Control Engineering Practice 19 (2011) 1377–1386

Contents lists available at ScienceDirect

Control Engineering Practice

0967-06

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/conengprac

High performance current control of a switched reluctance machine based ona gain-scheduling PI controller

Hala Hannoun, Mickael Hilairet �, Claude Marchand

LGEP/SPEE Labs, CNRS UMR8507, SUPELEC, Univ Pierre et Marie Curie-P6, Univ Paris Sud-P11, 11, rue Joliot Curie, Plateau de Moulon, F91192 Gif sur Yvette Cedex, France

a r t i c l e i n f o

Article history:

Received 11 June 2010

Accepted 17 July 2011Available online 10 August 2011

Keywords:

Switched reluctance machine

Speed control

Instantaneous torque control

Current control

Gain scheduling

61/$ - see front matter & 2011 Elsevier Ltd. A

016/j.conengprac.2011.07.011

esponding author.

ail address: mickael.hilairet@lgep.supelec.fr (M

a b s t r a c t

Switched reluctance motor drives are under consideration in various applications requiring speed

variation. This is certainly due to their mechanical robustness and low manufacturing cost. However,

the non-linear characteristics of the flux and the torque, and the high acoustic noise complicate

significantly the controller design. In order to take into account the phenomenon of magnetic

saturation and its dependence on the rotor position and the current, a PI controller with variable

gains is proposed. This controller compensates the inductance variation and maintains the dynamics of

the closed-loop system constant. Simulations and experimental results of the standard PI controller and

the gain-scheduling one are discussed. It shows the advantages of the gain adaptation compared to the

fixed gains.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The switched reluctance machine (SRM) had attracted manyresearchers over the last decade. This is certainly due to itsnumerous advantages such as simple and robust construction,high-speed and high-temperature performances, low costs, andfault tolerance control capabilities.

The performance of SRMs has been enhanced greatly due toadvances in power electronics and computer science. Nowadays,SRMs are under consideration in various applications requiring highperformances such as in electric vehicle propulsion (Kalan, Lovatt, &Prout, 2002; Krishnamurthy et al., 2006; Rekik et al., 2008; Schofield,Long, Howe, & McClelland, 2009), automotive starter-generators(Fahimi, Emadi, & Sepe, 2004; Faiz & Moayed-Zadeh, 2005), aero-space applications (Naayagi & Kamaraj, 2005; Radun, 1992), elevator(Lim, Krishnan, & Lobo, 2008) and PFC (Chang & Liaw, 2009).

However, several disadvantages like acoustic noise generation,torque ripple, non-linear electromagnetic characteristics and thestrong dependence on the rotor position are limiting its utiliza-tion compared to other types of machines. One of the mainlimitations of the SRM is the non-linear electromechanical beha-vior (dependence on the current and mechanical position) and theextreme magnetic saturation in order to achieve high torquedensity (Radun, 1995). Therefore, the design of an appropriatecontroller to achieve high performances must take into accountthis non-linearity.

ll rights reserved.

. Hilairet).

Several publications concerning linear and non-linear controllersthat achieve high dynamic control are available in the literature.Due to the fact that the SRM is a non-linear multivariable system,modern non-linear designs have been studied in order to achievehigh dynamic performances. The feedback linearization (Ben Amor,Dessaint, & Akhrif, 1995; Ilic’Spong, Marino, Peresada, & Taylor,1987) or the passivity-based method (Espinosa-Perez, Maya-Ortiz,Velasco-Villa, & Sira-Raminez, 2004) are good examples. However,experimental results show that these modern controllers are notrobust against parameter variation, in particular the feedbacklinearization. Moreover, the position or speed controllers do notcontain current inner loops in order to protect the machine andconverter against current surges. This latter constraint is mandatoryfor an industrial application.

Therefore, a classical structure of the controller is based on aninstantaneous torque control composed of two loops: current innerloops and an outer speed loop (or position loop), as shown in Fig. 1.

The most commonly used method for the inner loop is thehysteresis which is robust, easy to implement and does not requireany model of the system. However this type of controller has thedisadvantage of variable switching frequency that may cause asubsonic noise in SRM (Blaabjerg, Kjaer, Rasmussen, & Cossar, 1999).The alternative solution is a PWM fixed switching frequencyoperation with linear and non-linear controllers. In Bae andKrishna (1996), a hybrid controller has been proposed. This con-troller is a cascade combination of a PI current error amplifier with aPWM output and a hysteresis current controller. When the currenterror is within the hysteresis window, the PWM block is enabled.The hysteresis block becomes ineffective, thereby the output of thecontroller block comes only from the PWM part of the controller.

Fig. 1. Block diagram of the speed controller.

Fig. 2. 3D view of the 8/6 SRM prototype.

H. Hannoun et al. / Control Engineering Practice 19 (2011) 1377–13861378

The difficulty consists in choosing the optimal time transitionbetween the two controllers.

Generally, all of these contributions do not take into accountthe non-linear nature of the SRM, i.e. the magnetic saturation isneglected by assuming only the mechanical position dependenceon the magnetic flux.

In this paper, we address these issues by designing a gain-scheduled PI current controller. Because the phase inductance variesaccording to both rotor position and stator current, a controller withadjustable gains would give better performances than a regularfixed gain PI controller (Ho, Panda, Lim, & Huang, 1998). Anotherimportant aspect of this paper is that in the proposed controller, theback-EMF that is considered as a source of disturbance is compen-sated. In fact, the back-EMF introduces additional current harmonicsthat could be interesting to attenuate.

The paper is organized as follows: the next section introducesthe electromagnetic data obtained from the finite element analy-sis (FEA) and the analytical modeling of the SRM. In Section 3, thegain-scheduling PI current controller design is presented in detail.Finally, simulation and experimental results are presented toverify the performance and viability of the proposed currentcontroller in Section 4.

2. SRM modeling

This study considers four phases, 8/6 SRM prototype as shownin Fig. 2 whose characteristics are listed in Table 4. The SRMinverter used is an asymmetrical half-bridge inverter.

The current controller design is based on the machine magne-tization characteristics that are usually obtained from experi-mental measurements or from numerical calculations such asfinite element analysis (FEA). In this study, the flux linkage fði,yÞis generated by a numerical tool called MRVSIM based on FEA(Besbes & Multon, 2004). This is represented in Fig. 3(a) over oneelectrical period and for phase currents going up to 100 A. Mutualeffects are neglected in this study. The electromagnetic data isstored in look-up tables and is used in simulations through linearinterpolations. The self inductance L can be deduced from the fluxlinkage as Lði,yÞ ¼fði,yÞ=i. Fig. 3(b) shows the phase inductancevariation versus rotor position for different current values. Forcurrent values less than 20 A, the inductance is independent ofthe current. The magnetic saturation effect appears when thecurrent exceeds 20 A and the inductance becomes a function ofboth current and position.

To take into account the position and current dependence ofthe inductance in the control so as to improve the performance,the flux linkage is generally stored in a look-up table. However,this storage requires an excessively large amount of memory andis time consuming. Therefore an analytical modeling is adopted inthis study for the calculation of the phase inductance based on thecurves given in Hannoun, Hilairet, and Marchand (2007). Theposition dependency is represented by a limited number ofFourier series terms (Pþ1) and the non-linear variation withcurrent is expressed by N order polynomial functions. Theestimated inductance bL is a function of electrical rotor positiony and phase current i can be finally written as follows:

bLðy,iÞ ¼XP

p ¼ 0

apðiÞcosðpyÞ with apðiÞ ¼XN

n ¼ 0

bpnin ð1Þ

The choice of N and P depends on two factors:

�

The relative error, between the finite element data and theanalytical expression, that decreases with N and P. � The computational time needed by the processor to compute

one operating point bLðy,iÞ: it depends on the number of multi-plication and addition operations, which is (Pþ1)(3Nþ2).

0 20 40 60 80 1000

0.02

0.04

0.06

0.08

0.1

0.12

Phase current (A)

Flux

−lin

kage

(Wb)

Rotorpositionθ

Aligned position

Unaligned position

0 1 2 3 4 5 60

0.5

1

1.5

2

2.5

3

3.5x 10−3

Rotor position (°)

Pha

se in

duct

ance

(H)

Unalignedposition

Aligned positioni=0 to 20 A

i=100A

Phasecurrent i

Fig. 3. Flux-linkage characteristics based on FEA (a), phase inductance based on FEA (b).

0 1 2 3 4 5 6468

101214

x 10−4

Rotor position (rad)

Indu

ctan

ce (H

) MRVSIML(θ)

0 1 2 3 4 5 6−0.01

−0.005

0

0.005

0.01

Rotor position (rad)

Rel

ativ

e er

ror

Fig. 4. Phase inductance and relative error for i¼80 A.

0 1 2 3 4 5 60

0.5

1

1.5

2

2.5

3

3.5x 10−3

Rotor position (°)

Incr

emen

tal i

nduc

tanc

e (H

)

1A10A20A30A40A50A60A70A80A90A

Fig. 5. Incremental inductance variation.

H. Hannoun et al. / Control Engineering Practice 19 (2011) 1377–1386 1379

A compromise between accuracy and suitability for computeraided design must be done and a reasonable choice seems toselect N and P equal to 6 and 4, respectively. Fig. 4 shows acomparison between the inductance model and MRVSIM data for80 A (saturated region). The maximum relative error is about 1%.

3. Controller design

3.1. Electrical model

The differential equation describing the dynamical behavior ofone SRM phase is:

u¼ RiþLincðy,iÞ@i

@tþEðy,i,oÞ ð2Þ

with

Lincðy,iÞ ¼ Lðy,iÞþ i@Lðy,iÞ

@ið3Þ

Eðy,i,oÞ ¼ io @Lðy,iÞ

@yð4Þ

where u is the applied phase voltage, i the phase current, y theangular electrical position, o the angular electrical speed, R thephase winding resistance, E is the induced EMF and Lincðy,iÞ isthe incremental inductance that depends on the phase currentand rotor position, as can be seen in Fig. 5.

Eq. (2) indicates a non-linear model that depends on position,current and speed. The electrical time constant of a phase wind-ing and the back-EMF vary strongly with current and rotorposition. Therefore a controller that takes into consideration thevariation of the SRM plant (back-EMF and inductance) shouldnormally gives better performance.

3.2. Gain adaptation

It is clear from Eq. (2) that the design of the current controllercould not be obtained by the regular linear control tools. Therefore, anexact linearization via a static state feedback control has been opted.

Proposition. Consider one phase of the SRM represented by the model

_F ¼ u�Ri

i¼ hðF,yÞ ð5Þ

Table 1Loop dynamics variation for the fixed PI controller.

y (deg) L (mH) x wn (rad/s)

0 0.38 1 10,000

90 1.35 0.5305 5305

180 3.22 0.3435 3435

Fig. 6. Bloc diagram of the current control loop.

H. Hannoun et al. / Control Engineering Practice 19 (2011) 1377–13861380

where the flux F is the state, i is the current, R the phase resistance

and hðF,yÞ a non-linear function that represent the mapping

between the flux, the position and the current. With the control law:

u¼ K 0pðin�iÞþ

K 0isðin�iÞþRiþEðy,i,oÞ

K 0iðy,iÞ ¼ Lincðy,iÞw2n

K 0pðy,iÞ ¼ 2xLincðy,iÞwn ð6Þ

the closed-loop can be modeled by a second order system

s2þ2xwnsþw2n, where x is the damping ratio and wn is the

bandwidth.

Proof. The proof proceeds in two steps, introducing first a staticstate feedback control u¼ bðF,i,yÞmþaðF,i,yÞ, where m is anexternal input. It is shown that the compensation aðF,i,yÞ equalsto RhðF,yÞþEðy,i,oÞ leads to

_F ¼ bðF,i,yÞm ð7Þ

and that the choice of bðF,i,yÞ equals to Lincðy,iÞ gives theequation:

di

dt¼ m ð8Þ

Then, introducing a PI controller with a proportional gain Kp

and an integral gain Ki leads to the second-order transfer func-

tion:

i

in¼

KiþKps

s2þKpsþKið9Þ

Equating the denominator with s2þ2xwnsþw2n shows that

Ki ¼w2n

Kp ¼ 2xwn ð10Þ

From the definition of bðF,i,yÞ, aðF,i,yÞ and Eq. (10), one gets

the control law:

u¼ Lincðy,iÞ Kpðin�iÞþ

Ki

sðin�iÞ

� �þRiþEðy,i,oÞ

¼ K 0pðin�iÞþ

K 0isðin�iÞþRiþEðy,i,oÞ ð11Þ

where

K 0i ¼ Lincðy,iÞw2n

K 0p ¼ 2xLincðy,iÞwn & ð12Þ

3.3. Discussion

Compensation of the back-EMF term is essential in order toachieve high-performance current control. The back-EMF could beseen as a disturbance to be eliminated from the current loop.

In Bae and Krishna (1996), the back-EMF term has beendecoupled using a linear model of the inductance versus rotorposition. However, for a highly saturated machine it is necessaryto include the saturation effects due to current in the back-EMFcompensation. In Rahman and Schulz (2002), saturation has beentaken into consideration and the back-EMF term was computed asE¼oð@fðy,iÞ=@yÞ, where @fðy,iÞ=@y is stored in a two dimensionallook-up table. However, the look-up table approach requiresmemory and valuable processing time.

To overcome this issue, in this study the back-EMF is analy-tically computed using Eq. (1) as:

bEðy,i,oÞ ¼ io @bLðy,iÞ

@yð13Þ

Once the back-EMF term is calculated, it is added to the PIcontroller output to decouple its effect on the current loop asshown in Fig. 6.

As shown in Fig. 5, the incremental inductance is highly non-linear, i.e. it is a function of both position and current. This meansthat for a controller with fixed gains, the closed-loop transfercharacteristics change over the electrical cycle. To show thisvariation, a simple case where the inductance varies only withthe position, i.e. for current values less than 20 A is considered.For two different positions (y1 and y2), it is possible to write:

Ki ¼ L1w2n1 ¼ L2w2

n2 ¼ constant ð14Þ

Kp ¼ 2x1L1wn1 ¼ 2x2L2wn2 ¼ constant0 ð15Þ

)wn1

wn2

� �2

¼L2

L1and

x2

x1¼

wn2

wn1¼

ffiffiffiffiffiL1

L2

sð16Þ

Therefore, if the damping ratio is fixed to 1 and the bandwidthto 10,000 rad/s at the unaligned position (y¼ 01) where theinductance is equal to 0.38 mH, the dynamics will vary with theposition according to Eq. (16). The variation of the dynamics withthree different positions [the unaligned position (y¼ 01), anintermediate position (y¼ 901) and the aligned position(y¼ 1801)] is summarized in Table 1. It shows a slower systemand fluctuation increase while the inductance increases.

The Bode diagram of the closed-loop system corresponding tothose three operating points, when no adaptation is used, can beseen in Fig. 7. As it can be seen in this figure, the magnitude of theclosed-loop system varies widely according to the operating pointand thus the resulting bandwidth and the phase margin. Thebenefit of the gain adaptation is that controller parameters varywith current and position so that the dynamics remain constantwhen the inductance varies.

In Rahman and Schulz (2002), a linear gain adaptation hasbeen adopted. Nominal PI gains are set for maximum current inthe unaligned position. Two adaptation coefficients are intro-duced to adjust the PI gains with respect to the reference currentand the rotor position, respectively, in a linear way. This methodhas the advantage of being simple. The variations of the band-width and the phase margin are limited but still exist.

−50

−40

−30

−20

−10

0

10

Mag

nitu

de (d

B)

103 104 105 106−135

−90

−45

0

Pha

se (d

eg)

Bode Diagram

Frequency (rad/sec)

θ1=0°θ2=90°θ3=180°

Fig. 7. Bode diagram of the closed-loop system.

Fig. 8. Gain adaptation algorithm.

Table 2Number of operations to compute the gain scheduling.

Computation of Number of additions and

subtractions

Number of

multiplications

Number of

divisions

b, g, g2, g4 12 10 0

Trigonometric

function

8 6 0

Gains ap(i) 6 6 0

Lðy,iÞ 4 4 0

Total 30 26 0

Fig. 9. Discretize gain-scheduling PI controller.

Table 3Dynamics variation with the classical PI controller.

Linc (mH) x wn (rad/s) tr (ms) DHOL (dB) DFOL (deg)

0.17 2.27 3254 4 2.3 39

0.38 1.61 2300 3.9 8.5 63.5

1.8 0.7 1000 3 22.8 63

3.22 0.5234 747 7.1 27.85 53

Table 4Prototype characteristics.

Geometric parametersNumber of rotor poles 6 Stator pole arc 19.81

Number of stator poles 8 Rotor pole arc 20.651

Stator outer diameter 143 mm Airgap length 0.8 mm

Shaft diameter 23 mm

Electrical parametersNumber of phases 4 Nominal speed 3000 rpm

Nominal power 1.2 kW Nominal voltage 24 V

0 1 2 3 4 5 6

−10

−5

0

5

10

Rotor position (rad)

Ele

ctro

mag

netic

torq

ue (N

.m) Phase

current i

Fig. 10. Torque characteristics based on FEA.

H. Hannoun et al. / Control Engineering Practice 19 (2011) 1377–1386 1381

In the proposed controller, gain adaptations ensure exactly thesame dynamics when the position and the current vary. The gain-scheduling controller assumes that a measurement of the shaftposition as well as the current are available so that the inductancegiven by Eq. (1) can be computed. This value is then used to adjustthe parameters of the PI controller, according to Eq. (12). Theproportional and the integral gains vary with current and rotorposition so that the bandwidth and the damping ratio remainconstant. This procedure is summarized in Fig. 8.

Table 2 shows the number of arithmetic operations required ateach time sample by our algorithm. The complexity and thememory requirements are significantly increased. For the evalua-tion of the total number of arithmetic operations, the trigono-metric functions required by the estimator are supposed to becomputed by fifth degree polynomials, as done for example onDSPs. Therefore, each trigonometric functions uses 5 multiplica-tions and 5 additions by applying Horner’s rule to rearrangepolynomials in Horner form. This is useful for an effectiveimplementation. However, in order to increase the reduction ofthe computational complexity, the main operations required forcomputing these coefficients are the evaluation of b¼ cosðyÞ,g¼ sinðyÞ, g2, g4. No other trigonometry functions are required,because:

cosð2yÞ ¼ 1�2 sinðyÞ2 ð17Þ

cosð3yÞ ¼ cosðyÞð1�4 sinðyÞ2Þ ð18Þ

cosð4yÞ ¼ 1�8 sinðyÞ2þ8 sinðyÞ4 ð19Þ

cosð5yÞ ¼ cosðyÞð1�12 sinðyÞ2þ16 sinðyÞ4Þ ð20Þ

Therefore, the computation of the gains scheduling needs 30multiplications, 26 additions and no division, which is notexcessive.

Fig. 11. Block diagram of the SRM and controller.

1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 20

5

10

15

20

25

30

35

40

1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 20

5

10

15

20

25

Fig. 12. Simulation result of the current regulation using the GSPI controller.

1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 20

0.5

1

1.5x 10−3

1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 20

2000400060008000

1000012000

1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 20123456

Fig. 13. Gain-scheduling of the GSPI controller.

H. Hannoun et al. / Control Engineering Practice 19 (2011) 1377–1386 1383

3.4. Dynamic’s choice

The proposed controller has been implemented using a Dspaceboard, therefore it must be digitized first. This is achieved usingthe Euler transformation associated with an anti-windup fol-lowed by a zero-order holder, as shown in Fig. 9.

In order to tune gains Kp and Ki, the desired closed-loopresponse time tr need to be define in agreement with the

1.95 1.955 1.96 1.965 1.97 1.0

5

10

15

20

25

30

35

40

1.95 1.955 1.96 1.965 1.97 1.0

5

10

15

20

25

Fig. 14. Simulation result of the current reg

1.95 1.955 1.96 1.965 1.97 10

0.5

1

1.5x 10−3

1.95 1.955 1.96 1.965 1.97 10

500

1000

1500

2000

1.95 1.955 1.96 1.965 1.97 10

1

2

3

Fig. 15. Phase inductance variation and fix

sampling time. In our case, a Dspace board has been used so thatthe sampling time has been fixed to 100 ms. Considering aresponse time tr equal to 10 times the sampling period (tr¼1 ms),a reasonable choice of x and wn seems to be x and wn equal to0.7 and 3000 rad/s, respectively.

In order to compare the gain-scheduling with the regular PIcontroller, the dynamics of the latter must be settled. The choiceis more delicate in this case because the inductance variation can

975 1.98 1.985 1.99 1.995 2

975 1.98 1.985 1.99 1.995 2

ulation using the regular PI controller.

.975 1.98 1.985 1.99 1.995 2

.975 1.98 1.985 1.99 1.995 2

.975 1.98 1.985 1.99 1.995 2

ed gains with the regular PI controller.

H. Hannoun et al. / Control Engineering Practice 19 (2011) 1377–13861384

degrade the stability margin. The adopted dynamics must ensurethe system stability whatever the inductance value is. The criticalvalue is the minimal one, i.e. 0.17 mH.

Table 3 summarizes the dynamics variation of the closed-loop,the gain and phase margins for different inductance values(minimal, maximal, intermediate). Theses values are computedaccording to Eq. (16) together with an initial tuning. From thesesvalues, we conclude that the system is stable for every inductance

1.95 1.955 1.96 1.965 1.97 1.975 1.98 1.985 1.99 1.995 22

2.5

3

3.5

4

PIGV

PIGF

Fig. 16. Simulation result of a torque comparison.

1 1.5 2 2.5 3 30

5

10

15

20

25

30

35

40

45

1 1.5 2 2.5 3 30

5

10

15

20

25

Fig. 17. Robustness test o

value, therefore a reasonable choice for the regular PI controllerwould be equal to x¼ 0:7 and wn¼1000 rad/s at the mean valueof the inductance (1.8 mH). This is the adopted choice in thisstudy.

4. Simulation results

Simulation tests have been carried out using MATLAB-Simu-link software package. The non-linear characteristics of the SRMare modeled using the static data obtained by finite elementanalysis (see Figs. 3(a) and 10). Fig. 11 shows the SRM non-linearmodel and the controller. The controller contains two sampletimes: one for the current control (100 ms), and a second one forthe speed control (1 ms). In our application, the power supply isregular half-bridge inverter with a DC-bus voltage equal to 24 V.

The results consider a steady state of 500 rpm with a 3 N mload torque. Fig. 12 shows the four phases current regulationusing the gain-scheduling PI controller (GSPI) and the four meanvoltages obtained at the output of the controllers (one regulatorper phase). The output of the speed controller is nearly equal to30 A which corresponds to the saturated zone. The phase induc-tance variation is illustrated in Fig. 13 together with the resultinggain adaptation in order to maintain constant dynamics.

For the same operating point (500 rpm, 3 N m), the resultsobtained using the regular PI controller are represented in Figs. 14and 15. During the transient period, the voltage resulting from theGSPI controller is greater than the one given by the regular PIcontroller, therefore it boosts the phase current, resulting in abetter and faster response than the regular PI controller. This factis reflected on the produced torque shown in Fig. 16 where wecan notice that torque ripple is decreased with GSPI.

.5 4 4.5 5 5.5 6x 10−3

.5 4 4.5 5 5.5 6x 10−3

ΔL = 0%ΔL = +20%ΔL = −20%

f the GSPI controller.

20

25

30

35

40

H. Hannoun et al. / Control Engineering Practice 19 (2011) 1377–1386 1385

The performance of the proposed controller is limited becauseof the DC source voltage limitation (24 V). For a given speed, thecontroller is able to produce better current response until theresulting phase voltage saturates. In that case, the two controllersbecome equivalent and a regular PI one would be enough.

Inductance variation is introduced on the model in order totest the robustness of the new controller according to the phaseinductance uncertainties. Fig. 17 represents the current responseand the mean voltage at the controller output for a 720%inductance variation at 500 rpm. The current response is slightlyaffected by this parameter variation.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

5

10

15

35

40

5. Experimental results

The proposed controller has been implemented on a test benchshown in Fig. 18 using a DSPACE DS1103 board. Angular velocityand rotor position are detected by means of an incrementalencoder mounted on the SRM rotor shaft (on the left of the testbench). Phase currents are measured using a hall effect currentsensor and an electromagnetic particle brake is used in order tovary the load. Moreover, the test bench is equipped with a torquetransducer in order to evaluate the mean torque and torque ripple.

The tests performed in simulation have been repeated on thetest bench. Fig. 19 shows the measured currents with bothcontrollers. As noticed, the simulation and the experimental resultsagree excellently.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

5

10

15

20

25

30

Fig. 19. Experimental result of one phase current with GSPI controller (a) and

6. Conclusion

An adaptive PI current controller has been developed for SRmotor drives. The variable structure PI controller is self-tuning. Itsdesign is based on a regular PI controller concept, except that itsparameters are adjusted on-line as the current and the positionchange. In addition, a back-EMF compensation scheme has beenimplemented to reduce the bandwidth requirements placed uponthe controller.

This controller limits the loop bandwidth variations due to theradically changing plant gain seen by the controller, thus resultingin a well controlled system.

The proposed gain-scheduling PI controller has been tested bysimulation and validated on the experimental test bench. Theresults prove the interest of this type of regulation. However, the

Fig. 18. Experimental test bench.

regular PI controller (b).

improvement has been limited due to the DC voltage supplysaturation of the specific application.

References

Bae, H. K., & Krishna, R. (1996). A study of current controllers and development ofa novel current controller for high performance SRM drives. IEEE IAS annualmeeting (pp. 68–75).

Ben Amor, L., Dessaint, L. A., & Akhrif, O. (1995). Adaptive nonlinear torque controlof a switched reluctance motor via flux observation. Mathematics and Compu-ters in Simulation, 38, 345–358.

Besbes, M., & Multon, B. (2004). MRVSIM Logiciel de simulation et d’aide �a laconception de Machines �a reluctance variable �a double saillance �a alimentationelectronique. Deposit APP CNRS n.IDDN.FR.001.430010.000.S.C.2004.000.30645.

Blaabjerg, F., Kjaer, P. C., Rasmussen, P. O., & Cossar, C. (1999). Improved digitalcurrent control methods in switched reluctance motor drives. IEEE Transac-tions on Power Electronics, 14(3), 563–572.

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