signal rise at a time instant of 005 s while PMR

meas response modulus rise

is at ca 006 s what makes a real challenge for the follow-up-type-controller operational

quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations

present in Figs 13 and 14

5 CONCLUSION

The conducted experimental analysis proved the effectiveness of the proposed refined MR

damper force tracking algorithm in two versions The obtained output frequency response

function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels

former solutions (designated by ADPT PI and ADPT INV) and is comparable to the

frequency response of the ModGND system that previously demonstrated the best

performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range

while ModGND excels for frequencies higher than 435 Hz and marginally in the (300

320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope

best with the problem of the residual MR damper force magnetic remanence when zero

force is assumed due to the MR damper inability to generate active forces The

implementation of these logics for the ModGND algorithm along with the analysis of the

demanded value of γ for the real-world system with response time residual force and

inherent damping all of which are nonzero shall be a subject of the future research The

minimisation of the residual force negative effects and the quality of positive stiffness

tracking will also be investigated Based on these analyses results and laboratory model

measurements and considering the dynamic similarity study that includes determined time

and length scale factors [41] in combination with force scale factor [44] direct calculation of

the demanded control signal for a real-world full scale vibration reduction system MR TVA

will be possible

Acknowledgment

This work is supported by AGH University of Science and Technology under research

program No 1111130958

References

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

16

[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL

[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech

Struct amp Mach (1996) 24 (2) 155-187

[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering

low structural damping and soil structure interaction European Wind Energy Association

Annual Event (2012) Copenhagen 16-19042012

[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic

damping of operational wind turbine modes from experiments European Wind Energy

Association Annual Event (2012) Copenhagen 16-19042012

[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z

wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)

209-216

[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M

Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European

Wind Energy Association Annual Event (2012) Copenhagen 16-19042012

[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p

harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen

16-19042012

[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor

speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)

Monaco

[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind

turbines on two floating platforms Mechatronics (2011) 21 691-703

[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY

[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation

test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013

[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu

M Wind turbine tower load reduction using passive and semiactive dampers European Wind

Energy Association Annual Event (2011) Brussels

[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace

Exposition (2010) Orlando

[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej

z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198

[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR

damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds

Lisse CRC Press

[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and

experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State

Phenomena (2011) 177 (Control engineering in materials processing) 102-115

[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR

shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)

[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical

and Applied Mechanics (2007) 45 (1) 133-146

[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension

system with MR shock absorbers Computers and Structures (2008) 86 379-385

[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the

Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32

(1+2) 67-80

[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based

vibration reduction system Bulletin Of The Polish Academy Of

Sciences-Technical Sciences (2011) 59 (1) 75-80

[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes

Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

17

Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33

(3) 289-316

[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-

active vibration isolation systems using revised Bingham model Journal of Low Frequency

Noise Vibration and Active Control (2016) 35 (1) 17-24

[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration

absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoring (IACSM) (2014)

Barcelona Spain 15-17072014

[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with

magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi

1011771077546315591445

[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-

nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish

Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359

[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle

model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics

(2016) 54 (4) 1109-1123

[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled

semi-active damper Smart Mater Struct (2014) 23

[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers

for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control

Engineering

[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System

Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

5

actuator dynamics exhibits the inertia due to the coil electrical resistance and inductance

magnetic remanence as well as the time lag hysteresis resulting from the MR effect

(particle chains formation) delay MR fluid preyield operation regime These effects cannot

be eliminated by a simple PIPID feedback controller with the sign adjustments

[242526313237] as it can shape the force-velocity relationship only into a linear or a

higher-order polynomial function with the inherent time lag even utilising the adequate

current controller Thus a dedicated MR damper force follow-up PID-based control

algorithm that was specially developed and refined during the current study based on

[252631] is represented by the PID Force Controller with Correction Demagnetisation amp

Sharpening subsystem (see Fig 2) Apart from the demanded MR damper force PMRreq input

the measured actual MR damper force PMRmeas and the modelled MR damper force PMR

modelled

signals are fed to the input of this subsystem PMRmodelled is the real-time calculated force with

the use of the MR damper forward hyperbolic tangent model (the MR Damper Model

subsystem) in the form of

1 2 1 1 2 0 1 2 2 1 2tanh p pmodelled

MR cP P v v x x c v v x x (3)

where Pc = C1iMR + C2 and c0 = C3iMR + C4 are the MR damper current (iMR) dependent

friction force and viscous damping coefficients (respectively) while p1 and p2 are the

scaling parameters The parameters initial values taken from Ref [45] were modified

accordingly for the current analysis frequency and piston travel ranges Additionally p1 and

p2 values were lowered down to be negative to obtain the earlier MR damper response sign

changes serving as PMRmeas sign change prediction The resultant MR damper model

parameters are gathered in the Tab 1 The Kalman Filter subsystem as introduced in [27] is

used for the real-time reproduction of the unmeasured state namely the MR damper relative

velocity v1ndashv2 in a presence of measurement noise that otherwise would be amplified by the

simple differentiating of x1ndashx2

Table 1 The adopted parameters of the MR damper model

Parameter Value

ν 130

p1 -250

p2 -100

C1 202

C2 225

C3 312

C4 467

The PID Force Controller with Correction Demagnetisation amp Sharpening subsystem

representation in Simulink is depicted in Fig 3 Its three main elements are the PID

Controller with Correction the Demagnetisation and the Response Sharpening subsystems

The primary version (V1) of the PID Controller with Correction subsystem is depicted in

Fig 4 It consists of the Abs blocks the Gain block Alpha1 as the scaling factor (Alpha1gt1 is

necessary as |PMRreq|=|PMR

meas| case should not result in zero control) the PID Controller

with Alpha2 Constrained Integration block (Alpha2lt1 multiplier constraints the integral

action when Alpha1|PMRreq|le|PMR

meas|) the multiplying blocks sign relations of

PMRreqampPMR

meas PMRreqampPMR

modelled PMRmeasampPMR

modelled determination conditional (rhombus)

blocks with logical (marked in grey) outputs and the Switch blocks with grey logical inputs

and black switched signals inputs Standard automatic control PID tuning techniques were

used for selection of proportional P integral I and derivative D path gains Additionally the

Saturation block is used with constants idemag=1510ndash2 A (the MR damper magnetic path amp

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

6

MR fluid particles demagnetisation current value) and imax=15 A while the Gain ndash1 is for

negation and the Max block with ndash02imax (ndash03 A) constant input are used to sharpen the

system response when PMRmeas changes sign (while PMR

req sign is maintained) what is

predicted by PMRmodelled signal to set the instantaneous current adequately early to ndash03 A and

moreover obtain minimum MR damper residual force modulus (that is greater due to the

remanent magnetisation) after PMRmeas sign change (see time range of (0315 0350) s in Figs

18 19 and 21 (b) vs Figs 16 and 17) Such constructed MR damper force tracking idea is

insensitive to MR damper dynamics changes due to eg temperature or stroke amplitude

variation during its operation as PMRmodelled sign is considered here instead of PMR

modelled value

Figure 3 Simulink diagram of the PID Force Controller with Correction

Demagnetisation amp Sharpening subsystem

Figure 4 Simulink diagram of the PID Controller with Correction subsystem V1

The second version (V2) of the PID Controller with Correction concept is depicted in

Fig 5 It differs from V1 by an idea of the integrator resetting when PMRmeas and PMR

modelled

have the opposite signs while the integrator initial condition (after the reset) is Alpha3

(Alpha3lt1) times the most recent nonzero integrator state This solution is implemented to

cope with the integrator wind-up problem that may be observed for the V1 concept (see Fig

18 vs Fig 19 starting eg at 005 s) and comes along with possibly enlarged I path gain and

higher integration constraint Alpha2 (Alpha2lt1) in relation to V1 concept

The Demagnetisation subsystem (see Fig 3) is depicted in Fig 6 It produces the

exponentially decaying current pattern (due to the presence of derivative element with first

order inertia and T=0067tperiod where tperiod= 2 exc ) that is switched between positive and

negative values using Rectangle Pulse Generator multiplier block (with two levels ndashidemag

and idemag) when the force should be zero due to the MR damper inability to produce active

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

7

forces (see Fig 21 (b)) The Running Mean subsystem (Fig 7) calculates the difference of the

outputs of two integrator blocks with the level-type reset (integration runs only when the

required value of the control current is ndashidemag ie PMRreq and PMR

meas have opposite signs ndash

see Figs 4 and 5) with the delay time tdelay=0067tperiod between them assuming that the

vibration patterns are characterised by single dominant frequency which is the case in the

most real world wind turbine structures operation scenarios

Figure 5 Simulink diagram of the PID Controller with Correction subsystem V2

Figure 6 Simulink diagram of the Demagnetisation subsystem

Figure 7 Simulink diagram of the Running Mean subsystem

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

8

The Response sharpening subsystem (see Fig 3) is presented in Fig 8 Its aim is to

sharpen the MR damper response at the moment of PMRmeas signal sign change while PMR

req

sign has changed earlier however the MR damper (as a dissipative device) was unable to

produce the active force (see Figs 13 and 14) To fulfil this task the control current is

enlarged by the value of 05 A when PMRmeas modulus is decreasing and is lower than 10 of

PMRmeas running amplitude and PMR

meas sign is consistent within last two sampling periods t0

(see Figs 13 14 and 21 (a) t0=110ndash3 s was assumed) Thanks to such logics the required

value of the control current iMRreq precedes the sign change of PMR

meas thus the control current

that actually flows through the MR damper coil iMRmeas is set at the moment of the PMR

meas

sign change with no delay The Running Amplitude subsystem (Fig 9) calculates the

difference of the outputs of the two integrator blocks with delay of five oscillation periods

between them The input to both integrators is the quantity (PMRmeas) squared (Sqr block) The

resultant difference is multiplied by two and divided by a time of five periods to obtain the

amplitude squared thus finally the Sqrt (square root) block is needed only to obtain

amplitude A(bull) of the input signal (assuming that vibration pattern is characterised by single

dominant frequency)

The parameters imax idemag tdelay Alpha1 Alpha2 Alpha3 values were selected on the

basis of numerical simulations supported by MR damper dynamics experimental testing

Figure 8 Simulink diagram of the Response sharpening subsystem

Figure 9 Simulink diagram of the Running Amplitude subsystem

The system in Fig 2 also includes standard analogue PID Current Controller subsystem

aimed to control MR damper with the use of an electronic board that enforces the MR damper

current via a control voltage uMR based on iMRmeas and iMR

req signals (see Figs 22 (a)(b))

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

9

4 THE EXPERIMENTAL ANALYSIS

For the purpose of the current experimental analysis that is oriented to the development of the

refined MR damper force tracking algorithm the value of γ = 1 was assumed while the

selection of γ was not a scope of the present research The theoretical study of γ determination

for the idealised semiactive device case of negligible response time zero residual force and

zero inherent system damping is presented in [28]

The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic

horizontal excitation applied to the nacelle The frequency range comprised the

neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz

Several system configurations were regarded passive system with the constant control

current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the

newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2

respectively) or with the simple previously tested MR damper hyperbolic tangent inverse

model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm

(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)

that was previously proved to be the best approach [242526] was selected The obtained

output frequency response functions of the tower tip horizontal displacement x1 amplitude are

presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1

the MR damper force PMRreq PMR

meas and the MR damper current iMRreq iMR

meas (adequately

scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-

displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT

PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and

435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most

crucial concerning preferable control solutions (see Fig 10 open loop systems are not of

interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR

meas

and the MR damper current iMRreq iMR

meas (adequately scaled and zoomed) obtained for the

system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current

Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)

25 3 35 4 45 505

1

15

2

25

3

35

4

45

5

55x 10

-3

Frequency [Hz]

Dis

pla

cem

ent A

mplit

ude A

(x1)

[m]

P0 = 61 N

00 A

01 A

02 A

03 A

04 A

05 A

ADPT V1

ADPT V2

ADPT INV

ADPT PI

ModGND

Figure 10 Tower tip displacement amplitude output frequency response functions

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

10

0 01 02 03 04 05 06 07-3

-2

-1

0

1

2

3

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

11

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

12

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops

Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

005 006

-1

0

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

13

0 005 01 015 02 025 03 035 04 045-2

-15

-1

-05

0

05

1

15

2

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops

021 0215 022 0225 023

-14

-12

-1

-08

-06

-04

-02

0

02

04

06

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

0315 032 0325 033 0335 034 0345 035

-03

-02

-01

0

01

02

03

04

05

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

001 x

PMR

req

001 x

PMR

meas

i MR

req

i MR

meas

Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

14

0 001 002 003 004 005-01

0

01

02

03

04

05

06

07

08

09

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

0 001 002 003 004 005-04

-03

-02

-01

0

01

02

03

04

05

06

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

Figure 22 PID current controller operation at

(a) positive (b) negative step change of iMRreq

Table 2 presents values of the quality index Q (best values in bold) being a root-mean-

square of the PMRreqndashPMR

meas difference

2

1

Nreq meas

MR MR

j

Q P j P j

(4)

where j is the time sample number and N is the number of the regarded samples ModGND

solution is omitted here as it is not based on required MR damper force tracking idea

Table 2 Values of the quality index Q (4)

System 295 [Hz] 435 [Hz]

ADPT INV 3002 6531

ADPT PI 2679 6274

ADPT V1 2366 4955

ADPT V2 2273 5374

In Fig 10 two maxima that are typical for TVA operation are apparent for all the

solutions but 02 03 04 and 05 A for which the damping is relatively too high

Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most

favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood

(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)

however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or

some positive damping added may improve the system response (as higher amplitude of

PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR

req ADPT V2

may become a preferred choice as it copes better with the integrator wind-up (by changing

the value of γ either the first maxima is lowered while the second maxima is elevated or the

second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to

the previously introduced [242526313237] ADPT PI and especially to ADPT INV within

the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper

required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz

for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially

considering the time instants immediately following PMRmeas sign changes (all presented time

patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the

difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

15

MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI

and especially for ADPT INV are incomparable to the respective patterns registered for

ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The

same may be concluded concerning PMRreq force tracking quality just before PMR

meas sign

changes although ADPT INV characteristics (Fig 16) could not be even described as

acceptable Concerning the MR damper residual force minimisation both ADPT V1 and

ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted

for the demagnetisation and response sharpening do the job properly The MR damper force-

displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along

with the friction (due to the MR damper residual force) phenomena at 295 Hz and the

positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper

measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not

differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2

however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash

as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated

according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of

nonlinear damping

As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one

may observe iMRreq signal rise at a time instant of 005 s while PMR

meas response modulus rise

is at ca 006 s what makes a real challenge for the follow-up-type-controller operational

quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations

present in Figs 13 and 14

5 CONCLUSION

The conducted experimental analysis proved the effectiveness of the proposed refined MR

damper force tracking algorithm in two versions The obtained output frequency response

function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels

former solutions (designated by ADPT PI and ADPT INV) and is comparable to the

frequency response of the ModGND system that previously demonstrated the best

performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range

while ModGND excels for frequencies higher than 435 Hz and marginally in the (300

320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope

best with the problem of the residual MR damper force magnetic remanence when zero

force is assumed due to the MR damper inability to generate active forces The

implementation of these logics for the ModGND algorithm along with the analysis of the

demanded value of γ for the real-world system with response time residual force and

inherent damping all of which are nonzero shall be a subject of the future research The

minimisation of the residual force negative effects and the quality of positive stiffness

tracking will also be investigated Based on these analyses results and laboratory model

measurements and considering the dynamic similarity study that includes determined time

and length scale factors [41] in combination with force scale factor [44] direct calculation of

the demanded control signal for a real-world full scale vibration reduction system MR TVA

will be possible

Acknowledgment

This work is supported by AGH University of Science and Technology under research

program No 1111130958

References

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

16

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Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

6

MR fluid particles demagnetisation current value) and imax=15 A while the Gain ndash1 is for

negation and the Max block with ndash02imax (ndash03 A) constant input are used to sharpen the

system response when PMRmeas changes sign (while PMR

req sign is maintained) what is

predicted by PMRmodelled signal to set the instantaneous current adequately early to ndash03 A and

moreover obtain minimum MR damper residual force modulus (that is greater due to the

remanent magnetisation) after PMRmeas sign change (see time range of (0315 0350) s in Figs

18 19 and 21 (b) vs Figs 16 and 17) Such constructed MR damper force tracking idea is

insensitive to MR damper dynamics changes due to eg temperature or stroke amplitude

variation during its operation as PMRmodelled sign is considered here instead of PMR

modelled value

Figure 3 Simulink diagram of the PID Force Controller with Correction

Demagnetisation amp Sharpening subsystem

Figure 4 Simulink diagram of the PID Controller with Correction subsystem V1

The second version (V2) of the PID Controller with Correction concept is depicted in

Fig 5 It differs from V1 by an idea of the integrator resetting when PMRmeas and PMR

modelled

have the opposite signs while the integrator initial condition (after the reset) is Alpha3

(Alpha3lt1) times the most recent nonzero integrator state This solution is implemented to

cope with the integrator wind-up problem that may be observed for the V1 concept (see Fig

18 vs Fig 19 starting eg at 005 s) and comes along with possibly enlarged I path gain and

higher integration constraint Alpha2 (Alpha2lt1) in relation to V1 concept

The Demagnetisation subsystem (see Fig 3) is depicted in Fig 6 It produces the

exponentially decaying current pattern (due to the presence of derivative element with first

order inertia and T=0067tperiod where tperiod= 2 exc ) that is switched between positive and

negative values using Rectangle Pulse Generator multiplier block (with two levels ndashidemag

and idemag) when the force should be zero due to the MR damper inability to produce active

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

7

forces (see Fig 21 (b)) The Running Mean subsystem (Fig 7) calculates the difference of the

outputs of two integrator blocks with the level-type reset (integration runs only when the

required value of the control current is ndashidemag ie PMRreq and PMR

meas have opposite signs ndash

see Figs 4 and 5) with the delay time tdelay=0067tperiod between them assuming that the

vibration patterns are characterised by single dominant frequency which is the case in the

most real world wind turbine structures operation scenarios

Figure 5 Simulink diagram of the PID Controller with Correction subsystem V2

Figure 6 Simulink diagram of the Demagnetisation subsystem

Figure 7 Simulink diagram of the Running Mean subsystem

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

8

The Response sharpening subsystem (see Fig 3) is presented in Fig 8 Its aim is to

sharpen the MR damper response at the moment of PMRmeas signal sign change while PMR

req

sign has changed earlier however the MR damper (as a dissipative device) was unable to

produce the active force (see Figs 13 and 14) To fulfil this task the control current is

enlarged by the value of 05 A when PMRmeas modulus is decreasing and is lower than 10 of

PMRmeas running amplitude and PMR

meas sign is consistent within last two sampling periods t0

(see Figs 13 14 and 21 (a) t0=110ndash3 s was assumed) Thanks to such logics the required

value of the control current iMRreq precedes the sign change of PMR

meas thus the control current

that actually flows through the MR damper coil iMRmeas is set at the moment of the PMR

meas

sign change with no delay The Running Amplitude subsystem (Fig 9) calculates the

difference of the outputs of the two integrator blocks with delay of five oscillation periods

between them The input to both integrators is the quantity (PMRmeas) squared (Sqr block) The

resultant difference is multiplied by two and divided by a time of five periods to obtain the

amplitude squared thus finally the Sqrt (square root) block is needed only to obtain

amplitude A(bull) of the input signal (assuming that vibration pattern is characterised by single

dominant frequency)

The parameters imax idemag tdelay Alpha1 Alpha2 Alpha3 values were selected on the

basis of numerical simulations supported by MR damper dynamics experimental testing

Figure 8 Simulink diagram of the Response sharpening subsystem

Figure 9 Simulink diagram of the Running Amplitude subsystem

The system in Fig 2 also includes standard analogue PID Current Controller subsystem

aimed to control MR damper with the use of an electronic board that enforces the MR damper

current via a control voltage uMR based on iMRmeas and iMR

req signals (see Figs 22 (a)(b))

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

9

4 THE EXPERIMENTAL ANALYSIS

For the purpose of the current experimental analysis that is oriented to the development of the

refined MR damper force tracking algorithm the value of γ = 1 was assumed while the

selection of γ was not a scope of the present research The theoretical study of γ determination

for the idealised semiactive device case of negligible response time zero residual force and

zero inherent system damping is presented in [28]

The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic

horizontal excitation applied to the nacelle The frequency range comprised the

neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz

Several system configurations were regarded passive system with the constant control

current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the

newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2

respectively) or with the simple previously tested MR damper hyperbolic tangent inverse

model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm

(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)

that was previously proved to be the best approach [242526] was selected The obtained

output frequency response functions of the tower tip horizontal displacement x1 amplitude are

presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1

the MR damper force PMRreq PMR

meas and the MR damper current iMRreq iMR

meas (adequately

scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-

displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT

PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and

435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most

crucial concerning preferable control solutions (see Fig 10 open loop systems are not of

interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR

meas

and the MR damper current iMRreq iMR

meas (adequately scaled and zoomed) obtained for the

system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current

Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)

25 3 35 4 45 505

1

15

2

25

3

35

4

45

5

55x 10

-3

Frequency [Hz]

Dis

pla

cem

ent A

mplit

ude A

(x1)

[m]

P0 = 61 N

00 A

01 A

02 A

03 A

04 A

05 A

ADPT V1

ADPT V2

ADPT INV

ADPT PI

ModGND

Figure 10 Tower tip displacement amplitude output frequency response functions

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

10

0 01 02 03 04 05 06 07-3

-2

-1

0

1

2

3

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

11

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

12

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops

Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

005 006

-1

0

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

13

0 005 01 015 02 025 03 035 04 045-2

-15

-1

-05

0

05

1

15

2

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops

021 0215 022 0225 023

-14

-12

-1

-08

-06

-04

-02

0

02

04

06

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

0315 032 0325 033 0335 034 0345 035

-03

-02

-01

0

01

02

03

04

05

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

001 x

PMR

req

001 x

PMR

meas

i MR

req

i MR

meas

Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

14

0 001 002 003 004 005-01

0

01

02

03

04

05

06

07

08

09

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

0 001 002 003 004 005-04

-03

-02

-01

0

01

02

03

04

05

06

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

Figure 22 PID current controller operation at

(a) positive (b) negative step change of iMRreq

Table 2 presents values of the quality index Q (best values in bold) being a root-mean-

square of the PMRreqndashPMR

meas difference

2

1

Nreq meas

MR MR

j

Q P j P j

(4)

where j is the time sample number and N is the number of the regarded samples ModGND

solution is omitted here as it is not based on required MR damper force tracking idea

Table 2 Values of the quality index Q (4)

System 295 [Hz] 435 [Hz]

ADPT INV 3002 6531

ADPT PI 2679 6274

ADPT V1 2366 4955

ADPT V2 2273 5374

In Fig 10 two maxima that are typical for TVA operation are apparent for all the

solutions but 02 03 04 and 05 A for which the damping is relatively too high

Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most

favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood

(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)

however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or

some positive damping added may improve the system response (as higher amplitude of

PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR

req ADPT V2

may become a preferred choice as it copes better with the integrator wind-up (by changing

the value of γ either the first maxima is lowered while the second maxima is elevated or the

second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to

the previously introduced [242526313237] ADPT PI and especially to ADPT INV within

the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper

required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz

for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially

considering the time instants immediately following PMRmeas sign changes (all presented time

patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the

difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

15

MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI

and especially for ADPT INV are incomparable to the respective patterns registered for

ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The

same may be concluded concerning PMRreq force tracking quality just before PMR

meas sign

changes although ADPT INV characteristics (Fig 16) could not be even described as

acceptable Concerning the MR damper residual force minimisation both ADPT V1 and

ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted

for the demagnetisation and response sharpening do the job properly The MR damper force-

displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along

with the friction (due to the MR damper residual force) phenomena at 295 Hz and the

positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper

measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not

differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2

however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash

as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated

according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of

nonlinear damping

As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one

may observe iMRreq signal rise at a time instant of 005 s while PMR

meas response modulus rise

is at ca 006 s what makes a real challenge for the follow-up-type-controller operational

quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations

present in Figs 13 and 14

5 CONCLUSION

The conducted experimental analysis proved the effectiveness of the proposed refined MR

damper force tracking algorithm in two versions The obtained output frequency response

function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels

former solutions (designated by ADPT PI and ADPT INV) and is comparable to the

frequency response of the ModGND system that previously demonstrated the best

performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range

while ModGND excels for frequencies higher than 435 Hz and marginally in the (300

320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope

best with the problem of the residual MR damper force magnetic remanence when zero

force is assumed due to the MR damper inability to generate active forces The

implementation of these logics for the ModGND algorithm along with the analysis of the

demanded value of γ for the real-world system with response time residual force and

inherent damping all of which are nonzero shall be a subject of the future research The

minimisation of the residual force negative effects and the quality of positive stiffness

tracking will also be investigated Based on these analyses results and laboratory model

measurements and considering the dynamic similarity study that includes determined time

and length scale factors [41] in combination with force scale factor [44] direct calculation of

the demanded control signal for a real-world full scale vibration reduction system MR TVA

will be possible

Acknowledgment

This work is supported by AGH University of Science and Technology under research

program No 1111130958

References

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

16

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[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based

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Barcelona Spain 15-17072014

[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with

magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi

1011771077546315591445

[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-

nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish

Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359

[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle

model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics

(2016) 54 (4) 1109-1123

[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled

semi-active damper Smart Mater Struct (2014) 23

[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers

for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control

Engineering

[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System

Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

7

forces (see Fig 21 (b)) The Running Mean subsystem (Fig 7) calculates the difference of the

outputs of two integrator blocks with the level-type reset (integration runs only when the

required value of the control current is ndashidemag ie PMRreq and PMR

meas have opposite signs ndash

see Figs 4 and 5) with the delay time tdelay=0067tperiod between them assuming that the

vibration patterns are characterised by single dominant frequency which is the case in the

most real world wind turbine structures operation scenarios

Figure 5 Simulink diagram of the PID Controller with Correction subsystem V2

Figure 6 Simulink diagram of the Demagnetisation subsystem

Figure 7 Simulink diagram of the Running Mean subsystem

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

8

The Response sharpening subsystem (see Fig 3) is presented in Fig 8 Its aim is to

sharpen the MR damper response at the moment of PMRmeas signal sign change while PMR

req

sign has changed earlier however the MR damper (as a dissipative device) was unable to

produce the active force (see Figs 13 and 14) To fulfil this task the control current is

enlarged by the value of 05 A when PMRmeas modulus is decreasing and is lower than 10 of

PMRmeas running amplitude and PMR

meas sign is consistent within last two sampling periods t0

(see Figs 13 14 and 21 (a) t0=110ndash3 s was assumed) Thanks to such logics the required

value of the control current iMRreq precedes the sign change of PMR

meas thus the control current

that actually flows through the MR damper coil iMRmeas is set at the moment of the PMR

meas

sign change with no delay The Running Amplitude subsystem (Fig 9) calculates the

difference of the outputs of the two integrator blocks with delay of five oscillation periods

between them The input to both integrators is the quantity (PMRmeas) squared (Sqr block) The

resultant difference is multiplied by two and divided by a time of five periods to obtain the

amplitude squared thus finally the Sqrt (square root) block is needed only to obtain

amplitude A(bull) of the input signal (assuming that vibration pattern is characterised by single

dominant frequency)

The parameters imax idemag tdelay Alpha1 Alpha2 Alpha3 values were selected on the

basis of numerical simulations supported by MR damper dynamics experimental testing

Figure 8 Simulink diagram of the Response sharpening subsystem

Figure 9 Simulink diagram of the Running Amplitude subsystem

The system in Fig 2 also includes standard analogue PID Current Controller subsystem

aimed to control MR damper with the use of an electronic board that enforces the MR damper

current via a control voltage uMR based on iMRmeas and iMR

req signals (see Figs 22 (a)(b))

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

9

4 THE EXPERIMENTAL ANALYSIS

For the purpose of the current experimental analysis that is oriented to the development of the

refined MR damper force tracking algorithm the value of γ = 1 was assumed while the

selection of γ was not a scope of the present research The theoretical study of γ determination

for the idealised semiactive device case of negligible response time zero residual force and

zero inherent system damping is presented in [28]

The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic

horizontal excitation applied to the nacelle The frequency range comprised the

neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz

Several system configurations were regarded passive system with the constant control

current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the

newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2

respectively) or with the simple previously tested MR damper hyperbolic tangent inverse

model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm

(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)

that was previously proved to be the best approach [242526] was selected The obtained

output frequency response functions of the tower tip horizontal displacement x1 amplitude are

presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1

the MR damper force PMRreq PMR

meas and the MR damper current iMRreq iMR

meas (adequately

scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-

displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT

PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and

435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most

crucial concerning preferable control solutions (see Fig 10 open loop systems are not of

interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR

meas

and the MR damper current iMRreq iMR

meas (adequately scaled and zoomed) obtained for the

system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current

Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)

25 3 35 4 45 505

1

15

2

25

3

35

4

45

5

55x 10

-3

Frequency [Hz]

Dis

pla

cem

ent A

mplit

ude A

(x1)

[m]

P0 = 61 N

00 A

01 A

02 A

03 A

04 A

05 A

ADPT V1

ADPT V2

ADPT INV

ADPT PI

ModGND

Figure 10 Tower tip displacement amplitude output frequency response functions

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

10

0 01 02 03 04 05 06 07-3

-2

-1

0

1

2

3

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

11

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

12

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops

Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

005 006

-1

0

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

13

0 005 01 015 02 025 03 035 04 045-2

-15

-1

-05

0

05

1

15

2

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops

021 0215 022 0225 023

-14

-12

-1

-08

-06

-04

-02

0

02

04

06

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

0315 032 0325 033 0335 034 0345 035

-03

-02

-01

0

01

02

03

04

05

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

001 x

PMR

req

001 x

PMR

meas

i MR

req

i MR

meas

Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

14

0 001 002 003 004 005-01

0

01

02

03

04

05

06

07

08

09

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

0 001 002 003 004 005-04

-03

-02

-01

0

01

02

03

04

05

06

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

Figure 22 PID current controller operation at

(a) positive (b) negative step change of iMRreq

Table 2 presents values of the quality index Q (best values in bold) being a root-mean-

square of the PMRreqndashPMR

meas difference

2

1

Nreq meas

MR MR

j

Q P j P j

(4)

where j is the time sample number and N is the number of the regarded samples ModGND

solution is omitted here as it is not based on required MR damper force tracking idea

Table 2 Values of the quality index Q (4)

System 295 [Hz] 435 [Hz]

ADPT INV 3002 6531

ADPT PI 2679 6274

ADPT V1 2366 4955

ADPT V2 2273 5374

In Fig 10 two maxima that are typical for TVA operation are apparent for all the

solutions but 02 03 04 and 05 A for which the damping is relatively too high

Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most

favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood

(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)

however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or

some positive damping added may improve the system response (as higher amplitude of

PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR

req ADPT V2

may become a preferred choice as it copes better with the integrator wind-up (by changing

the value of γ either the first maxima is lowered while the second maxima is elevated or the

second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to

the previously introduced [242526313237] ADPT PI and especially to ADPT INV within

the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper

required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz

for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially

considering the time instants immediately following PMRmeas sign changes (all presented time

patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the

difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

15

MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI

and especially for ADPT INV are incomparable to the respective patterns registered for

ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The

same may be concluded concerning PMRreq force tracking quality just before PMR

meas sign

changes although ADPT INV characteristics (Fig 16) could not be even described as

acceptable Concerning the MR damper residual force minimisation both ADPT V1 and

ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted

for the demagnetisation and response sharpening do the job properly The MR damper force-

displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along

with the friction (due to the MR damper residual force) phenomena at 295 Hz and the

positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper

measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not

differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2

however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash

as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated

according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of

nonlinear damping

As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one

may observe iMRreq signal rise at a time instant of 005 s while PMR

meas response modulus rise

is at ca 006 s what makes a real challenge for the follow-up-type-controller operational

quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations

present in Figs 13 and 14

5 CONCLUSION

The conducted experimental analysis proved the effectiveness of the proposed refined MR

damper force tracking algorithm in two versions The obtained output frequency response

function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels

former solutions (designated by ADPT PI and ADPT INV) and is comparable to the

frequency response of the ModGND system that previously demonstrated the best

performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range

while ModGND excels for frequencies higher than 435 Hz and marginally in the (300

320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope

best with the problem of the residual MR damper force magnetic remanence when zero

force is assumed due to the MR damper inability to generate active forces The

implementation of these logics for the ModGND algorithm along with the analysis of the

demanded value of γ for the real-world system with response time residual force and

inherent damping all of which are nonzero shall be a subject of the future research The

minimisation of the residual force negative effects and the quality of positive stiffness

tracking will also be investigated Based on these analyses results and laboratory model

measurements and considering the dynamic similarity study that includes determined time

and length scale factors [41] in combination with force scale factor [44] direct calculation of

the demanded control signal for a real-world full scale vibration reduction system MR TVA

will be possible

Acknowledgment

This work is supported by AGH University of Science and Technology under research

program No 1111130958

References

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

16

[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL

[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech

Struct amp Mach (1996) 24 (2) 155-187

[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering

low structural damping and soil structure interaction European Wind Energy Association

Annual Event (2012) Copenhagen 16-19042012

[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic

damping of operational wind turbine modes from experiments European Wind Energy

Association Annual Event (2012) Copenhagen 16-19042012

[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z

wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)

209-216

[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M

Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European

Wind Energy Association Annual Event (2012) Copenhagen 16-19042012

[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p

harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen

16-19042012

[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor

speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)

Monaco

[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind

turbines on two floating platforms Mechatronics (2011) 21 691-703

[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY

[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation

test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013

[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu

M Wind turbine tower load reduction using passive and semiactive dampers European Wind

Energy Association Annual Event (2011) Brussels

[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace

Exposition (2010) Orlando

[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej

z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198

[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR

damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds

Lisse CRC Press

[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and

experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State

Phenomena (2011) 177 (Control engineering in materials processing) 102-115

[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR

shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)

[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical

and Applied Mechanics (2007) 45 (1) 133-146

[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension

system with MR shock absorbers Computers and Structures (2008) 86 379-385

[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the

Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32

(1+2) 67-80

[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based

vibration reduction system Bulletin Of The Polish Academy Of

Sciences-Technical Sciences (2011) 59 (1) 75-80

[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes

Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

17

Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33

(3) 289-316

[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-

active vibration isolation systems using revised Bingham model Journal of Low Frequency

Noise Vibration and Active Control (2016) 35 (1) 17-24

[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration

absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoring (IACSM) (2014)

Barcelona Spain 15-17072014

[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with

magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi

1011771077546315591445

[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-

nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish

Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359

[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle

model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics

(2016) 54 (4) 1109-1123

[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled

semi-active damper Smart Mater Struct (2014) 23

[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers

for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control

Engineering

[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System

Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

8

The Response sharpening subsystem (see Fig 3) is presented in Fig 8 Its aim is to

sharpen the MR damper response at the moment of PMRmeas signal sign change while PMR

req

sign has changed earlier however the MR damper (as a dissipative device) was unable to

produce the active force (see Figs 13 and 14) To fulfil this task the control current is

enlarged by the value of 05 A when PMRmeas modulus is decreasing and is lower than 10 of

PMRmeas running amplitude and PMR

meas sign is consistent within last two sampling periods t0

(see Figs 13 14 and 21 (a) t0=110ndash3 s was assumed) Thanks to such logics the required

value of the control current iMRreq precedes the sign change of PMR

meas thus the control current

that actually flows through the MR damper coil iMRmeas is set at the moment of the PMR

meas

sign change with no delay The Running Amplitude subsystem (Fig 9) calculates the

difference of the outputs of the two integrator blocks with delay of five oscillation periods

between them The input to both integrators is the quantity (PMRmeas) squared (Sqr block) The

resultant difference is multiplied by two and divided by a time of five periods to obtain the

amplitude squared thus finally the Sqrt (square root) block is needed only to obtain

amplitude A(bull) of the input signal (assuming that vibration pattern is characterised by single

dominant frequency)

The parameters imax idemag tdelay Alpha1 Alpha2 Alpha3 values were selected on the

basis of numerical simulations supported by MR damper dynamics experimental testing

Figure 8 Simulink diagram of the Response sharpening subsystem

Figure 9 Simulink diagram of the Running Amplitude subsystem

The system in Fig 2 also includes standard analogue PID Current Controller subsystem

aimed to control MR damper with the use of an electronic board that enforces the MR damper

current via a control voltage uMR based on iMRmeas and iMR

req signals (see Figs 22 (a)(b))

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

9

4 THE EXPERIMENTAL ANALYSIS

For the purpose of the current experimental analysis that is oriented to the development of the

refined MR damper force tracking algorithm the value of γ = 1 was assumed while the

selection of γ was not a scope of the present research The theoretical study of γ determination

for the idealised semiactive device case of negligible response time zero residual force and

zero inherent system damping is presented in [28]

The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic

horizontal excitation applied to the nacelle The frequency range comprised the

neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz

Several system configurations were regarded passive system with the constant control

current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the

newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2

respectively) or with the simple previously tested MR damper hyperbolic tangent inverse

model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm

(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)

that was previously proved to be the best approach [242526] was selected The obtained

output frequency response functions of the tower tip horizontal displacement x1 amplitude are

presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1

the MR damper force PMRreq PMR

meas and the MR damper current iMRreq iMR

meas (adequately

scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-

displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT

PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and

435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most

crucial concerning preferable control solutions (see Fig 10 open loop systems are not of

interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR

meas

and the MR damper current iMRreq iMR

meas (adequately scaled and zoomed) obtained for the

system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current

Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)

25 3 35 4 45 505

1

15

2

25

3

35

4

45

5

55x 10

-3

Frequency [Hz]

Dis

pla

cem

ent A

mplit

ude A

(x1)

[m]

P0 = 61 N

00 A

01 A

02 A

03 A

04 A

05 A

ADPT V1

ADPT V2

ADPT INV

ADPT PI

ModGND

Figure 10 Tower tip displacement amplitude output frequency response functions

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

10

0 01 02 03 04 05 06 07-3

-2

-1

0

1

2

3

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

11

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

12

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops

Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

005 006

-1

0

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

13

0 005 01 015 02 025 03 035 04 045-2

-15

-1

-05

0

05

1

15

2

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops

021 0215 022 0225 023

-14

-12

-1

-08

-06

-04

-02

0

02

04

06

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

0315 032 0325 033 0335 034 0345 035

-03

-02

-01

0

01

02

03

04

05

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

001 x

PMR

req

001 x

PMR

meas

i MR

req

i MR

meas

Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

14

0 001 002 003 004 005-01

0

01

02

03

04

05

06

07

08

09

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

0 001 002 003 004 005-04

-03

-02

-01

0

01

02

03

04

05

06

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

Figure 22 PID current controller operation at

(a) positive (b) negative step change of iMRreq

Table 2 presents values of the quality index Q (best values in bold) being a root-mean-

square of the PMRreqndashPMR

meas difference

2

1

Nreq meas

MR MR

j

Q P j P j

(4)

where j is the time sample number and N is the number of the regarded samples ModGND

solution is omitted here as it is not based on required MR damper force tracking idea

Table 2 Values of the quality index Q (4)

System 295 [Hz] 435 [Hz]

ADPT INV 3002 6531

ADPT PI 2679 6274

ADPT V1 2366 4955

ADPT V2 2273 5374

In Fig 10 two maxima that are typical for TVA operation are apparent for all the

solutions but 02 03 04 and 05 A for which the damping is relatively too high

Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most

favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood

(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)

however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or

some positive damping added may improve the system response (as higher amplitude of

PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR

req ADPT V2

may become a preferred choice as it copes better with the integrator wind-up (by changing

the value of γ either the first maxima is lowered while the second maxima is elevated or the

second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to

the previously introduced [242526313237] ADPT PI and especially to ADPT INV within

the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper

required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz

for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially

considering the time instants immediately following PMRmeas sign changes (all presented time

patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the

difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

15

MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI

and especially for ADPT INV are incomparable to the respective patterns registered for

ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The

same may be concluded concerning PMRreq force tracking quality just before PMR

meas sign

changes although ADPT INV characteristics (Fig 16) could not be even described as

acceptable Concerning the MR damper residual force minimisation both ADPT V1 and

ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted

for the demagnetisation and response sharpening do the job properly The MR damper force-

displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along

with the friction (due to the MR damper residual force) phenomena at 295 Hz and the

positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper

measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not

differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2

however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash

as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated

according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of

nonlinear damping

As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one

may observe iMRreq signal rise at a time instant of 005 s while PMR

meas response modulus rise

is at ca 006 s what makes a real challenge for the follow-up-type-controller operational

quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations

present in Figs 13 and 14

5 CONCLUSION

The conducted experimental analysis proved the effectiveness of the proposed refined MR

damper force tracking algorithm in two versions The obtained output frequency response

function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels

former solutions (designated by ADPT PI and ADPT INV) and is comparable to the

frequency response of the ModGND system that previously demonstrated the best

performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range

while ModGND excels for frequencies higher than 435 Hz and marginally in the (300

320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope

best with the problem of the residual MR damper force magnetic remanence when zero

force is assumed due to the MR damper inability to generate active forces The

implementation of these logics for the ModGND algorithm along with the analysis of the

demanded value of γ for the real-world system with response time residual force and

inherent damping all of which are nonzero shall be a subject of the future research The

minimisation of the residual force negative effects and the quality of positive stiffness

tracking will also be investigated Based on these analyses results and laboratory model

measurements and considering the dynamic similarity study that includes determined time

and length scale factors [41] in combination with force scale factor [44] direct calculation of

the demanded control signal for a real-world full scale vibration reduction system MR TVA

will be possible

Acknowledgment

This work is supported by AGH University of Science and Technology under research

program No 1111130958

References

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

16

[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL

[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech

Struct amp Mach (1996) 24 (2) 155-187

[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering

low structural damping and soil structure interaction European Wind Energy Association

Annual Event (2012) Copenhagen 16-19042012

[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic

damping of operational wind turbine modes from experiments European Wind Energy

Association Annual Event (2012) Copenhagen 16-19042012

[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z

wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)

209-216

[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M

Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European

Wind Energy Association Annual Event (2012) Copenhagen 16-19042012

[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p

harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen

16-19042012

[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor

speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)

Monaco

[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind

turbines on two floating platforms Mechatronics (2011) 21 691-703

[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY

[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation

test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013

[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu

M Wind turbine tower load reduction using passive and semiactive dampers European Wind

Energy Association Annual Event (2011) Brussels

[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace

Exposition (2010) Orlando

[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej

z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198

[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR

damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds

Lisse CRC Press

[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and

experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State

Phenomena (2011) 177 (Control engineering in materials processing) 102-115

[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR

shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)

[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical

and Applied Mechanics (2007) 45 (1) 133-146

[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension

system with MR shock absorbers Computers and Structures (2008) 86 379-385

[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the

Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32

(1+2) 67-80

[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based

vibration reduction system Bulletin Of The Polish Academy Of

Sciences-Technical Sciences (2011) 59 (1) 75-80

[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes

Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

17

Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33

(3) 289-316

[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-

active vibration isolation systems using revised Bingham model Journal of Low Frequency

Noise Vibration and Active Control (2016) 35 (1) 17-24

[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration

absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoring (IACSM) (2014)

Barcelona Spain 15-17072014

[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with

magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi

1011771077546315591445

[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-

nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish

Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359

[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle

model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics

(2016) 54 (4) 1109-1123

[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled

semi-active damper Smart Mater Struct (2014) 23

[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers

for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control

Engineering

[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System

Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

9

4 THE EXPERIMENTAL ANALYSIS

For the purpose of the current experimental analysis that is oriented to the development of the

refined MR damper force tracking algorithm the value of γ = 1 was assumed while the

selection of γ was not a scope of the present research The theoretical study of γ determination

for the idealised semiactive device case of negligible response time zero residual force and

zero inherent system damping is presented in [28]

The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic

horizontal excitation applied to the nacelle The frequency range comprised the

neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz

Several system configurations were regarded passive system with the constant control

current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the

newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2

respectively) or with the simple previously tested MR damper hyperbolic tangent inverse

model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm

(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)

that was previously proved to be the best approach [242526] was selected The obtained

output frequency response functions of the tower tip horizontal displacement x1 amplitude are

presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1

the MR damper force PMRreq PMR

meas and the MR damper current iMRreq iMR

meas (adequately

scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-

displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT

PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and

435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most

crucial concerning preferable control solutions (see Fig 10 open loop systems are not of

interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR

meas

and the MR damper current iMRreq iMR

meas (adequately scaled and zoomed) obtained for the

system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current

Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)

25 3 35 4 45 505

1

15

2

25

3

35

4

45

5

55x 10

-3

Frequency [Hz]

Dis

pla

cem

ent A

mplit

ude A

(x1)

[m]

P0 = 61 N

00 A

01 A

02 A

03 A

04 A

05 A

ADPT V1

ADPT V2

ADPT INV

ADPT PI

ModGND

Figure 10 Tower tip displacement amplitude output frequency response functions

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

10

0 01 02 03 04 05 06 07-3

-2

-1

0

1

2

3

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

11

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

12

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops

Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

005 006

-1

0

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

13

0 005 01 015 02 025 03 035 04 045-2

-15

-1

-05

0

05

1

15

2

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops

021 0215 022 0225 023

-14

-12

-1

-08

-06

-04

-02

0

02

04

06

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

0315 032 0325 033 0335 034 0345 035

-03

-02

-01

0

01

02

03

04

05

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

001 x

PMR

req

001 x

PMR

meas

i MR

req

i MR

meas

Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

14

0 001 002 003 004 005-01

0

01

02

03

04

05

06

07

08

09

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

0 001 002 003 004 005-04

-03

-02

-01

0

01

02

03

04

05

06

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

Figure 22 PID current controller operation at

(a) positive (b) negative step change of iMRreq

Table 2 presents values of the quality index Q (best values in bold) being a root-mean-

square of the PMRreqndashPMR

meas difference

2

1

Nreq meas

MR MR

j

Q P j P j

(4)

where j is the time sample number and N is the number of the regarded samples ModGND

solution is omitted here as it is not based on required MR damper force tracking idea

Table 2 Values of the quality index Q (4)

System 295 [Hz] 435 [Hz]

ADPT INV 3002 6531

ADPT PI 2679 6274

ADPT V1 2366 4955

ADPT V2 2273 5374

In Fig 10 two maxima that are typical for TVA operation are apparent for all the

solutions but 02 03 04 and 05 A for which the damping is relatively too high

Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most

favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood

(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)

however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or

some positive damping added may improve the system response (as higher amplitude of

PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR

req ADPT V2

may become a preferred choice as it copes better with the integrator wind-up (by changing

the value of γ either the first maxima is lowered while the second maxima is elevated or the

second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to

the previously introduced [242526313237] ADPT PI and especially to ADPT INV within

the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper

required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz

for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially

considering the time instants immediately following PMRmeas sign changes (all presented time

patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the

difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

15

MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI

and especially for ADPT INV are incomparable to the respective patterns registered for

ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The

same may be concluded concerning PMRreq force tracking quality just before PMR

meas sign

changes although ADPT INV characteristics (Fig 16) could not be even described as

acceptable Concerning the MR damper residual force minimisation both ADPT V1 and

ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted

for the demagnetisation and response sharpening do the job properly The MR damper force-

displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along

with the friction (due to the MR damper residual force) phenomena at 295 Hz and the

positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper

measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not

differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2

however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash

as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated

according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of

nonlinear damping

As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one

may observe iMRreq signal rise at a time instant of 005 s while PMR

meas response modulus rise

is at ca 006 s what makes a real challenge for the follow-up-type-controller operational

quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations

present in Figs 13 and 14

5 CONCLUSION

The conducted experimental analysis proved the effectiveness of the proposed refined MR

damper force tracking algorithm in two versions The obtained output frequency response

function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels

former solutions (designated by ADPT PI and ADPT INV) and is comparable to the

frequency response of the ModGND system that previously demonstrated the best

performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range

while ModGND excels for frequencies higher than 435 Hz and marginally in the (300

320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope

best with the problem of the residual MR damper force magnetic remanence when zero

force is assumed due to the MR damper inability to generate active forces The

implementation of these logics for the ModGND algorithm along with the analysis of the

demanded value of γ for the real-world system with response time residual force and

inherent damping all of which are nonzero shall be a subject of the future research The

minimisation of the residual force negative effects and the quality of positive stiffness

tracking will also be investigated Based on these analyses results and laboratory model

measurements and considering the dynamic similarity study that includes determined time

and length scale factors [41] in combination with force scale factor [44] direct calculation of

the demanded control signal for a real-world full scale vibration reduction system MR TVA

will be possible

Acknowledgment

This work is supported by AGH University of Science and Technology under research

program No 1111130958

References

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

16

[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL

[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech

Struct amp Mach (1996) 24 (2) 155-187

[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering

low structural damping and soil structure interaction European Wind Energy Association

Annual Event (2012) Copenhagen 16-19042012

[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic

damping of operational wind turbine modes from experiments European Wind Energy

Association Annual Event (2012) Copenhagen 16-19042012

[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z

wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)

209-216

[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M

Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European

Wind Energy Association Annual Event (2012) Copenhagen 16-19042012

[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p

harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen

16-19042012

[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor

speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)

Monaco

[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind

turbines on two floating platforms Mechatronics (2011) 21 691-703

[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY

[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation

test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013

[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu

M Wind turbine tower load reduction using passive and semiactive dampers European Wind

Energy Association Annual Event (2011) Brussels

[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace

Exposition (2010) Orlando

[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej

z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198

[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR

damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds

Lisse CRC Press

[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and

experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State

Phenomena (2011) 177 (Control engineering in materials processing) 102-115

[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR

shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)

[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical

and Applied Mechanics (2007) 45 (1) 133-146

[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension

system with MR shock absorbers Computers and Structures (2008) 86 379-385

[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the

Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32

(1+2) 67-80

[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based

vibration reduction system Bulletin Of The Polish Academy Of

Sciences-Technical Sciences (2011) 59 (1) 75-80

[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes

Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

17

Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33

(3) 289-316

[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-

active vibration isolation systems using revised Bingham model Journal of Low Frequency

Noise Vibration and Active Control (2016) 35 (1) 17-24

[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration

absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoring (IACSM) (2014)

Barcelona Spain 15-17072014

[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with

magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi

1011771077546315591445

[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-

nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish

Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359

[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle

model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics

(2016) 54 (4) 1109-1123

[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled

semi-active damper Smart Mater Struct (2014) 23

[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers

for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control

Engineering

[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System

Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

10

0 01 02 03 04 05 06 07-3

-2

-1

0

1

2

3

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

11

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

12

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops

Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

005 006

-1

0

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

13

0 005 01 015 02 025 03 035 04 045-2

-15

-1

-05

0

05

1

15

2

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops

021 0215 022 0225 023

-14

-12

-1

-08

-06

-04

-02

0

02

04

06

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

0315 032 0325 033 0335 034 0345 035

-03

-02

-01

0

01

02

03

04

05

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

001 x

PMR

req

001 x

PMR

meas

i MR

req

i MR

meas

Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

14

0 001 002 003 004 005-01

0

01

02

03

04

05

06

07

08

09

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

0 001 002 003 004 005-04

-03

-02

-01

0

01

02

03

04

05

06

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

Figure 22 PID current controller operation at

(a) positive (b) negative step change of iMRreq

Table 2 presents values of the quality index Q (best values in bold) being a root-mean-

square of the PMRreqndashPMR

meas difference

2

1

Nreq meas

MR MR

j

Q P j P j

(4)

where j is the time sample number and N is the number of the regarded samples ModGND

solution is omitted here as it is not based on required MR damper force tracking idea

Table 2 Values of the quality index Q (4)

System 295 [Hz] 435 [Hz]

ADPT INV 3002 6531

ADPT PI 2679 6274

ADPT V1 2366 4955

ADPT V2 2273 5374

In Fig 10 two maxima that are typical for TVA operation are apparent for all the

solutions but 02 03 04 and 05 A for which the damping is relatively too high

Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most

favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood

(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)

however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or

some positive damping added may improve the system response (as higher amplitude of

PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR

req ADPT V2

may become a preferred choice as it copes better with the integrator wind-up (by changing

the value of γ either the first maxima is lowered while the second maxima is elevated or the

second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to

the previously introduced [242526313237] ADPT PI and especially to ADPT INV within

the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper

required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz

for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially

considering the time instants immediately following PMRmeas sign changes (all presented time

patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the

difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

15

MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI

and especially for ADPT INV are incomparable to the respective patterns registered for

ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The

same may be concluded concerning PMRreq force tracking quality just before PMR

meas sign

changes although ADPT INV characteristics (Fig 16) could not be even described as

acceptable Concerning the MR damper residual force minimisation both ADPT V1 and

ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted

for the demagnetisation and response sharpening do the job properly The MR damper force-

displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along

with the friction (due to the MR damper residual force) phenomena at 295 Hz and the

positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper

measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not

differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2

however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash

as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated

according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of

nonlinear damping

As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one

may observe iMRreq signal rise at a time instant of 005 s while PMR

meas response modulus rise

is at ca 006 s what makes a real challenge for the follow-up-type-controller operational

quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations

present in Figs 13 and 14

5 CONCLUSION

The conducted experimental analysis proved the effectiveness of the proposed refined MR

damper force tracking algorithm in two versions The obtained output frequency response

function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels

former solutions (designated by ADPT PI and ADPT INV) and is comparable to the

frequency response of the ModGND system that previously demonstrated the best

performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range

while ModGND excels for frequencies higher than 435 Hz and marginally in the (300

320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope

best with the problem of the residual MR damper force magnetic remanence when zero

force is assumed due to the MR damper inability to generate active forces The

implementation of these logics for the ModGND algorithm along with the analysis of the

demanded value of γ for the real-world system with response time residual force and

inherent damping all of which are nonzero shall be a subject of the future research The

minimisation of the residual force negative effects and the quality of positive stiffness

tracking will also be investigated Based on these analyses results and laboratory model

measurements and considering the dynamic similarity study that includes determined time

and length scale factors [41] in combination with force scale factor [44] direct calculation of

the demanded control signal for a real-world full scale vibration reduction system MR TVA

will be possible

Acknowledgment

This work is supported by AGH University of Science and Technology under research

program No 1111130958

References

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

16

[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL

[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech

Struct amp Mach (1996) 24 (2) 155-187

[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering

low structural damping and soil structure interaction European Wind Energy Association

Annual Event (2012) Copenhagen 16-19042012

[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic

damping of operational wind turbine modes from experiments European Wind Energy

Association Annual Event (2012) Copenhagen 16-19042012

[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z

wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)

209-216

[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M

Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European

Wind Energy Association Annual Event (2012) Copenhagen 16-19042012

[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p

harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen

16-19042012

[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor

speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)

Monaco

[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind

turbines on two floating platforms Mechatronics (2011) 21 691-703

[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY

[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation

test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013

[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu

M Wind turbine tower load reduction using passive and semiactive dampers European Wind

Energy Association Annual Event (2011) Brussels

[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace

Exposition (2010) Orlando

[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej

z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198

[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR

damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds

Lisse CRC Press

[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and

experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State

Phenomena (2011) 177 (Control engineering in materials processing) 102-115

[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR

shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)

[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical

and Applied Mechanics (2007) 45 (1) 133-146

[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension

system with MR shock absorbers Computers and Structures (2008) 86 379-385

[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the

Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32

(1+2) 67-80

[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based

vibration reduction system Bulletin Of The Polish Academy Of

Sciences-Technical Sciences (2011) 59 (1) 75-80

[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes

Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

17

Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33

(3) 289-316

[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-

active vibration isolation systems using revised Bingham model Journal of Low Frequency

Noise Vibration and Active Control (2016) 35 (1) 17-24

[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration

absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoring (IACSM) (2014)

Barcelona Spain 15-17072014

[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with

magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi

1011771077546315591445

[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-

nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish

Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359

[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle

model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics

(2016) 54 (4) 1109-1123

[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled

semi-active damper Smart Mater Struct (2014) 23

[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers

for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control

Engineering

[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System

Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

11

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 01 02 03 04 05 06 07-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

12

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops

Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

005 006

-1

0

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

13

0 005 01 015 02 025 03 035 04 045-2

-15

-1

-05

0

05

1

15

2

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops

021 0215 022 0225 023

-14

-12

-1

-08

-06

-04

-02

0

02

04

06

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

0315 032 0325 033 0335 034 0345 035

-03

-02

-01

0

01

02

03

04

05

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

001 x

PMR

req

001 x

PMR

meas

i MR

req

i MR

meas

Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

14

0 001 002 003 004 005-01

0

01

02

03

04

05

06

07

08

09

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

0 001 002 003 004 005-04

-03

-02

-01

0

01

02

03

04

05

06

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

Figure 22 PID current controller operation at

(a) positive (b) negative step change of iMRreq

Table 2 presents values of the quality index Q (best values in bold) being a root-mean-

square of the PMRreqndashPMR

meas difference

2

1

Nreq meas

MR MR

j

Q P j P j

(4)

where j is the time sample number and N is the number of the regarded samples ModGND

solution is omitted here as it is not based on required MR damper force tracking idea

Table 2 Values of the quality index Q (4)

System 295 [Hz] 435 [Hz]

ADPT INV 3002 6531

ADPT PI 2679 6274

ADPT V1 2366 4955

ADPT V2 2273 5374

In Fig 10 two maxima that are typical for TVA operation are apparent for all the

solutions but 02 03 04 and 05 A for which the damping is relatively too high

Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most

favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood

(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)

however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or

some positive damping added may improve the system response (as higher amplitude of

PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR

req ADPT V2

may become a preferred choice as it copes better with the integrator wind-up (by changing

the value of γ either the first maxima is lowered while the second maxima is elevated or the

second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to

the previously introduced [242526313237] ADPT PI and especially to ADPT INV within

the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper

required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz

for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially

considering the time instants immediately following PMRmeas sign changes (all presented time

patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the

difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

15

MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI

and especially for ADPT INV are incomparable to the respective patterns registered for

ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The

same may be concluded concerning PMRreq force tracking quality just before PMR

meas sign

changes although ADPT INV characteristics (Fig 16) could not be even described as

acceptable Concerning the MR damper residual force minimisation both ADPT V1 and

ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted

for the demagnetisation and response sharpening do the job properly The MR damper force-

displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along

with the friction (due to the MR damper residual force) phenomena at 295 Hz and the

positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper

measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not

differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2

however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash

as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated

according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of

nonlinear damping

As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one

may observe iMRreq signal rise at a time instant of 005 s while PMR

meas response modulus rise

is at ca 006 s what makes a real challenge for the follow-up-type-controller operational

quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations

present in Figs 13 and 14

5 CONCLUSION

The conducted experimental analysis proved the effectiveness of the proposed refined MR

damper force tracking algorithm in two versions The obtained output frequency response

function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels

former solutions (designated by ADPT PI and ADPT INV) and is comparable to the

frequency response of the ModGND system that previously demonstrated the best

performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range

while ModGND excels for frequencies higher than 435 Hz and marginally in the (300

320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope

best with the problem of the residual MR damper force magnetic remanence when zero

force is assumed due to the MR damper inability to generate active forces The

implementation of these logics for the ModGND algorithm along with the analysis of the

demanded value of γ for the real-world system with response time residual force and

inherent damping all of which are nonzero shall be a subject of the future research The

minimisation of the residual force negative effects and the quality of positive stiffness

tracking will also be investigated Based on these analyses results and laboratory model

measurements and considering the dynamic similarity study that includes determined time

and length scale factors [41] in combination with force scale factor [44] direct calculation of

the demanded control signal for a real-world full scale vibration reduction system MR TVA

will be possible

Acknowledgment

This work is supported by AGH University of Science and Technology under research

program No 1111130958

References

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

16

[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL

[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech

Struct amp Mach (1996) 24 (2) 155-187

[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering

low structural damping and soil structure interaction European Wind Energy Association

Annual Event (2012) Copenhagen 16-19042012

[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic

damping of operational wind turbine modes from experiments European Wind Energy

Association Annual Event (2012) Copenhagen 16-19042012

[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z

wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)

209-216

[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M

Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European

Wind Energy Association Annual Event (2012) Copenhagen 16-19042012

[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p

harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen

16-19042012

[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor

speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)

Monaco

[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind

turbines on two floating platforms Mechatronics (2011) 21 691-703

[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY

[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation

test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013

[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu

M Wind turbine tower load reduction using passive and semiactive dampers European Wind

Energy Association Annual Event (2011) Brussels

[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace

Exposition (2010) Orlando

[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej

z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198

[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR

damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds

Lisse CRC Press

[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and

experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State

Phenomena (2011) 177 (Control engineering in materials processing) 102-115

[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR

shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)

[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical

and Applied Mechanics (2007) 45 (1) 133-146

[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension

system with MR shock absorbers Computers and Structures (2008) 86 379-385

[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the

Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32

(1+2) 67-80

[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based

vibration reduction system Bulletin Of The Polish Academy Of

Sciences-Technical Sciences (2011) 59 (1) 75-80

[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes

Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

17

Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33

(3) 289-316

[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-

active vibration isolation systems using revised Bingham model Journal of Low Frequency

Noise Vibration and Active Control (2016) 35 (1) 17-24

[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration

absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoring (IACSM) (2014)

Barcelona Spain 15-17072014

[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with

magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi

1011771077546315591445

[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-

nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish

Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359

[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle

model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics

(2016) 54 (4) 1109-1123

[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled

semi-active damper Smart Mater Struct (2014) 23

[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers

for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control

Engineering

[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System

Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

12

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops

Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops

0 005 01 015 02 025 03 035 04 045-25

-2

-15

-1

-05

0

05

1

15

2

25

Time[s]

x1 [

mm

] P

MR

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

005 006

-1

0

(a) (b)

(a) (b)

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

13

0 005 01 015 02 025 03 035 04 045-2

-15

-1

-05

0

05

1

15

2

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops

021 0215 022 0225 023

-14

-12

-1

-08

-06

-04

-02

0

02

04

06

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

0315 032 0325 033 0335 034 0345 035

-03

-02

-01

0

01

02

03

04

05

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

001 x

PMR

req

001 x

PMR

meas

i MR

req

i MR

meas

Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

14

0 001 002 003 004 005-01

0

01

02

03

04

05

06

07

08

09

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

0 001 002 003 004 005-04

-03

-02

-01

0

01

02

03

04

05

06

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

Figure 22 PID current controller operation at

(a) positive (b) negative step change of iMRreq

Table 2 presents values of the quality index Q (best values in bold) being a root-mean-

square of the PMRreqndashPMR

meas difference

2

1

Nreq meas

MR MR

j

Q P j P j

(4)

where j is the time sample number and N is the number of the regarded samples ModGND

solution is omitted here as it is not based on required MR damper force tracking idea

Table 2 Values of the quality index Q (4)

System 295 [Hz] 435 [Hz]

ADPT INV 3002 6531

ADPT PI 2679 6274

ADPT V1 2366 4955

ADPT V2 2273 5374

In Fig 10 two maxima that are typical for TVA operation are apparent for all the

solutions but 02 03 04 and 05 A for which the damping is relatively too high

Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most

favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood

(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)

however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or

some positive damping added may improve the system response (as higher amplitude of

PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR

req ADPT V2

may become a preferred choice as it copes better with the integrator wind-up (by changing

the value of γ either the first maxima is lowered while the second maxima is elevated or the

second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to

the previously introduced [242526313237] ADPT PI and especially to ADPT INV within

the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper

required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz

for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially

considering the time instants immediately following PMRmeas sign changes (all presented time

patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the

difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

15

MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI

and especially for ADPT INV are incomparable to the respective patterns registered for

ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The

same may be concluded concerning PMRreq force tracking quality just before PMR

meas sign

changes although ADPT INV characteristics (Fig 16) could not be even described as

acceptable Concerning the MR damper residual force minimisation both ADPT V1 and

ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted

for the demagnetisation and response sharpening do the job properly The MR damper force-

displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along

with the friction (due to the MR damper residual force) phenomena at 295 Hz and the

positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper

measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not

differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2

however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash

as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated

according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of

nonlinear damping

As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one

may observe iMRreq signal rise at a time instant of 005 s while PMR

meas response modulus rise

is at ca 006 s what makes a real challenge for the follow-up-type-controller operational

quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations

present in Figs 13 and 14

5 CONCLUSION

The conducted experimental analysis proved the effectiveness of the proposed refined MR

damper force tracking algorithm in two versions The obtained output frequency response

function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels

former solutions (designated by ADPT PI and ADPT INV) and is comparable to the

frequency response of the ModGND system that previously demonstrated the best

performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range

while ModGND excels for frequencies higher than 435 Hz and marginally in the (300

320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope

best with the problem of the residual MR damper force magnetic remanence when zero

force is assumed due to the MR damper inability to generate active forces The

implementation of these logics for the ModGND algorithm along with the analysis of the

demanded value of γ for the real-world system with response time residual force and

inherent damping all of which are nonzero shall be a subject of the future research The

minimisation of the residual force negative effects and the quality of positive stiffness

tracking will also be investigated Based on these analyses results and laboratory model

measurements and considering the dynamic similarity study that includes determined time

and length scale factors [41] in combination with force scale factor [44] direct calculation of

the demanded control signal for a real-world full scale vibration reduction system MR TVA

will be possible

Acknowledgment

This work is supported by AGH University of Science and Technology under research

program No 1111130958

References

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

16

[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL

[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech

Struct amp Mach (1996) 24 (2) 155-187

[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering

low structural damping and soil structure interaction European Wind Energy Association

Annual Event (2012) Copenhagen 16-19042012

[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic

damping of operational wind turbine modes from experiments European Wind Energy

Association Annual Event (2012) Copenhagen 16-19042012

[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z

wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)

209-216

[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M

Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European

Wind Energy Association Annual Event (2012) Copenhagen 16-19042012

[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p

harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen

16-19042012

[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor

speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)

Monaco

[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind

turbines on two floating platforms Mechatronics (2011) 21 691-703

[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY

[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation

test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013

[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu

M Wind turbine tower load reduction using passive and semiactive dampers European Wind

Energy Association Annual Event (2011) Brussels

[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace

Exposition (2010) Orlando

[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej

z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198

[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR

damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds

Lisse CRC Press

[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and

experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State

Phenomena (2011) 177 (Control engineering in materials processing) 102-115

[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR

shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)

[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical

and Applied Mechanics (2007) 45 (1) 133-146

[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension

system with MR shock absorbers Computers and Structures (2008) 86 379-385

[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the

Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32

(1+2) 67-80

[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based

vibration reduction system Bulletin Of The Polish Academy Of

Sciences-Technical Sciences (2011) 59 (1) 75-80

[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes

Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

17

Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33

(3) 289-316

[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-

active vibration isolation systems using revised Bingham model Journal of Low Frequency

Noise Vibration and Active Control (2016) 35 (1) 17-24

[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration

absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoring (IACSM) (2014)

Barcelona Spain 15-17072014

[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with

magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi

1011771077546315591445

[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-

nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish

Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359

[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle

model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics

(2016) 54 (4) 1109-1123

[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled

semi-active damper Smart Mater Struct (2014) 23

[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers

for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control

Engineering

[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System

Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

13

0 005 01 015 02 025 03 035 04 045-2

-15

-1

-05

0

05

1

15

2

Time[s]

x1 [

mm

] P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

x1

01 x

PMR

meas

i MR

req

i MR

meas

Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops

021 0215 022 0225 023

-14

-12

-1

-08

-06

-04

-02

0

02

04

06

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

01 x

PMR

req

01 x

PMR

meas

i MR

req

i MR

meas

0315 032 0325 033 0335 034 0345 035

-03

-02

-01

0

01

02

03

04

05

Time[s]

PM

R

req

P

MR

meas [

N]

i M

R

req

i

MR

meas [

A]

001 x

PMR

req

001 x

PMR

meas

i MR

req

i MR

meas

Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz

(a) (b)

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

14

0 001 002 003 004 005-01

0

01

02

03

04

05

06

07

08

09

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

0 001 002 003 004 005-04

-03

-02

-01

0

01

02

03

04

05

06

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

Figure 22 PID current controller operation at

(a) positive (b) negative step change of iMRreq

Table 2 presents values of the quality index Q (best values in bold) being a root-mean-

square of the PMRreqndashPMR

meas difference

2

1

Nreq meas

MR MR

j

Q P j P j

(4)

where j is the time sample number and N is the number of the regarded samples ModGND

solution is omitted here as it is not based on required MR damper force tracking idea

Table 2 Values of the quality index Q (4)

System 295 [Hz] 435 [Hz]

ADPT INV 3002 6531

ADPT PI 2679 6274

ADPT V1 2366 4955

ADPT V2 2273 5374

In Fig 10 two maxima that are typical for TVA operation are apparent for all the

solutions but 02 03 04 and 05 A for which the damping is relatively too high

Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most

favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood

(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)

however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or

some positive damping added may improve the system response (as higher amplitude of

PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR

req ADPT V2

may become a preferred choice as it copes better with the integrator wind-up (by changing

the value of γ either the first maxima is lowered while the second maxima is elevated or the

second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to

the previously introduced [242526313237] ADPT PI and especially to ADPT INV within

the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper

required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz

for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially

considering the time instants immediately following PMRmeas sign changes (all presented time

patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the

difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

15

MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI

and especially for ADPT INV are incomparable to the respective patterns registered for

ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The

same may be concluded concerning PMRreq force tracking quality just before PMR

meas sign

changes although ADPT INV characteristics (Fig 16) could not be even described as

acceptable Concerning the MR damper residual force minimisation both ADPT V1 and

ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted

for the demagnetisation and response sharpening do the job properly The MR damper force-

displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along

with the friction (due to the MR damper residual force) phenomena at 295 Hz and the

positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper

measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not

differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2

however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash

as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated

according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of

nonlinear damping

As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one

may observe iMRreq signal rise at a time instant of 005 s while PMR

meas response modulus rise

is at ca 006 s what makes a real challenge for the follow-up-type-controller operational

quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations

present in Figs 13 and 14

5 CONCLUSION

The conducted experimental analysis proved the effectiveness of the proposed refined MR

damper force tracking algorithm in two versions The obtained output frequency response

function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels

former solutions (designated by ADPT PI and ADPT INV) and is comparable to the

frequency response of the ModGND system that previously demonstrated the best

performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range

while ModGND excels for frequencies higher than 435 Hz and marginally in the (300

320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope

best with the problem of the residual MR damper force magnetic remanence when zero

force is assumed due to the MR damper inability to generate active forces The

implementation of these logics for the ModGND algorithm along with the analysis of the

demanded value of γ for the real-world system with response time residual force and

inherent damping all of which are nonzero shall be a subject of the future research The

minimisation of the residual force negative effects and the quality of positive stiffness

tracking will also be investigated Based on these analyses results and laboratory model

measurements and considering the dynamic similarity study that includes determined time

and length scale factors [41] in combination with force scale factor [44] direct calculation of

the demanded control signal for a real-world full scale vibration reduction system MR TVA

will be possible

Acknowledgment

This work is supported by AGH University of Science and Technology under research

program No 1111130958

References

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

16

[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL

[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech

Struct amp Mach (1996) 24 (2) 155-187

[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering

low structural damping and soil structure interaction European Wind Energy Association

Annual Event (2012) Copenhagen 16-19042012

[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic

damping of operational wind turbine modes from experiments European Wind Energy

Association Annual Event (2012) Copenhagen 16-19042012

[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z

wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)

209-216

[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M

Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European

Wind Energy Association Annual Event (2012) Copenhagen 16-19042012

[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p

harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen

16-19042012

[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor

speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)

Monaco

[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind

turbines on two floating platforms Mechatronics (2011) 21 691-703

[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY

[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation

test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013

[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu

M Wind turbine tower load reduction using passive and semiactive dampers European Wind

Energy Association Annual Event (2011) Brussels

[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace

Exposition (2010) Orlando

[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej

z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198

[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR

damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds

Lisse CRC Press

[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and

experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State

Phenomena (2011) 177 (Control engineering in materials processing) 102-115

[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR

shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)

[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical

and Applied Mechanics (2007) 45 (1) 133-146

[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension

system with MR shock absorbers Computers and Structures (2008) 86 379-385

[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the

Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32

(1+2) 67-80

[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based

vibration reduction system Bulletin Of The Polish Academy Of

Sciences-Technical Sciences (2011) 59 (1) 75-80

[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes

Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

17

Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33

(3) 289-316

[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-

active vibration isolation systems using revised Bingham model Journal of Low Frequency

Noise Vibration and Active Control (2016) 35 (1) 17-24

[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration

absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoring (IACSM) (2014)

Barcelona Spain 15-17072014

[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with

magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi

1011771077546315591445

[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-

nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish

Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359

[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle

model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics

(2016) 54 (4) 1109-1123

[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled

semi-active damper Smart Mater Struct (2014) 23

[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers

for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control

Engineering

[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System

Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

14

0 001 002 003 004 005-01

0

01

02

03

04

05

06

07

08

09

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

0 001 002 003 004 005-04

-03

-02

-01

0

01

02

03

04

05

06

Time[s]

i M

R

req

i M

R

meas [

A]

uM

R [

V]

i MR

req

01 x

uMR

i MR

meas

Figure 22 PID current controller operation at

(a) positive (b) negative step change of iMRreq

Table 2 presents values of the quality index Q (best values in bold) being a root-mean-

square of the PMRreqndashPMR

meas difference

2

1

Nreq meas

MR MR

j

Q P j P j

(4)

where j is the time sample number and N is the number of the regarded samples ModGND

solution is omitted here as it is not based on required MR damper force tracking idea

Table 2 Values of the quality index Q (4)

System 295 [Hz] 435 [Hz]

ADPT INV 3002 6531

ADPT PI 2679 6274

ADPT V1 2366 4955

ADPT V2 2273 5374

In Fig 10 two maxima that are typical for TVA operation are apparent for all the

solutions but 02 03 04 and 05 A for which the damping is relatively too high

Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most

favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood

(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)

however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or

some positive damping added may improve the system response (as higher amplitude of

PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR

req ADPT V2

may become a preferred choice as it copes better with the integrator wind-up (by changing

the value of γ either the first maxima is lowered while the second maxima is elevated or the

second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to

the previously introduced [242526313237] ADPT PI and especially to ADPT INV within

the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper

required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz

for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially

considering the time instants immediately following PMRmeas sign changes (all presented time

patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the

difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

15

MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI

and especially for ADPT INV are incomparable to the respective patterns registered for

ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The

same may be concluded concerning PMRreq force tracking quality just before PMR

meas sign

changes although ADPT INV characteristics (Fig 16) could not be even described as

acceptable Concerning the MR damper residual force minimisation both ADPT V1 and

ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted

for the demagnetisation and response sharpening do the job properly The MR damper force-

displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along

with the friction (due to the MR damper residual force) phenomena at 295 Hz and the

positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper

measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not

differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2

however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash

as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated

according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of

nonlinear damping

As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one

may observe iMRreq signal rise at a time instant of 005 s while PMR

meas response modulus rise

is at ca 006 s what makes a real challenge for the follow-up-type-controller operational

quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations

present in Figs 13 and 14

5 CONCLUSION

The conducted experimental analysis proved the effectiveness of the proposed refined MR

damper force tracking algorithm in two versions The obtained output frequency response

function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels

former solutions (designated by ADPT PI and ADPT INV) and is comparable to the

frequency response of the ModGND system that previously demonstrated the best

performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range

while ModGND excels for frequencies higher than 435 Hz and marginally in the (300

320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope

best with the problem of the residual MR damper force magnetic remanence when zero

force is assumed due to the MR damper inability to generate active forces The

implementation of these logics for the ModGND algorithm along with the analysis of the

demanded value of γ for the real-world system with response time residual force and

inherent damping all of which are nonzero shall be a subject of the future research The

minimisation of the residual force negative effects and the quality of positive stiffness

tracking will also be investigated Based on these analyses results and laboratory model

measurements and considering the dynamic similarity study that includes determined time

and length scale factors [41] in combination with force scale factor [44] direct calculation of

the demanded control signal for a real-world full scale vibration reduction system MR TVA

will be possible

Acknowledgment

This work is supported by AGH University of Science and Technology under research

program No 1111130958

References

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

16

[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL

[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech

Struct amp Mach (1996) 24 (2) 155-187

[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering

low structural damping and soil structure interaction European Wind Energy Association

Annual Event (2012) Copenhagen 16-19042012

[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic

damping of operational wind turbine modes from experiments European Wind Energy

Association Annual Event (2012) Copenhagen 16-19042012

[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z

wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)

209-216

[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M

Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European

Wind Energy Association Annual Event (2012) Copenhagen 16-19042012

[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p

harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen

16-19042012

[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor

speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)

Monaco

[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind

turbines on two floating platforms Mechatronics (2011) 21 691-703

[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY

[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation

test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013

[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu

M Wind turbine tower load reduction using passive and semiactive dampers European Wind

Energy Association Annual Event (2011) Brussels

[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace

Exposition (2010) Orlando

[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej

z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198

[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR

damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds

Lisse CRC Press

[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and

experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State

Phenomena (2011) 177 (Control engineering in materials processing) 102-115

[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR

shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)

[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical

and Applied Mechanics (2007) 45 (1) 133-146

[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension

system with MR shock absorbers Computers and Structures (2008) 86 379-385

[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the

Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32

(1+2) 67-80

[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based

vibration reduction system Bulletin Of The Polish Academy Of

Sciences-Technical Sciences (2011) 59 (1) 75-80

[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes

Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

17

Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33

(3) 289-316

[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-

active vibration isolation systems using revised Bingham model Journal of Low Frequency

Noise Vibration and Active Control (2016) 35 (1) 17-24

[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration

absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoring (IACSM) (2014)

Barcelona Spain 15-17072014

[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with

magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi

1011771077546315591445

[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-

nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish

Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359

[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle

model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics

(2016) 54 (4) 1109-1123

[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled

semi-active damper Smart Mater Struct (2014) 23

[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers

for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control

Engineering

[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System

Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

15

MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI

and especially for ADPT INV are incomparable to the respective patterns registered for

ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The

same may be concluded concerning PMRreq force tracking quality just before PMR

meas sign

changes although ADPT INV characteristics (Fig 16) could not be even described as

acceptable Concerning the MR damper residual force minimisation both ADPT V1 and

ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted

for the demagnetisation and response sharpening do the job properly The MR damper force-

displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along

with the friction (due to the MR damper residual force) phenomena at 295 Hz and the

positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper

measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not

differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2

however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash

as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated

according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of

nonlinear damping

As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one

may observe iMRreq signal rise at a time instant of 005 s while PMR

meas response modulus rise

is at ca 006 s what makes a real challenge for the follow-up-type-controller operational

quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations

present in Figs 13 and 14

5 CONCLUSION

The conducted experimental analysis proved the effectiveness of the proposed refined MR

damper force tracking algorithm in two versions The obtained output frequency response

function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels

former solutions (designated by ADPT PI and ADPT INV) and is comparable to the

frequency response of the ModGND system that previously demonstrated the best

performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range

while ModGND excels for frequencies higher than 435 Hz and marginally in the (300

320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope

best with the problem of the residual MR damper force magnetic remanence when zero

force is assumed due to the MR damper inability to generate active forces The

implementation of these logics for the ModGND algorithm along with the analysis of the

demanded value of γ for the real-world system with response time residual force and

inherent damping all of which are nonzero shall be a subject of the future research The

minimisation of the residual force negative effects and the quality of positive stiffness

tracking will also be investigated Based on these analyses results and laboratory model

measurements and considering the dynamic similarity study that includes determined time

and length scale factors [41] in combination with force scale factor [44] direct calculation of

the demanded control signal for a real-world full scale vibration reduction system MR TVA

will be possible

Acknowledgment

This work is supported by AGH University of Science and Technology under research

program No 1111130958

References

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

16

[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL

[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech

Struct amp Mach (1996) 24 (2) 155-187

[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering

low structural damping and soil structure interaction European Wind Energy Association

Annual Event (2012) Copenhagen 16-19042012

[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic

damping of operational wind turbine modes from experiments European Wind Energy

Association Annual Event (2012) Copenhagen 16-19042012

[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z

wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)

209-216

[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M

Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European

Wind Energy Association Annual Event (2012) Copenhagen 16-19042012

[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p

harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen

16-19042012

[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor

speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)

Monaco

[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind

turbines on two floating platforms Mechatronics (2011) 21 691-703

[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY

[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation

test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013

[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu

M Wind turbine tower load reduction using passive and semiactive dampers European Wind

Energy Association Annual Event (2011) Brussels

[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace

Exposition (2010) Orlando

[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej

z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198

[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR

damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds

Lisse CRC Press

[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and

experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State

Phenomena (2011) 177 (Control engineering in materials processing) 102-115

[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR

shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)

[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical

and Applied Mechanics (2007) 45 (1) 133-146

[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension

system with MR shock absorbers Computers and Structures (2008) 86 379-385

[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the

Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32

(1+2) 67-80

[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based

vibration reduction system Bulletin Of The Polish Academy Of

Sciences-Technical Sciences (2011) 59 (1) 75-80

[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes

Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

17

Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33

(3) 289-316

[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-

active vibration isolation systems using revised Bingham model Journal of Low Frequency

Noise Vibration and Active Control (2016) 35 (1) 17-24

[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration

absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoring (IACSM) (2014)

Barcelona Spain 15-17072014

[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with

magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi

1011771077546315591445

[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-

nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish

Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359

[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle

model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics

(2016) 54 (4) 1109-1123

[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled

semi-active damper Smart Mater Struct (2014) 23

[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers

for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control

Engineering

[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System

Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

16

[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL

[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech

Struct amp Mach (1996) 24 (2) 155-187

[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering

low structural damping and soil structure interaction European Wind Energy Association

Annual Event (2012) Copenhagen 16-19042012

[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic

damping of operational wind turbine modes from experiments European Wind Energy

Association Annual Event (2012) Copenhagen 16-19042012

[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z

wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)

209-216

[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M

Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European

Wind Energy Association Annual Event (2012) Copenhagen 16-19042012

[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p

harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen

16-19042012

[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor

speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)

Monaco

[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind

turbines on two floating platforms Mechatronics (2011) 21 691-703

[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY

[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation

test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013

[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu

M Wind turbine tower load reduction using passive and semiactive dampers European Wind

Energy Association Annual Event (2011) Brussels

[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace

Exposition (2010) Orlando

[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej

z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198

[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR

damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds

Lisse CRC Press

[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and

experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State

Phenomena (2011) 177 (Control engineering in materials processing) 102-115

[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR

shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)

[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical

and Applied Mechanics (2007) 45 (1) 133-146

[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension

system with MR shock absorbers Computers and Structures (2008) 86 379-385

[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the

Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32

(1+2) 67-80

[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based

vibration reduction system Bulletin Of The Polish Academy Of

Sciences-Technical Sciences (2011) 59 (1) 75-80

[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes

Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

17

Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33

(3) 289-316

[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-

active vibration isolation systems using revised Bingham model Journal of Low Frequency

Noise Vibration and Active Control (2016) 35 (1) 17-24

[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration

absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoring (IACSM) (2014)

Barcelona Spain 15-17072014

[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with

magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi

1011771077546315591445

[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-

nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish

Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359

[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle

model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics

(2016) 54 (4) 1109-1123

[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled

semi-active damper Smart Mater Struct (2014) 23

[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers

for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control

Engineering

[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System

Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

17

Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33

(3) 289-316

[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-

active vibration isolation systems using revised Bingham model Journal of Low Frequency

Noise Vibration and Active Control (2016) 35 (1) 17-24

[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration

absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoring (IACSM) (2014)

Barcelona Spain 15-17072014

[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with

magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi

1011771077546315591445

[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-

nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish

Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359

[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle

model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics

(2016) 54 (4) 1109-1123

[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled

semi-active damper Smart Mater Struct (2014) 23

[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers

for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control

Engineering

[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System

Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937

[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of

nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21

doi1010880964-1726214045006

[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping

implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22

doi1010880964-17262210105010

[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart

Mater Struct (2013) 22

[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR

damper Smart Mater Struct (2012) 21

[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its

application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct

(2014) 23

[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit

(2015) DOI 101002stc1750

[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping

the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11

945-58

[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord

Co

[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc

[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System

with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51

[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle

system and its scaled model Solid State Phenomena (2014) 208 29-39

[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological

tuned vibration absorber the laboratory test rig Proceedings of the 14th International

Carpathian Control Conference (2013) 238-242

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917

Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined

Force Tracking Algorithm

18

[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based

Tuned Vibration Absorber Structural Engineering and Mechanics (in review)

[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle

system from investigation of its scaled model 6WCSCM Sixth World Conference on

Structural Control and Monitoring proceedings of the 6th edition of the World conference of

the International Association for Structural Control and Monitoirng (IACSM) (2014)

Barcelona Spain 15-17072014

[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable

With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)

893ndash917