Modeling, Simulation, And Control of Switched Reluctance Motor Drives

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 6, DECEMBER 2005 1625

Modeling, Simulation, and Control of SwitchedReluctance Motor Drives

Iqbal Husain, Senior Member, IEEE, and Syed A. Hossain, Member, IEEE

Abstract—This paper presents the modeling, simulation, andcontrol aspects of four-quadrant switched reluctance motor(SRM) drives. The design of SRM drive systems must be focusedon application-based appropriate control and engineering solu-tions needed to overcome the practical issues. A complex modelis described for the physical motor simulation to incorporate theimportant dynamics of the SRM. A simpler, but quite accurate,model is presented for the SRM controller. Various practical limi-tations have been incorporated in the simulation model to make itcloser to the experimental setup. The SRM control parameters arechosen based on torque-per-ampere maximization requirement.Experimental results for a 1.0-kW SRM obtained on a digitalplatform are presented along with useful guidelines for prototypeimplementation.

Index Terms—Four-quadrant controls, switched reluctancemachines.

I. INTRODUCTION

THE INHERENT simplicity, ruggedness, and low cost ofa switched reluctance motor (SRM) makes it a viable

candidate for various general-purpose adjustable-speed andservo-type applications. The SRM drives have the additionalattractive features of fault tolerance and the absence of magnets.However, due to the doubly salient construction and the discretecommutation from one phase to another, high-performancetorque control of this type of motor is a critical issue forservo-type applications. A sophisticated control technique canimprove the operating performance for the entire motor drivesystem.

The development of a servo-category drive system demandsa good computer-simulation model to reduce the expensive andtime-consuming experimental stage. The block diagram of anSRM drive system is given in Fig. 1. The controller has twoparts: outer loop controller and inner loop controller. The outerloop generates the reference torque or reference speed fromthe position or speed error. The SRM drive system is in theinner loop. Dynamic modeling and simulation play critical rolesin the inner loop controller design, drive system analysis, andfuture development. The importance of appropriate modeling

Manuscript received September 24, 2003; revised May 6, 2005. Abstractpublished on the Internet September 26, 2005. This work was supported in partby a research award from Delphi.

I. Husain is with the Department of Electrical and Computer Engineer-ing, University of Akron, Akron, OH 44325-3904 USA (e-mail: [email protected]).

S. A. Hossain was with the Department of Electrical and Computer Engi-neering, University of Akron, Akron, OH 44325-3904 USA. He is now withGlobe Motors, Dayton, OH 45404-1249 USA.

Digital Object Identifier 10.1109/TIE.2005.858710

is significant during both the computer-simulation and the real-time implementation stages of the drive system.

The performance of an SRM drive system is enhancedthrough optimization of a desired criterion, which set the appro-priate control parameters of turn-on angle, turn-off angle, andreference current [1]. The maximization of torque per ampereby an SRM is considered in this paper. This optimization mayyield the use of a smaller motor for a given application ora faster response time for a given motor. Electromechanicalactuators and traction-type loads require motor operation inthe position-controlled mode with fast response characteristics.A four-quadrant drive is essential for such servo-type applica-tions. In any operating quadrant, maximum torque per ampere isthe desirable quantity, either for fast forward or reverse motionor for fast motion-direction reversal.

This paper demonstrates the development of an SRM driveconsidering all the practical implementation issues. The issuesarising at the hardware and software development stages havebeen addressed.

II. SRM MODEL

The motor modeling lends itself to two distinctive ap-proaches when considering the objective of modeling. A precisemodel is presented for the physical motor simulation to incor-porate the important dynamics of the SRM. A simple, but quiteaccurate, model is presented for the SRM controller.

A. Physical Motor Model

In the computer-simulation stage, an accurate model of thephysical motor is necessary to depict the real scenario, wherethe computation time is not at all critical. In the case of SRM,the machine is always operated in the magnetically saturatedmode to maximize the energy transfer. The magnetic nonlin-earities of an SRM can be taken into account by appropriatemodeling of the nonlinear flux–current–angle (λ−i−θ) charac-teristics of the machine. The output electromagnetic torque ofthe machine is described by the nonlinear torque–current–angle(T−i−θ) data. The machine model may then be described by

λ = λ(i, θ) (1)

T = T (i, θ). (2)

A first approach consists of look-up tables, with the predictedflux linked λ(i, θ) and the static torque T (i, θ) expressed asfunctions of current level i and rotor position θ. The look-up

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1626 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 52, NO. 6, DECEMBER 2005

Fig. 1. SRM drive system.

table is typically populated using data from static tests or resultsfrom finite-element analysis (FEA).

An alternative approach consists of using a geometry-basedanalytical model described in [2] and [3]. The model uses ananalytical solution for the flux linked and static torque producedby one SRM phase. Separate analytical models for the fluxlinked by a phase of the SRM when its stator and rotor poles doand do not overlap are combined to provide a complete modelof a given motor phase. When the poles overlap, saturationmust be included, especially in the pole tips, whereas a linearrepresentation can be used in the unaligned position. The fluxlinked by the SRM phase is determined from the sum of themain flux and the fringing flux that is linked by the phase. Theanalytical model could be used to populate the look-up tablesmentioned earlier, or to directly calculate the motor parameters.

The analytical model is preferably described in terms ofthe machine geometry and material properties. The geometry-based model allows extensive computer-simulation studiesduring the drive design stage. The general form of a geometry-based analytical expression for flux linkage used is

λ(i, θ) = Am(θ, ξ) + Af(θ, ξ)

− Bm(θ, ξ)√

Cm(ξ) + Dm(i, ξ) + Em(i2, ξ)

− Bf(θ, ξ)√

Cf(ξ) + Df(i, ξ) + Ef(i2, ξ) (3)

where A, B, C, D, and E are ξ- and θ-dependent constants. ξstands for geometry and magnetic properties and θ stands forrotor position. Subscripts m and f are for main and fringingcomponents of the flux linkage.

The physical motor is simulated using either flux λ or currenti as the state variables. Rotor position and speed (ω) constitutethe state variables for the mechanical subsystem. The state-space format that describes the SRM dynamics is

λj = vj − ijrj or ij =(

∂λj

∂ij

)−1 [−ijrj −

∂λj

∂θω + vj

]

(for each jth phase) (4)

θ =ω (5)

ω = − B

Jω +

1J

Nph∑

j=1

Tj − TL

(6)

vj is the applied phase voltage, rj is the phase resistance, Bis the viscous damping constant, TL is the load torque, and Tj

is the torque of each phase. The output variable i is obtainedfrom the machine (λ−i−θ) characteristics when flux is usedas the electrical state variable. If currents are used as the elec-trical state variables, then (∂λj)/(∂θ) and (∂λj)/(∂ij) needto be calculated from the (λ−i−θ) characteristics. The elec-tromagnetic torque is derived from the flux-linkage expressionof (3) using

Tj(θ, i) =∂

∂θ

i∫

0

λ(i, θ)di

.

The magnetic and mechanical loss models must also beincorporated in the physical motor, since the static (λ−i−θ)characteristics does not include the losses.

B. Controller SRM Model

The analytical-model equations are too complex to be imple-mented directly in the controller code for the real-time controlof a machine. The controller model requires being fairly simpleso that the computation cycle time is minimized. The followingSRM flux model [5] expressed as a function of phase currentand rotor position has been used in the implementation

λ = λu + (λa − λu) · f(θ)

=Lui + (ai + b −√

b2 − ci + di2) · f(θ) (7)

where a, b, c, and d are the machine-geometry- and iron-magnetic-property-dependent terms, which are given inAppendix I. The use of two different models for the controllerand physical motor in the computer-simulation stage representsthe real scenario.

Equation (7) has been validated by comparing the model-predicted result with the FEA result. The static plots of flux-linkage (λ) and torque (T ) characteristics of an SRM obtainedfrom the two models described above and the FEA method werecompared with each other to ensure that the prediction from theproposed models are satisfactory. The characteristic data fromthe FEA method and static experiments are typically very close.Fig. 2 shows the λ−i−θ and T−i−θ characteristic plots for afour-phase 8/6 SRM.

HUSAIN AND HOSSAIN: MODELING, SIMULATION, AND CONTROL OF SRM DRIVES 1627

Fig. 2. Comparison of torque and flux characteristics between analytical model, controller model, and FEA.

III. SRM CONTROLLER DESIGN

The SRM drive controller parameters must be selected tooptimize the design objective. The choice of control parametersto maximize the torque per ampere (T/A) is described inthis section. For a high-performance drive, the SRM driveinner loop controller functions to deliver the reference torquecommanded by the outer control loop. At high speeds, theavailable torque of SRM decreases due to back-electromotiveforce (EMF) voltage and input dc voltage saturation. The max-imization of T/A is achieved by a field-weakening technique,which requires the advancement of turn-on and turn-off angles.At low speeds, the current limit restricts the available torqueand a fixed set of turn-on and turn-off angles is sufficient forsuccessful magnetization and demagnetization. Depending onthe operating speed, the optimization problem can be dividedinto two parts under constraints of current or voltage limits. Thetransition from one constraint to the other is based on the motorbase speed.

A. Maximization With Current Constraint

At low speeds, the current constraint is active and the control-output parameters are turn-on angle θon, turn-off angle θoff , andreference current Iref . Therefore, the optimization problem canbe defined as

maxθon,θoff ,iref

Tav

iref= max

θon,θoff ,iref

qphNr

2πiref

∮i(ψ, θ)dψ

where the performance index J(θon, θoff , Iref) is Tav/Iref . Theoptimization problem can be solved by defining the followingnecessary conditions:

dJ(θon, θoff , iref)dθon

= 0

dJ(θon, θoff , iref)dθoff

= 0

dJ(θon, θoff , iref)diref

= 0.

An analytical solution of the necessary conditions is dif-ficult due to the highly nonlinear characteristics of the SRmachine. Numerical or graphical optimization techniques canbe employed to accommodate models containing significantnonlinearities [5]. Therefore, the reference current is generatedfrom the torque requirement using

i = − h

2g+

√h2 − 4gT

f ′(θ)

2g(8)

where g and h are machine-geometry-dependent terms ex-plained in [4], and f ′(θ) is a position-dependent term. Equation(8) has been validated by comparing the model-predicted resultwith the FEA result in Fig. 2. Defining the reference currentin terms of the reference torque, a univariate-search techniquehas been used to determine the turn-on and turn-off angles [1].The guiding logic behind univariate search is to change onevariable at a time so that the function is maximized in each ofthe coordinate directions. The optimal-control parameters foroperating speed below base speed can be represented by thefollowing equations

Optimal turn-on angle = a1

Optimal turn-off angle = a2

where the constant a’s are determined through the optimizationprogram. The optimization results show little or no variationof the turn-on and turn-off angles with motor speed as long asthe speed is below the base speed. The torque is regulated bycontrolling the phase current according to (8).

B. Maximization With Voltage Constraint

The SRM operates in single-pulse mode above the basespeed. Torque-per-ampere maximization under voltage con-straint yields a solution that is referred to as optimal field weak-ening. The control parameters are only the turn-on and turn-off


Fig. 3. Energy versus speed with: (a) turn-off angle and (b) turn-on angle variations.

Fig. 4. Schematic representation of the controller.

angles, with the peak-current limit set to the rated value. Theproblem can now be defined as

maxθon,θoff

Tav = maxθon,θoff

qphNr

2π∗

∮i(ψ, θ)dψ

.

Using the univariate-search technique, the overall solution isa function of speed ω given by

Optimal turn-on angle = a11 + a∗12ω + a∗

13ω2

Optimal turn-off angle = a21 + a∗22ω + a∗

23ω2

where the coefficient a’s are determined through the optimiza-tion program. The influence of the turn-on angle and turn-offangles on energy conversion per stroke in the motoring mode atdifferent speeds is shown in Fig. 3(a) and (b). The turn-on angleis kept constant in Fig. 3(a), while the turn-off angle is kept con-stant in Fig. 3(b). Observing the two figures, it is obvious thatthe energy conversion is increasing by advancing the turn-onand turn-off angles at high speed.

IV. FOUR-QUADRANT CONTROL STRATEGIES

In many applications, the SRM operates in the torque-controlled mode, with the command torque set by an outer loopposition controller. The SR drive controller in the inner loopfunctions to maintain the desired command torque. Fast re-sponse is critical for highly dynamic loads, where the commandtorque and the motor speed may reverse quickly from positive

to negative and vice versa. The motor operates in all fourquadrants of its torque-speed characteristic. The flow diagramof the controller is shown in Fig. 4. The controller switches themotor between the motoring and braking regions according tothe control command. The appropriate and different turn-on andturn-off angles are used depending on the operating quadrant.

The turn-on and turn-off angles determined in Section II areused for first- and fourth-quadrant operation. These angles arescheduled as a smooth function of speed, which maximizesthe average torque at all operating points. Operation in thesecond and third quadrants is the mirror symmetry of that of thefourth and first quadrants, as shown in Fig. 5. The relationshipsbetween the firing angles are

θon,III = − 2π

Nr− θon,I

θoff,III = − 2π

Nr− θoff,I

θon,II = − θon,IV

θoff,II = − θoff,IV.

The four-quadrant drive may be required to operate eitherin the position-controlled loop or in the speed-controlled loop.In the controller, the operating quadrant is determined fromthe sign of reference torque (or reference speed for speed-controlled drive) and motor speed, as shown in Fig. 4.

V. SIMULATION OF SR DRIVE

The objective of the simulation model is to predict resultsthat would match the experimental results such that lengthyexperimental procedures can be eliminated during product de-velopment. The disparity between results from the computer-simulation stage and the hardware implementation can betraced to two aspects, which are: 1) accuracy of the measuredvariables and 2) the delay in signal processing. Some of thisdisparity can be accounted for in the simulation by insertingdelays in the controller execution cycle according to the speedof the processor used and the number of instructions of thecontroller algorithm. The delays in acquiring measured data


Fig. 5. Operating points in different quadrants.

Fig. 6. Simulation block diagram of the SRM drive.

through the analog-to-digital (A/D) channels can also be ac-counted for according to the A/D sampling and conversiontime required.

The SRM analytical model described in Section II, havingthe significant nonlinear saturation characteristics, has beenused to represent the motor in the simulation setup. Thesimulation block diagram of the SRM drive is shown in Fig. 6.The simulation setup incorporated the practical nonidealitiessuch as controller delay time, position-sensor resolution, anderrors in current measurements. These measures providedresults that closely matched the experimental results.

A. Simulating the Execution-Time Delay

The input signals to the controller e(t) are approximatelyconstant within the execution-time interval, at a value equalto those of the signals at the preceding sampling instant. A

zeroth-order hold (ZOH) is introduced to incorporate this effectinto the simulation [5]. The ZOH implements a sample-and-hold function operating at execution-time (Tex) period rate.Therefore, for a ZOH

ek(t) = e(kTex), kTex ≤ t < (k + 1)Tex.

Fig. 7 shows a comparison of measured current and simu-lated current when the motor was operated at 2000 r/min witha load torque of 0.4 N·m. The simulation-current waveformwithout any limitation and using 5 µs of simulation time stepand the same execution time step deviates significantly from themeasured current. However, the simulated current with consid-eration of the practical limitations such as the A/D quantizationerror and the delay due to execution loop frequency gives agood estimation of the actual current.


Fig. 7. Measured and simulated phase current at 2000 rpm and 0.4 N·m.

TABLE IQUANTIZATION INTERVAL

B. Simulating the Quantization Effect

The output of the encoder used for rotor-position sensing isquantized, which may lead to limit cycles in digital control sys-tems. The quantization process involved in A/D conversion alsocause errors in the measurements [6]. The dc-link voltage andphase currents are commonly digitized for the SRM controller.Both the dc-link voltage and the phase current are unipolar.Accordingly, the quantization errors of voltage and currents foran n-bit A/D converter are given by

∆ν =Vmax

2n − 1∆i =

Imax

2n − 1.

The rotor position, dc-link voltage, and phase currents usedin the controller are to be quantized according to Table I in orderto incorporate the quantization effect in the simulation.

VI. REAL-TIME IMPLEMENTATIONS

An experimental setup was established to test the optimal-control algorithms of Section III and also to evaluate thedeveloped simulation tool. The prototype setup of the SR driveis shown in Fig. 8. The test setup was designed for motion-control applications, which can be operated in variable-speed-controlled or position-controlled loop. The parameters of theSRM are given in Appendix II.

A. Processor-Speed Metrics

The choice of the required processor depends on two im-portant factors: the processor speed and the facility to allowfast and efficient programming. The performance of the drive

system is directly related to controller execution time. Theexecution time is given by

Execution time TE = Nins ∗ CPI ∗ Clock period

where Nins is the number of instructions executed in onecontrol cycle, and CPI is the average clock cycles required perinstruction.

The floating-point digital signal processor (DSP), pro-grammed using C compiler, is advantageous in terms of ac-curacy and ease of implementation compared to a fixed-pointDSP. The fixed-point processors require significant time forscaling and shifting operations for complex computations. Theexecution times required for a simple SRM drive controllerwith fixed turn-on and turn-off angles and hysteresis currentcontrol for a four-phase 8/6 SRM developed in TMS320C240and TMS320C30 (clock speed = 40 MHz) were observed tobe about 40 and 35 µs, respectively. A more advanced SRMcontroller implementation in TMS320C30 would typically takebetween 80–100 µs.

B. Position-Sensor Resolution

The resolution of the position is effective only when everyposition update information can be utilized in each controllerexecution period. The time for each updated position informa-tion when the motor is in steady state depends on the operatingspeed of the machine. If the position feedback system sends NA

number of pulses for each mechanical revolution of the rotor,then the time for one pulse is

Tp =60

Np · NAs

where Np is the operating speed of the machine in revolutionsper minute. The condition for the position-sensor feedbackinformation to be utilized effectively is TE > TP. Alternatively,a critical speed Ncr can be defined as the maximum speed atwhich any particular program will be able to capture and utilizeeach and every updated position pulse. The critical speed is

Critical speed, Ncr =60

TE · NArev/m.

C. Filtering Effects

In SRM drives with a discrete position sensor, the encoderoutput is quantized, and the velocity is determined by differ-entiating the quantized signal. The position is also obtained bydifferentiation in some position-sensorless control algorithms.The differentiation amplifies the high-frequency noise. More-over, the A/D converters introduce measurement noise to thesignal. A digital recursive filter can be implemented to removenoise from the speed signal as follows:

yk+1 = auk+1 + (1 − a)yk, 0 < a < 1 (9)

where u and y are the input and output of the filter, respectively.The coefficient “a” determines the cutoff frequency of the


Fig. 8. Hardware setup for the SRM drive system.

Fig. 9. Filtering effect on speed measurement.

filter. The coefficient “a” can be chosen through simulationby analyzing the effect of the inherent delay introduced by thefilter. Fig. 9 shows the motor speed derived from differentiationof the encoder output and then smoothened by a digital filter.The value of the coefficient a has been chosen to be 0.01.

VII. EXPERIMENTAL RESULTS

In this section, experimental results are presented to showthe performance of the SRM drive system. Four A/D channelshaving a sampling time of 4 µs are used to digitize the phase-current information. One A/D channel having a sampling timeof 4 µs is also used to receive the bus-voltage informationfor the controller. The phase voltages are reconstructed fromthe bus voltage and gate signals. A 360-pulses-per-revolutionencoder is used to provide the rotor-position feedback infor-mation. The current control is implemented through softwareto avoid the necessity of any additional hardware. The currenthysteresis control inside the digital controller increases thehysteresis band, which leads to higher torque ripple. It alsobecomes difficult to maintain current within the band dueto processor computation cycle time. However, the inside-hysteresis current control is a good choice for many cost-effective actuator applications where the torque ripple is not animportant issue. A significantly smaller hysteresis band can bedesigned when the hysteresis current regulator is built outsidethe digital controller.

A. Speed-Controlled Loop

The SRM was first connected to an inertia load to verifythe variable-speed operation. The closed-loop response for atoggling speed command from 1000 to −1000 rpm is shownin Fig. 10. The motor was thus required to switch operation

Fig. 10. Measured four-quadrant closed-loop speed response.

Fig. 11. Measured phase voltage, current, and estimated flux at 500 rpm.

from forward motoring (first-quadrant operation) to reversemotoring (third-quadrant operation) through regenerating mode(fourth-quadrant operation), and also from reverse motoring toforward motoring through regenerating mode (second-quadrantoperation). The current is regulated in the active phase by chop-ping at the reference level commanded by the speed regulator.Fig. 11 presents the measured phase voltage, phase current, andestimated phase flux with inside-hysteresis current control.

In the speed-controlled mode, the current is regulated in theactive phase by chopping at the reference level commanded bythe speed regulator. Fig. 12(a) shows the measured phase cur-rents during motor acceleration. Fig. 12(b) shows the measuredphase-A current along with the wrapped rotor position duringthe deceleration mode. In the wrapped rotor position, 0 is thealigned position and ±30 are the unaligned positions. Thefigure also shows the correct positioning of the phase currentwith respect to the rotor position in the regeneration mode. Theoptimized turn-on and turn-off angles produce a small amount


Fig. 12. Measured phase currents during: (a) acceleration and (b) deceleration.

Fig. 13. Hydraulic drive system.

of opposite polarity torque. The opposite polarity torque pro-duced by the rising or decaying phase current may appear to beundesirable, since it will adversely affect the machine efficiencyand torque ripple. However, the small opposite polarity torquehelps to maximize the average torque in each phase cycle ofoperation, which is required for fast actuation.

B. Position-Controlled Loop

In this test, the SRM was used to drive a linear actuatorcoupled through a ballscrew arrangement. Any position changeof the motor is converted into force on the piston that has arestoring spring, as shown in Fig. 13. The experimental resultsof the closed-loop position-controlled system are shown inFig. 14. The rotor-position information is used to measure thetranslational displacement of the piston.

Figs. 14 and 15 show the linear displacement and speedresponses, respectively, under load-torque disturbances. Theperformance of the drive system is also compared with thesimulation results to evaluate the prediction performance ofthe simulation tool. These figures represent four-quadrantresponse of the SRM for the linear displacement control of theactuator system.

The optimized turn-on and turn-off angles obtained inSection III are used in the inner loop of the SRM drive. Table IIshows the effect of the variations of turn-on and turn- off angles

Fig. 14. Measured and simulated closed-loop position-control response.

Fig. 15. Measured and simulated motor speed during closed-loop position-control response.

on response time. The response time (rise time) is consideredas the time required for translational movement of 10%–90%of the position command. The position-controlled drive systemwas operated in a test bench by varying the turn-on and turn-off


TABLE IIRESPONSE-TIME COMPARISON

Fig. 16. Comparison of normal and optimal-control strategies for positioncontrol with sudden command change.

angles one mechanical degree around the optimal angles. Thetest results prove that the optimal turn-on and turn-off anglesgive the fastest response.

C. Response in Highly Dynamic Operation

The linear-actuator load was used to evaluate the systemresponse in a highly dynamic mode. Fig. 16 shows the lin-ear position versus time for a ramp command. The positioncommand is reversed when a linear position of 0.2 mm isreached in the forward direction. The target is to minimize thesubsequent overshoot and the reverse time. The figure showsthe comparison of position overshoot (ξ) and reversal time(T ) for two different control strategies: one for optimal-controlstrategy, as described in Section III-B, and the other is thecontrol strategy suggested by Kjaer et al. [7]. The latter controlstrategy used a turn-off angle at lower speeds, then switched toanother turn-off angle at higher speeds.

The a, b, and c reference points in Fig. 16 are for the optimal-control response plot. In the figure, the position commandchanges to 0 at point a, which changes the motor operation fromforward motoring to the forward braking region. The motoroperates in the forward braking region between points a and b.The forward movement after the command change leads tothe overshoot of the system. From points b to c, the motorfirst operates in the reverse motoring mode and then in thereverse braking mode. Fig. 17 shows the motor-speed dynamicsfor optimal-control position response in Fig. 16. The optimallycontrolled four-quadrant operation of the SRM helps minimizethe overshoot and reversal time of the mechanical drive system.

Fig. 17. Motor speed versus time with sudden command change.

VIII. CONCLUSION

The importance of a good modeling and simulation toolfor digital implementation of an SRM motor drive system hasbeen emphasized in this paper. Modeling and simulation, incor-porating the practical nonidealities as accurately as possible,drastically reduces the time and cost associated with exten-sive experimentation. Practical problems, such as measurementerror, processor delay time, and quantization factors can beeasily incorporated in the simulation model. Once satisfiedwith the performance obtained from simulation, one can starta prototype system development on a test bench. The practicalproblems experienced on the test bench can be used to improvethe simulation model. The iterative process in developing a veryuseful simulation tool has been shown to be very effective in thedevelopment of a servo-type four-quadrant switched reluctancemotor (SRM) drive system presented in this paper. The resultsobtained from the final simulation model and the experimentsare extremely close. Such a model could be reliably used forperformance evaluation and future development.

APPENDIX I

The coefficients used in (7) and (8) are dependent on machinegeometry as follows:

a = λmam − Lu b = λmbm c = λ2mcm d = λ2

m

and

g =

(a

2−

√d

2

)

h =(

b

2− c

4√

d

)

f(θ) =(

12

)∗ (1 − cos θ)

f ′(θ) = 0.5 ∗ Nr ∗ (sin θe), θe < Nr(π − βr)

= 0.5 ∗ Nr ∗ tanh(π − θ), θe ≥ Nr(π − βr)


where

λm =nser

npar· µ0 ·

Np

2· lstk · stf .

Rg

g· βr

am = 1 +2g

lp

bm =npar · Bsat

µNp· [lp + (µr + 1)g]

cm =2npar · Bsat

µNp· [lp − (µr − 1)g].

Here, Np is the number of turns per pole, nser is the numberof series paths, npar is the number of parallel paths, lstk isthe stack length, stf is the stacking factor, Rg is the radius torotor pole tips, g is the air-gap length, lp is the total lengthof rotor and stator poles, βr is the rotor-pole width, µ is theiron permeability, µr is the relative permeability, and Bsat isthe saturation flux density.

APPENDIX II

SRM Ratings and ParametersInverter dc bus voltage 30 VPower 1000 WPeak current 40 ANumber of stator poles 8; 22 pole arcNumber of rotor poles 6; 22 pole arcStator winding resistance 0.179 Ω

ACKNOWLEDGMENT

The authors are grateful to Delphi for providing an experi-mental hardware for this research.

REFERENCES

[1] S. Hossain, I. Husain, H. Klode, B. Lequesne, and A. Omekanda, “Fourquadrant control of a switched reluctance motor for a highly dynamicactuator load,” in Applied Power Electronics Conf. and Expo. (APEC),Dallas, TX, Mar. 2002, pp. 41–47.

[2] A. Radun, “Analytically computing the flux linked by a switched reluctancemotor phase when the stator and rotor poles overlap,” IEEE Trans. Magn.,vol. 36, no. 4, pp. 1996–2003, Jul. 2000.

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[4] I. Husain, A. Radun, and J. Nairus, “Unbalanced force calculation inswitched reluctance machines,” IEEE Trans. Magn., vol. 36, no. 1, pp. 330–338, Jan. 2000.

[5] S. Hossain and I. Husain, “A geometry based simplified analytical model ofswitched reluctance machines for real-time controller implementation,” inProc. IEEE Power Electronics Specialists Conf. (PESC), Cairns, Australia,Jun. 2002, pp. 839–844.

[6] T. Hartley, G. Beale, and S. Chicatelli, Digital Simulation of DynamicSystems: A Control Theory Approach. Englewood Cliffs, NJ: Prentice-Hall, 1994.

[7] P. C. Kjaer, J. J. Gribble, and T. J. E. Miller, “High-grade control ofswitched reluctance machines,” in Proc. IEEE Conf. Industry Applications,San Diego, CA, Oct. 1996, pp. 92–100.

Iqbal Husain (S’89–M’89–SM’99) received theB.Sc. degree from the Bangladesh University ofEngineering and Technology, Dhaka, Bangladesh, in1987, and the M.S. and Ph.D. degrees from TexasA&M University, College Station, in 1989 and 1993,respectively, all in electrical engineering.

Previously, he was a Lecturer at Texas A&M Uni-versity and a Consulting Engineer at Delco Chassis,Dayton, OH. In 1996 and 1997, he was a SummerResearcher at Wright Patterson AFB Laboratories.He is currently a Professor at the Department of Elec-

trical and Computer Engineering, University of Akron, Akron, OH, engaged inteaching and research. His research interests are in the areas of control andmodeling of electrical drives, design of electric machines, and development ofpower conditioning circuits. He has worked extensively in the development ofswitched reluctance motor drives including sensorless controllers.

Dr. Husain received the 1998 IEEE Industry Applications Society (IAS)Outstanding Young Member Award, the 2000 IEEE Third Millenium Medal,and the 2004 College of Engineering Outstanding Researcher Award. He wasalso the recipient of three IEEE IAS Committee Prize Paper Awards.

Syed A. Hossain (S’01–M’02) received the B.Sc.and M.Sc. degrees in electrical and electronic engi-neering from Bangladesh University of Engineeringand Technology, Dhaka, Bangladesh, in 1994 and1997, and the Ph.D. degree in electrical engineeringfrom the University of Akron, Akron, OH, in 2002.

From 1994 to 1998, he was a Lecturer and thenan Assistant Professor at Bangladesh Universityof Engineering and Technology. In Summer 2000and 2001, he was at Delphi Research Laborato-ries, Shelby Township, MI. He is currently a Senior

Project Engineer at Globe Motors, Dayton, OH, where he is engaged in thedesign and development of controls for brushless motors. His technical interestsinclude the development of high-performance brushless motor servo drives forautomotive applications.

Documents

Modeling, Simulation, And Control of Switched Reluctance Motor Drives