Special Issue Speed and Rotor displacement control of Be aring … · 2018-03-15 · Speed and...

Speed and Rotor displacement control of Bearing Less

Switched Reluctance Motor by using Sliding Mode Control

1Nageswara Rao Pulivarthi, 2G.V.Siva Krishna Rao and 3G.V.

Nagesh Kumar 1,3Department of EEE, GITAM University, Visakhapatnam, India

2Dept. of EEE, AUCE (A), Andhra University, Visakhapatnam,

India [email protected], [email protected],

[email protected].

Abstract

In this paper sliding mode control based speed and rotor displacement control

methods are proposed, to get the desired constant speed, the rotor position and its

displacements when the Bearing less switched reluctance motor(BSRM) under

different loads and change of motor parameters. By using this proposed sliding mode

controller, the BSRM drive exhibits the robustness and the more stable position

operation and constant speed as compared with the PID controller. Before applying

suspension loads and torque loads to the rotor, the rotor has to be suspended to the

center and keeps in the stationary position. To maintain the current within a preset

band a hysteresis controller is employed in both torque phase currents and

suspension force currents. When the torque load changes, the rotor has an eccentric

displacement, but it can be pulled back quickly to its center position, due to control

action in suspension phase currents.

Key words: Bearing less, hysteresis controller, displacement, magnetic suspension, sliding mode

control.

1. Introduction:

Bearing less switched reluctance motor (BSRM) have a wide range of applications

in industry as generator starters, electric vehicle, wind turbine ventilators and so on.

Now a days the need of bearing less drive open a massive market and it sets the new

trend to electric drives and motors. The bearing less SRM has the superiorities of

both the magnetic bearing and the SRM[1], such as no friction, no lubrication, and

high speed capability.

In recent times, a number of structures of BSRM have been proposed, firstly, R.

Bosch and J. Bichsel are proposed Bearing less Electric motor concepts and

advantages and winding patterns [1-2]. After that an 8/6 BSRM model was

introduced by M Takemoto, Suzuki and Akira Chiba, in which suspending forces and

motor net torque are coupled each other, due to that, the controlling problem turn

into difficulty while operating this conventional drive [3-5]. To get the decouple

International Journal of Pure and Applied MathematicsVolume 114 No. 7 2017, 175-184ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

175

nature between suspending Force and motor torque, a single layer winding on a

single pole design was proposed by H. J. Wang, Dong. H. Lee and Jin-Woo Ahn. A

separate windings for suspension force and torque production purposes which are

wound on separate salient poles [6-10]. The same was applied to in this particular

10/8 and 12/14 BSRM. An attractive radial force will be built up between stator poles

and rotor due to its saliency nature between stator poles and rotor poles [11-12]. This

produced radial net force can be further distributed into two components, one is the

suspension force component in x-y direction which useful for levitating the rotor

towards the desired center position (0, 0) in an x-y coordinate system and another one

is motor torque component which is useful for the rotation of the rotor in radial

direction [13-15].

In this paper, speed and the magnetically levitated rotor position and its

displacements are controlled by using Sliding Mode controller (SMC), under different

loads and change of both electrical and mechanical type motor parameters. The

performance of the drive is tested at different load conditions in a systematic manner.

Agreeing to the suspended rotor in air at the center position by using suspension

winding magnetic forces, the control scheme of the proposed BSRM, is separated into

three stages. First one is, only suspend the rotor to the center position by applying

suspension currents to all suspension windings through asymmetric converter along

with current hysteresis controller and SMC controller Secondly, when the rotor is

levitated and kept in center position then excite the main motor torque currents to

the stator main winding to accelerate the rotor to the desired speed. After confirming

the desired speed, then apply torque loads the rotor shaft. The 12/14 BSRM winding

pattern and its structure is illustrated in Fig.1.

The drive incorporates two hysteresis control loops for the torque currents, and

four for the suspension force. To get the desired speed and rotor position a sliding

mode controller with Variable Structure System is applied to the proposed 12/14

BSRM. The drive speed performance and rotor displacements and suspension forces

in X and Y directions under Sliding mode controller (SMC) is compared with PI/PID

controller, the SMC shows the better performance for all conditions.

Is3

Is2

Is4

Is1

Fig.1. 12/14 BSRM Structure and winding pattern.

International Journal of Pure and Applied Mathematics Special Issue

176

2. The mathematical modeling of 12/14 BSRM.

Due to decoupled nature exist between torque and suspension forces the state

equations are considered separately. The state equations of motoring are given by

dt

idRiu

),( (1)

dtiL

wiDRiudi m ]

),(

),([

(2)

dRiudt

d (3),

dwwJ

K

J

TT

dt

dwm

F

m

j

Lej

m

1

(4),

dwdt

dm (5)

Therefore, the net torque T in Phase-A is explained as follows:

LiT 2

2

1 (6)

Where Ψ, R, θ, V are per phase flux linkages, per phase resistance, rotor position per

phase, phase voltage, and Te , Tl, J, KF, W are Net electromagnetic torque produced,

load torque applied, combined moment of Inertia of the rotor, damping coefficient,

Rotor speed respectively.

The rotor dynamics of Bearing Less SRM at standstill position or rest is written by

kxdt

xdmFx

2

2

; mgkydt

ydmFy

2

2

(7)

Where m, k, g are mass, spring constant and gravity in y- direction.

The net suspending force produced by proposed BSRM is given by

2

2

2

2

xn

xn

yp

xp

yynyxnyypyxp

xynxypxxp

y

x

i

i

i

i

KKKK

KKKK

F

Fxxn (8)

By combining above two equations, we get


177

xXx IKkxdt

xdmF

2

, YY IKmgkydt

ydmFy

2

(9)

Where kxynKxxnKxypKxxpdiagK X KyynKyxnKyypKyxpdiagKY

2

2

xn

xpx

I

II ,

2

2

yn

yp

YI

II

3. Proposed Sliding Mode control (SMC) method.

The objective of continuous SMC is to place the system states on a pre-determined

sliding surface, which is designed in the state space. The new derived sliding mode

control input is given by )]sgn()[()( 1 xSkxqSASBSu (10)

Where S is switching function, q and k are constants, A and B are system matrix and

Input matrix respectively. The new state equation with control input is given by

)sgn()()]()([ 11 xSkBSxqSASxSBAx (11)

The derived speed state equation is given by

)sgn()()]()([ 11 xSkBSxqSASxSBAw

(12)

+

-x* SMC

x

Mathematical

formulae

θr

Δx Fx*

x

+

-SMC

y

Mathematical

formulae

iy*

θr

Δyy*

y

Fy*

ix*

Fig.2.Rotor Displacement Control Diagram. Fig .3.Suspension winding Asymmetric converter.

Table.1: Switching rules for the suspension winding currents.

Desired force Suspending force poles selection

If oFF yx ,0 21 & ss II





178

Fig.4.Over all control diagram of Proposed BSRM

4. Simulation results.

Healthy conditions of Motor:

When the rotor is at the center position, the torque currents are injected to the

main phases through asymmetric converter to accelerate the rotor to the desired

speed with initial torque load of 0.01 N.mt. From Fig.5.It can be seen that the process

of the proposed BLSRM is same with that of general SRM. When the motor rotates

steadily at rated rpm, and steadily suspended at center position, the phase currents

and output torque are stable and the torque current has almost no effect on the

suspending force.

Fig.5. (a) Y-directional rotor Displacement. Fig.5. (b) X-directional rotor Displacement


179

Fig.5. (c) Y-directional suspension Force. Fig.5. (d) X-directional suspension Force.

Fig.5. (e) Rotor Positions. Fig.5. (f) suspension currents

Fig.5. (g) suspension Controlled voltages Fig.5. (h). Main Phase Currents

Fig.5. (i) No-load speed Fig.5. (j) Controlled Main Phase Voltages


180

Speed and displacement control of BSRM:

In order to investigate the proposed control strategies, the BSRM drive has been

simulated under different working conditions.

Fig.6. when the reference speed is doubled at t=0.5sec. Fig.7. when load torque changed at 0.05 sec.

Fig.6. Illustrates the simulated speed response with the reference speeds of 3000

and 6000 rpm, at load torque of 0.01, the speed graphs are compared with PI

controller and SMC, it can be seen that the speed response is quite good under Sliding

mode controller. Fig.7. shows the operation of the drive under load torque

disturbance. The load torque is changed from 0.2Nm to 0.4 Nm at t=0.05 sec. when

the load torque is increased there is a slight dip in the motor speed. As compare with

PI controller, the SMC gives good speed track which is very close to reference speed.

Fig.8. when the rotor Inertia J is doubled. Fig.9. when the phase resistance is increased by 25%.

Figure.8&9. Shows the speed response when the drive is subjected to uncertainties

in the electrical and mechanical parameters i.e. phase resistance and rotor inertia is

changed. Here the rotor inertia is doubled and the phase resistance is increased by

25%. Inspection of these two figures (8) & (9), indicates that there is no major changes

in speed response with the help of SMC.

0

5000

10000

0 0.05 0.1

SPEE

D IN

RP

M

TIME IN SEC

S P E E D W H E N R E F E R E N C E S P E E D C H A N G E S

speed with pi

speed withSMC

0

5000

0 0.02 0.04 0.06 0.08 0.1

spee

d in

rp

m

time in sec

speed when load changed 0.2 to 0.4 at 0..5 sec

speed with PI

speed with SMC

0

5000

10000

0 0.05 0.1

spee

d in

rp

m

time in sec

speed when Stator Phase resistance chaged by 1.25 times

speedwith PIspeedwith SMCref speed

0

5000

10000

0 0.05 0.1

spee

d in

rp

m

time in sec

speed when Moment of Inertia doubled

speed withPIspeedwithSMCref speed


181

For this drive, the maximum conduction angle for each phase is 12.85 mechanical

degrees. From figure.10. It shows that the speed response with SMC is settled quickly

i.e. less than 0.02 sec when conduction angle is reduced by 2 mechanical degrees. By

using this method even improvement in speed profile, but there is a more ripples in

torque profile. The main advantage of SMC is giving robustness to the drive. This is

achieved in all aspects of speed profiles.

Fig.10. when the switching angle is decreased by 2 deg. Fig. (11). Total Torque Profile of BSRM drive

5. Conclusion.

In this paper, the speed and displacement control of BSRM was done by using

Sliding Mode Controller. The robustness and the desired speed of BSRM was

achieved at different loading conditions by using Sliding mode controller and

compared with conventional PI controller to know its superior performance. The fast

convergence rate and more robustness and disturbance rejection capability properties

were carefully analyzed.

6. References.

[1] R. Bosch, "Development of a Bearingless Electric Motor," in Proc. Int. Conf. Electric Machines (ICEM’88), Pisa,

Italy, 1988: 373-375.

[2] J. Bichsel, "The Bearingless Electrical Machine," in Proc. Int. Symp. Magn. Suspension. Technol, NASA Langley

Res. Center, Hampton, 1991: 561-573.

[3] M. Takemoto, A. Chiba, H. Akagi and T. Fukao, “Suspending force and Torque of a Bearingless Switched

Reluctance Motor Operating in a Region of Magnetic Saturation” in Conf. Record IEEE-IAS Annual Meeting,

2002: 35–42.

[4] M. Takemoto, K. Shimada, A. Chiba, et al., "A Design and Characteristics of Switched Reluctance Type

Bearingless Motors, 4th International Symposium on Magnetic Suspension Technology," NASA/CP-1998-

207654, May 1998: 49-63.

[5] M. Takemoto, A. Chiba and T. Fukao, "A New Control Method of Bearingless Switched Reluctance Motors Using

Square-wave Currents," Proceedings of the 2000 IEEE Power Engineering Society Winter Meeting, Singapore,

CD-ROM, Jan. 2000: 375-380.

[6] H. J. Wang, D. H. Lee and J. W. Ahn, "Novel Bearingless Switched Reluctance Motor with Hybrid Stator Poles:

Concept, Analysis, Design and Experimental Verification," The Eleventh International Conference on Electrical

Machines and Systems, 2008: 3358-3363.

0

2000

4000

6000

8000

0 0.02 0.04 0.06 0.08 0.1

spee

d in

rp

m

time in sec

speed when switching angle is reduced

speed with PI

speed withSMC


182

[7] Dong-Hee Lee, Jin-Woo Ahn, "Design and Analysis of Hybrid Stator Bearingless SRM", Journal of Electrical

Engineering & Technology, 2011, 6(1): 94-103.

[8] D.H. Lee, Z. G. Lee, Liang Jianing, J.W. Ahn, "Single-Phase SRM Drive With Torque Ripple Reduction and

Power Factor Correction", IEEE Trans. on Industry Applications, Vol 43, Issue 6, pp.1578 – 1587, Nov.-dec.

2007.

[9] H. J. Wang, "Design and Control of a Novel Bearingless Switched Reluctance Motor," Industrial System

Engineering of the Kyungsung University, Busan, Korea, PhD’s thesis, June. 2009:6.

[10] Zhenyao Xu, Dong-Hee Lee, Jin-Woo Ahn," Modeling and Control of a Bearingless Switched Reluctance Motor

with Separated Torque and Suspending Force Poles".

[11] Zhenyao Xu, Fengge Zhang, Jin-Woo Ahn." Design and Analysis of a Novel 12/14 Hybrid Pole Type Bearingless

Switched Reluctance Motor"

[12] Zhenyao Xu, Dong-Hee Lee, Jin-Woo Ahn," Control Characteristics of 8/10 and 12/14 Bearingless Switched

Reluctance Motor", the 2014 International Power Electronics Conference.

[13] L. Chen and W. Hofman, "Analytically Computing Winding Currents to Generate Torque and Levitation Force

of a New Bearingless Switched Reluctance Motor," in Proc 12th International Power Electronics and Motion

Control Conference, Portoroz Slovenia, 2006: 1058-1063.

[14] L. Chen and W. Hofman, "Performance Characteristics of One Novel Switched Reluctance Bearingless Motor

Drive," in Power Conversion Conference 2007 (PCC '07), Nagoya, 2007:608-613.

[15] L. Chen, W. Hofmann, "Analysis of Radial Forces Based on Rotor Eccentricity of Bearingless Switched

Reluctance Motors," in International Conference on Electrical Machines, Rome, 2010.


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