THE 7th STUDENT SYMPOSIUM ON MECHANICAL AND MANUFACTURING ENGINEERING

Permanent Magnet Synchronous Machine-Magnetic Lead Screw

model based studies on passive and semi-active suspension

A. Stupakowski, A. Højris, M. Pentek, M. Stati, V. Mishukov

Department of Materials and Production, Aalborg UniversityFibigerstraede 16, DK-9220 Aalborg East, Denmark

Email: {astupa18, ahajri15, mpente18, mstati18, vmishu18}@student.aau.dkWeb page: http://www.mechman.m-tech.aau.dk/

AbstractThis paper encompasses model based studies on passive and semi-active suspension implemented with a MagneticLead Screw (MLS) in combination with Permanent Magnet Synchronous Machine (PMSM). Initially, a brief state ofart concerning different suspension schemes is given, leading to an introduction of the PMSM-MLS assembly usedas a damping system. Subsequently, the completion of hardware and software controlling the Vehicle Test Platform(VTP) is described. The modelling considerations were narrowed to Quarter Vehicle Model (QVM). The controllerdesign was performed on the linearised PMSM model. As the initial system parameters found through laboratory testsdid not represent behaviour of the VTP correctly, new parameters were calculated based on the performed systemidentification studies from frequency response test. The model with updated parameters was exposed to speed bumptest developed in accordance to [1]. The damping force produced by the MLS is calculated from torque, which islinear dependent with the iq current. The currents are controlled by the PI compensators that equalise the output tothe reference and reduce the steady state error. The investigation of damping schemes was limited to model semi-active systems with Skyhook (SH) algorithms and passive suspension. The studies indicate that the use of semi-activesystems results in reduction of vertical movement of the chassis and lower energy consumption of PMSM-MLSassembly compared to passive suspension scheme.

Keywords: Permanent Magnet Synchronous Motor, Magnetic Lead Screw, Vehicle Suspension Control, Skyhook,Inverter, Embedded System

1. IntroductionIn the recent years, the suspension systems have becomea trending research area in the automotive industry.Depending on the principal of operation, there can bedistinguished passive, semi-active and active systems.

The passive suspension reduces the motion of the bodyand wheel by reducing their relative velocities to a ratethat gives the required comfort. This is achieved by theuse of damping element placed between the chassis andthe wheels, such as hydraulic shock absorber [2]. It isthe simplest way to protect a vehicle from vibrations andit has proven to be reasonably effective, however due toits passivity, its implementation is always a compromisebetween resonance control and high frequency isolation[3].

The semi-active systems are based on shock-absorberswith controllable damping coefficients what allows toavoid the trade-off associated with passive systems.They are also known to be cheap to implement and

to have low power consumption. Their main limitationis inability to deliver vertical forces in the directionof the suspension velocity. The design of semi-activesystem is typically made based on SH algorithm.Conceptually, the SH is based on the damper attachedbetween the sprung mass and a fictional reference in thesky. It results that the shock absorber delivers a forceproportional purely to the chassis speed rather than therelative velocity between the sprung and unsprung mass[4].

The active systems do not suffer from drawbacks ofsemi-active systems, as their damping element cangenerate forces along the direction of the suspensionvelocity. The method is however associated with largeequipment size. Therefore, in the historical view, theresearch evolved from active to semi-active systems,that have proved to deliver comparable vibrationsisolation [5]. The interest of the automotive industry incontinuous development of different suspension systemsled to intensified research within this field by AAU.

1

The work has been concentrated on investigating theproperties of MLS as a force transmitter. The MLSis inspired by the design of mechanical lead screwconsisting of a screw and a nut. The thread is howevermade of helically shaped magnets. Thereby, when thescrew (rotor) is rotated one complete revolution, the nut(translator) translates a certain distance defined by leadγ. The advantage of using magnets is no direct contactresulting in low friction and limited wear while havingan efficiency of 90% [6]. This provoked to investigateapplication of MLS further, that in conjunction withPMSM and an air spring constituted the design of anew shock absorber which can be seen in Fig. 1. Thesetup allows to generate a damping force independentof suspension velocity and therefore can be used as anytype of damper.

MLS PMSM Air-spring

Fig. 1 MLS-PSMS assembly

The PMSM-MLS assembly requires a digital controland therefore, the challenge to be faced in this paper isto implement the passive and the semi-active suspensionsystems on the microprocessor and to compare theirperformance characteristic. The research shown in thepaper is thus restricted to QVM and aspires to bepre-study for expanding the technology to a completevehicle model.

The project has been carried out with the use ofthe VTP developed in [7] consisting of the vehiclewith PMSM-MLS assembly and linear transducer. Theremaining hardware components were designed in orderto complete the prototype consisting of a vehicle withthe PMSM-MLS assembly replacing the suspension forone wheel. Depending on the scenario, the PMSM exertsdifferent torque transformed by the MLS into lineardamping force. The interconnection between hardwareis controlled by the processed sensor’s measurementsthrough the microprocessor running with developedsoftware. Subsequently, the model of the test platformwas developed and juxtaposed with the physical system.The passive and SH suspension algorithms are modelledand compared to investigate the difference in theirbehaviour.

2. Method2.1 HardwareThe completion of hardware setup extends the compo-nents of the VTP by additional modules that can beclassified as power transmitting elements and sensors.The inverter supplies PMSM with three phase current,which phase magnitudes are measured by dedicatedtransducers. The inverter’s DC-link voltage is measuredby a dedicated transducer, what allows to identify ifdue to the generated back emf, breaking action isneeded. The measurements are brought down to valuesthe microprocessor can process by self-designed volt-age shifter. It consists of four channels correspondingto each phase and DC-link. The extension of MLSis measured by linear transducer, while the PMSM’sangular position and velocity are monitored by the useof a resolver and read by R/D converter. The completelayout of hardware setup with interconnections betweenelements marked is shown in Fig. 2.

Danfoss FC302

inverter

400V DC

Brake Resistor

IPC3

opticalconnection

IPC2DSP

3 phase AC

PMSMResolver

Voltagetransducer

Currenttransducers

DC-link VoltageDSP

USB

R/DConverter

Voltageshifter

PC

MLS

Fig. 2 Hardware layout.

2.2 SoftwareThe interconnection between hardware componentsis controlled based on the collected and processedmeasurements through the software implemented on theDSP. The main output from the DSP composes of threePWM signals controlling the IGBTs in the inverter, aPWM signal that enables the breaking resistor to protectthe inverter when the PMSM is in generating action.

The PWM signals generation for the inverter is ac-complished by the use of three current transducersthat feed back the measurements to the controllers.To obtain the average current, the measurements beginwhen the triangular carrier wave starts counting up whatcorresponds to the middle point of the high pulse. Thecurrents and DC-voltage are read by ADC module,while the position and velocity are collected throughR/D converter and sent via SPI communication protocol.To perform Park transformation, the sine and cosinefunctions of the electrical angles are found. The phasecurrents are subsequently transformed into dq-currentby Clark and Park transformation schemes and fed tocontrollers. The dq-voltage requested by the controllers

2

is transformed into PWM signal through inverse trans-formations and modulated with SVM algorithm, beingthe chosen modulation scheme.

To ensure trouble less operation of PMSM at highrotational speed, the inverter runs at a frequency of10 kHz, what also secures low harmonic content inthe output [8]. This restricts main code completiontime to 100 µs and makes efficient resource man-agement inevitable. Consequently, the trigonometricalfunctions were replaced with fast approximation LookUp Table with resolution of 360 entries. Each time atrigonometrical operation is needed, function is linearlyapproximated based on the table content. The resourceutilisation for each executed instruction at samplingfrequency of 10 kHz is juxtaposed with code loopcompletion time and can be seen in Fig. 3.

100 μs

44 μs

20.8 μsCurrent &VoltageMeasurement

8.24 μsResolver to digitalcommunication& conversion

3.43 μsReference generation& Controlleriteration

1.49 μsClark & Parktransformation

4.37 μsDuty cycleCalculation& Update

3.36 μsLook Up TableSine & Cosine

1.11 μsInverseClark & Parktransformation

Fig. 3 Resource utilisation of the main code at samplingfrequency of 10 kHz.

In order to verify the model, the sensor readings alongwith controllers inputs and outputs values are beingstored in a data table. Accomplishing the operation issucceeded by sending the data to the computer at alow priority to ensure that it does not affect the mainfunctionalities.

2.3 System ModellingThe system behaviour was modelled based on mathe-matical interpretations of physical phenomena linkingthe separate components into a single suspension unit.The following section contains methodological descrip-tion of the modelling procedure for each component.

2.3.1 PMSMThe core foundation of the PMSM is a rotor made ofpermanent magnets. When the rotor is being rotateda sinusoidal back EMF is generated. To produce aconstant torque a constant current is needed on the

rotor’s q-axis which corresponds to sinusoidal phasecurrents obtained when the motor rotates. The torque isproportional to the machine constant KT . The presenceof id current does not result in any torque and thereforeis considered as a loss. The equations were derived inaccordance to [9] and can be seen in Eq. 1.

ud = R · id + Ld ·diddt

− ωE · Lq · iq

uq = R · iq + Lq ·diqdt

+ ωE · (Ld · id + λpm)

TM = KT · iq

θM =TM − Text −B · θM

J

(1)

where:

ud: d-axis voltageuq: q-axis voltageTM : Mechanical torqueText: Load torqueθM : Angular velocityθM : Angular accelerationR: Phase resistanceid: d-axis current

iq: q-axis currentLd: d-axis inductanceLq: q-axis inductanceλpm: Flux linkageωE : Electrical speedKT : Machine constantB: Damping coefficientJ : Moment of inertia

2.3.2 MLSThe MLS can be viewed as a rotary to transnationalgear with a sinusoidal tension spring. Rotating thePMSM’s rotor causes the translator to experiencelinear displacement. Its magnitude is dictated by thelead γ of the MLS. The sinusoidal spring effectis associated with presence of magnets which getmisaligned while transferring forces. The magnets arearranged in a Halbach array. The maximum force thatcan be transmitted is referred to as stall force Fstall.Exceeding its value results in braking off the interactionsbetween corresponding magnets and snapping to anotherposition. The schematic of the MLS can be seen in Fig.4, while the equations used for deriving a mathematicalmodel in Eq. 2.

Rod

RotorFMLS

FMLS

Pitch κ

Lead γ

xM

xMLS

Fig. 4 Principle of MLS With applied load.

3

xM =γ

2π· θM

FMLS = Fstall · sin(2π

κ(xM − xMLS))

TMLS =γ

2π· FMLS

(2)

where:

xM : Rotor offsetxMLS : MLS positionFMLS : MLS forceFstall: Stall force

θM : Rotor angleTMLS : MLS torqueγ: Leadκ: Pitch

2.3.3 QVMThe QVM is modelled as a two degree of freedomspring-damper-mass system. The rim, tire, brake andaxle constitute the wheel mass being attached to thechassis by a spring, small passive damper due tofriction and the MLS. The resilience of the tire ismodelled as an additional spring bonding it with theroad. The QVM concept is illustrated in Fig. 5. Thedynamic equations (Eq. 5) of motion were derived usingLagrange approach.

y2 =1

mc

(FMLS − k1(y2 − y1)

−mc · g −B(y2 − y1))

y1 =1

mw

(k1(y2 − y1) − k2(y1 − y0) − FMLS

−mw · g +B(y2 − y1))

Fn = − k2(y1 − y0)

(3)

mc

mw

y2

y1

y0

k2

k1 B

FN

FMC

FMLS

FMW

mc: Mass of the chassismw: Mass of the wheelk1: Spring stiffnessk2: Tire stiffnessB: Damping coefficienty0: Road profiley1: Wheel heighty2: Chassis heightFMC : Force due to mc

FMLS : MLS forceFMW : Force due to mw

FN : Normal force

Fig. 5 Quarter vehicle model.2.4 LinearisationDue to cross-couplings between ud-uq voltages causedby mutual inductance, flux linkage (Eq. 1) and thesinusoidal spring effect in MLS (Eq. 2), the PMSM-MLS assembly show non-linear behaviour. To design

the controller, the system was linearised by first orderTaylor expansion presented in Eq. 4. The calculationswere conducted in accordance to [10].

f(x) = f(x0) + f ′(x0) · ∆x (4)

The system was linearised with the assumption, that ataverage the PMSM-MLS assembly does not move andno torque is needed. The chosen linearisation constantscan be seen in Tab. I.

Linearisation constant ValueId0 0 AIq0 0 A

θM0 0 rad/s

Tab. I Point of linearisation.

2.5 TestsThe system parameters were investigated through lab-oratory tests. This approach allows to maximise thereliability of the model and minimise inaccuracies.The performed studies are described in the followingsubsections.

2.5.1 Motor parameter testsParameters to be determined:

• Phase resistance• Phase inductance• Flux-linkage constant• Iron and friction losses• Resolver misalignment

a) Phase resistance: The phase resistances were de-termined by performing a DC-test. The constant DC-voltage with values varying between 0.3 − 1 V wasapplied to each phase and the corresponding currentsmeasured. The resistances were calculated by the useof Ohm’s law and averaged for all collected results.

b) Flux-linkage constant: The flux-linkage was deter-mined by the use of drilling machine mounted to therotor. The oscilloscope was connected to the phaseterminals. The drilling machine was ran with differentvelocities resulting in voltage induction in the statorwindings. The induced line to neutral voltage peakvalues and frequency spectrum were logged to theoscilloscope. The flux-linkage constant was calculatedin accordance with Eq. 5.

4

λpm =epk

fe · 2π(5)

where:

λpm: Flux-linkageepk: Line to neutral voltage peakfe: Electrical frequency

c) Phase inductance: On account of surface mountedmagnets having a flux-permeability comparable withair, the flux-linkage in the motor is independent on therotor position. Consequently the Ld and Lq inductanceare assumed to be equal. Its magnitude was measuredexclusively in the d-axis, which excitation does notresult in rotational movement. It was determined bythe use of "Wayne Kerr 3260B Precision MagneticsAnalyzer" and a "Wayne Kerr 3265B DC Bias CurrentUnit".

d) Iron and friction losses: The iron and friction losseswere found by performing no-load test with keepingthe rotor uncoupled from any mechanical load. Thebalanced three phase voltages were applied to the statorwindings at rated frequency and the currents weremeasured. The test was performed in accordance toprocedure described in [11]. The iq current is directlyproportional to the no load torque through machineconstant KT and is equal to the product of viscousfriction Bvisc with rotational velocity ωM and summedwith dry friction forces Fdry as shown in Eq. 6. Boththe iron and friction losses were considered as viscousfriction.

iq ·KT = Bvisc · ωM + Fdry (6)

e) Alignment test: The test was performed to align thed-axis of PMSM rotor with the resolver readings. Themotor was spun what induced phase to neutral backemf which measurements were collected simultaneouslywith the position from the resolver readings. The offsetwas found by measuring the difference between theposition reading from the resolver with beginning ofthe sine wave corresponding to the d-axis of the rotor.

2.5.2 Frequency testThe behaviour of the system was validated by the fre-quency sweep test. The sinusoidal iq current referencewith constant amplitude and varying frequency was usedto excite the system. The obtained position responseswere used to obtain a frequency spectrum of the system,

which subsequently was used to verify the designedcontroller and the QVM.

2.6 ControllersThe controllers were designed based on the systemtransfer function, that was derived from the state spacerepresentation of the PMSM. The model was derived inaccordance to [12] and has a general form of Eq. 7.

x = Ax+Bu

y = Cx+Du(7)

For the chosen point of linearisation, the Eq. 1 wasreduced to the state space form shown in Eq. 8,exclusively connecting the id and iq states to thecorresponding ud and uq inputs.

[idiq

]=

−RL 0

0 −RL

[idiq

]+

1

L0

01

L

[uduq

][y1y2

]=

[1 00 1

] [idiq

] (8)

The resulting system matrix does not include off-diagonal terms and hence is controllable and perfectlydecoupled. On account of both states have transferfunctions of the same form, the control strategy for ud-id and uq-iq voltage-current pairs is the same. Sincethe id current does not produce torque, to minimiselosses, its reference is set to 0 value. The torque hasa linear dependence with current iq and therefore theiqref is calculated as a product of torque reference withinverse of machine constant KT . The control strategyfor PMSM-MLS assembly can be seen in Fig. 6.

c1

c2

gc11 gc12

gc21 gc22

C(s) Gc(s)

+-

+-Iqref

IqUqkt

0

ττref cτ

e2

e1 Ud

Fig. 6 Control strategy for PMSM-MLS.

The requirements stated for the controllers were chosenbased on engineering judgement. They should cancellow frequency disturbances and secure reference track-ing ability up to 140% of the resonance frequency ofthe system measured to be 12Hz. Since, the uq-iqsubsystem has a transfer function of the first order the

5

control scheme was completed by PI-controller havinga final form of Eq. 9.

C(s) = Kp +Ki

s(9)

where:

C: ControllerKp: Proportional gain of 0.2337Ki: Integrator gain of 1200

The designed controller is frequency dependent andtherefore its behaviour after discretisation was analysed.The controller was discretised by Tustin method de-scribed in [13] approximating the continuous Laplaceoperator as in Eq. 10.

s ≈ 2

Ts

z − 1

z + 1(10)

where:

Ts: is the sampling time of1

10kHz

The closed loop step response of the system withcontinuous and digital controllers is shown in Fig.7. The discretisation did not affect the controller’sperformance.

0 0.005 0.01 0.015 0.02 0.025 0.030

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

Closed loop step responseClosed loop step response - discrete

Step Response

Time (seconds)

Am

plitu

de

Fig. 7 Closed loop step response for Gc11/Gc22 withcontinuous and discontinuous controllers.

2.7 Sky hookThe PMSM-MLS can be configured as passive andsemi-acitve damper. The passive system can be obtainedby calculating the product of relative velocity between

the wheel and the chassis with damping factor Bp

converting calculations into the torque reference for themotor. Among the semi-active schemes the SH methodis best known [4]. It solely acts with regards to thevelocity of the chassis to isolate it from vibrations. Thedifference between the passive and SH concept basedsemi-active system is shown in Fig. 8.

mcy2

y1

k1 Bp

mcy2

y1

k1

Bsh

Fig. 8 Passive damper and SH damper scheme

where:

mc: mass of the chassisk1: stiffness of the springBp: damping coefficient for the passive damperBsh: damping coefficient for the SH dampery1: vertical position of the wheely2: vertical position of the chassis

The concept of attaching the damper to a fixed point ispurely fictional, however there are two main algorithmsfor implementation, the linear approximation and itssimplification constituted by an on/off control policy[14]. The methods are subsequently presented in Eq.11 and Eq. 12.

Bsh =

Bp · y2y2 − y1

if y2(y2 − y1) > 0,

0 if y2(y2 − y1) ≤ 0

(11)

Bsh =

{Bp if y2(y2 − y1) ≥ 0,

0 if y2(y2 − y1) < 0(12)

Both methods are able to achieve comparable results[3]. To simulate a scenario where the suspension isutilised a speed bump was modelled according to theDanish Road Ministry’s guideline [1]. The chosen low-speed sinusoidal bump profile (Modificeret cirkelbump20 km/h) can be seen in Fig. 9.

6

0 1 2 3 4 4.5Road length (m)

0

0.05

0.1

Hei

ght

(m)

Fig. 9 20 km/h sinusoidal speed-bump profile.

3. ResultsThis section contains summary of results from per-formed tests and studies.

3.1 Parameter testThe motor parameters found through laboratory testscan be seen in Tab. II.

Description Parameter ValueFlux-linkage λpm 0.03 Nm

A

Motor Constant Kt 0.482 NmA

Inductance L 1.33 mHResistance RLN 0.339 ohmDry Friction µS 0.0654 NmViscous Friction Bvisc 0.0017 Nm

rad/s

Electrical offset 145◦

Tab. II Results from the PMSM parameters & alignmenttests.

3.2 Controller testThe performance of the controllers exposed to sinu-soidal current input of 3 A with frequency correspond-ing to resonance behaviour of the VTP is shown in Fig.10.

0 50 100 150 200 250 300 350 400 450 500

Time [ms]

-4

-3

-2

-1

0

1

2

3

4

Cur

rent

[A]

Current output 12Hz - VTP

iq

iqref

id

idref

Fig. 10 Reference tracking test of controllers.

The id current frequently reaches peaks up to 1.2 A,before it catches the reference, whereas the iq lags theiqref current by 4 − 10 ms and has overshoot of 1

3 ofthe amplitude.

3.3 Model VerificationThe initial verification of the QVM was performedbased on the time domain model with estimated QVMparameters. This approach did not result in the modelfitting the behaviour of the VTP. Thus the collectedfrequency spectrum data was used to identify newparameter values in SISO transfer function describingposition of the chassis yL with respect to input forceFMLS . The method does not account for non-linearbehaviour of the MLS, which was assumed to haveideal gearing ratio. The results of the performed systemidentification from frequency response studies on thetime domain model can be seen in Fig. 11.

Amplitude at specific frequencies

1 3 5 7 9 11 12 13 15 17

Frequency [Hz]

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

Am

plitu

de [m

]MeasuredSimulated

Amplitude at specific frequencies

1 3 5 7 9 11 12 13 15 17

Frequency [Hz]

0

0.5

1

1.5

2

2.5

3

Am

plitu

de [m

]

10-3

MeasuredSimulated

Amplitude at specific frequencies

1 3 5 7 9 11 12 13 15 17

Frequency [Hz]

0

0.005

0.01

0.015

0.02

0.025

Am

plitu

de [m

]MeasuredSimulated

Fig. 11 Frequency spectrum of VTP and the QVM.

The obtained model tends to over-amplify the lowfrequency inputs. The simulated response is 7.6 and 6times greater for 1Hz and 3Hz respectively. The modelfits measurements at remaining frequencies.

3.4 SkyhookThe performance of different suspension schemes wasvalidated based on the QVM model derived throughfrequency response studies. The results given belowhold for empirically chosen damping coefficient Bp

being 4479.75 N ·sm .

The ability of the suspension to restore the relativeposition yL between the sprung mass and the wheelexposed to speed bump to its original state can be seenin Fig. 12. The corresponding torques are shown in Fig.13.

7

0 0.5 1 1.5 2 2.5

Time(s)

-0.14

-0.13

-0.12

-0.11

-0.1

-0.09

-0.08Position (m)

Passive damping2-state sky-hookinear sky-hookL

Fig. 12 Relative position yL under speed bump test.

0 0.5 1 1.5 2 2.5

Time(s)

-4

-3

-2

-1

0

1

2

3

4Torque required (Nm)

Passive damping2-state sky-hookLinear sky-hook

Fig. 13 Torque demands to compensate speed bump oscilla-tions.

The torque requested by linear SH reaches highestextremes, however the values do not compromisefunctionality of the MLS. The spikes are also shortestobserved. The passive scheme noted 40% lower peakwhich was yet extended in time.

The velocity and acceleration of the chassis are shownin Fig. 14, and in Fig. 15 respectively.

Independent of damping system, the peak velocitiesreach similar values. The two state SH and the passivesystem are faster to settle than the linear scheme.

The acceleration in the two state SH has the lowestpeaks. The highest peak value is observed in the passivesystem, however the linear SH needs longest time tosettle.

The two-state SH demanded least torque and dampedthe oscillations first. The work done by each of the

0 0.5 1 1.5 2 2.5

Time(s)

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5Velocity (m/s)

Passive damping2-state sky-hookLinear sky-hook

Fig. 14 Velocity of the chassis under speed bump test.

0 0.5 1 1.5 2 2.5

Time(s)

-8

-6

-4

-2

0

2

4

6

8Acceleration (m/s2)

Passive damping2-state sky-hookLinear sky-hook

Fig. 15 Acceleration of the chassis under speed bump test.

suspensions schemes was calculated as in Eq. 13 andis summarised in Tab. III.

W =

∫ tend

t0

τ · ωM dt (13)

Suspension scheme ValuePassive 30.84 JSkyhook - On/Off 19.64 JSkyhook - Linear 18.73 J

Tab. III Work done to damp oscillations.

The SH methods needed subsequently 36.3% and 39.3%less work to damp all fluctuations than passive scheme.

4. ConclusionsIn this paper, to investigate behaviour of passive andsemi-active suspension schemes the PMSM-MLS as-sembly has been incorporated with the establishedQVM. On account of building an expectation concern-ing provided drive characteristics, the systems were

8

simulated. The studies show that while the traditionalpassive damping scheme is capable to provide goodoverall performance, the SH schemes offer improve-ments in different areas. The SH schemes manage toreduce the variation in vertical position and velocity ofthe chassis by allowing the suspension to be compressedmore. Furthermore, the two-state SH also lowers thepeaks in vertical acceleration of the sprung mass. TheSH schemes show reduction in work performed todamp the oscillations, while the two-state SH demandsleast torque. Consequently, the SH with on/off policyis expected to be the most suitable system among thestudied suspension schemes.

AcknowledgementThe authors of this work gratefully acknowledgeGrundfos for sponsoring the 7th MechMan symposium.

References[1] Vejdirektoratet, Katalog over typegodkendte

bump.http://www.saferoad.dk/gfx/pdf/pdf08.pdf?fbclid=IwAR3aIA9BvCu4jdFZwfGRaf6asptPQvyEJPDoX4a_u9_ekKRHOEPOExRbFFU, 2013. Downloaded:07-05-2019.

[2] A. R. Bhise, R. G. Desai, R. N. Yerrawar,A. Mitra, and R. R. Arakerimath, “Comparisonbetween passive and semi-active suspensionsystem using matlab/simulink,” IOSR Journal ofMechanical and Civil Engineering, vol. 13, no. 4,pp. 1–6, 2016.

[3] Y. Liu, T. Waters, and M. Brennan, “Acomparison of semi-active damping controlstrategies for vibration isolation of harmonicdisturbances,” Journal of Sound and Vibration,vol. 280, no. 1, pp. 21 – 39, 2005.

[4] S. M. Savaresi, E. Silani, and S. Bittanti,“Semi-active suspensions: An optimal controlstrategy for a quarter-car model,” IFACProceedings Volumes, vol. 37, no. 22, pp. 553 –558, 2004. IFAC Symposium on Advances inAutomotive Control 2004, Salerno, Italy, 19-23April 2004.

[5] I. Naoki, “Semi-active suspension,” KYBTechnical Review, vol. 1, no. 55, pp. 31–32,2017.

[6] R. K. Holm, N. I. Berg, and P. O. Rasmussen,“Theoretical and experimental loss and efficiencystudies of a magnetic lead screw,” IEEE

Transactions on Industry Applications, vol. 51,pp. 1438–1445, 4 2015.

[7] N. I. Berg, “Active suspension - wp1&2. technicalreport, aalborg university,” tech. rep., 2016.

[8] N. Mohan, T. M. Undeland, and W. P. Robbins,Power Electronics Converters, Applicaitons andDesign. No. ISBN: 978-81-265-1090-0 inPaperback, John Wiley & Sons Ltd., 2006.

[9] P. Pillay and R. Krishnan, “Modeling ofpermanent magnet motor drives,” IEEETransactions on Industrial Electronics, vol. 35,no. 4, pp. 537–541, 2004.

[10] C. L. Phillips and J. M. Parr, Feedback ControlSystems. Prentice Hall, 5th ed., 2011.

[11] P. C. Sen, Principle of electric machines andpower electronics. John Wiley & Sons, 3rd ed.,2014.

[12] S. Skogestad and I. Postlehwaite, MultivariableFeedback Control: Analysis and Design. JohnWiley & Sons, 2nd ed., 2005.

[13] T. Wescott, Applied Control Theory of EmbeddedSystems. No. ISBN: 978-0-7506-7839-1 inPaperback, Elsevier Inc., 2006.

[14] X. Wu and M. Griffin, “A semi-active controlpolicy to reduce the occurrence and severity ofend-stop impacts in a suspension seat with anelectrorheological fluid damper,” Journal ofSound and Vibration, vol. 203, no. 5, pp. 781 –793, 1997.

9