Direct Torque Control for the 4-phase Switched Reluctance Motor Drives

B. H. Jeong', K. Y. Lee, J. D. Na, G. B. Cho, H. L. Baek'Department of Electrical Engineering, Chosun University, Gwang-Ju, South Korea

Abstract This paper presents a novel control methodfor the sensor-less four phase Switched Reluctance Motordrives, i.e 8 stator and 6 rotor. The sensor-less control isbased on Direct Torque Control with direct flux compensa-tion (DFC) for switched reluctance motor drives. The use ofdirect torque control, implemented in AC drives with a var-ies degree of success, has yet been completely applied forSRM especially 8/6, 4-phase SRM. Direct torque controlstrategy implemented to control unit, well known advan-tages such as simple and robust structure, wide torque speedrange and no maintenance. In this paper, We propose anovel way to utilize the 8/6 4 phase switched reluctance mo-tor and the paper then explains the algorithm to be em-ployed in new DTC scheme in SRM drives with simulationresults are presented.

I. INTRODUCTION

Switched reluctance motors are rugged and inexpen-sive motors. They are known to have high peak torque toinertia rations and the rotor mechanical structure is wellsuited for high speed application. However, Switchedreluctance motor application filed have been strongly lim-ited in their use due to the high ripple content of torqueinherent in their doubly salient design.[1]-[4] This is par-ticularly due to the advantages such as their simple androbust structure, low manufacturing cost, excellent overallperformance and uni-polar operation which avoided cur-rent shoot-though faults in the drivers. More recently, theadvent of digital signal processors and power semi-conductors, in conjunction with some emerging controlparadigms, such as neural networks, fuzzy logic, Al, andobservers, provides a aspect of opportunity to revisit andexploit the many advantages the switched reluctance mo-tor have to offer.[3]-[10] But inherent torque ripple,acoustic noise and nonlinearity characterizes switchedreluctance motor technologies yet. The doubly salientgeometry of the machine in addition to the nonlinearitiesof the magnetic characteristics are main reasons for thisattribution. In particular, at low speeds torque ripple cangenerate speed oscillations and may stimulate resonantfrequencies in the mechanical parts of a drive train.Therefore some of techniques have been proposed so farfor torque ripple minimization in switched reluctance mo-tor drives.[4] Some of method for Torque ripple minimi-zation provided pervious studies for example, mechanicalmethod which is rotor skewing, pole shaping, and bifur-cated teeth with asymmetrical air gap and Control tech-nologies which is current or flux linkage control, on-linecalculation of current profiles, flux linkage profiling withoff-line calculation of profiles, harmonic current injectionand Instantaneous torque control. [3]

In practically, applied SRM drives provide frommany problems. For example, the firing and extinguishing

angles of phase current have been found to be very criticalfor good efficiency and torque performance. The determi-nation of optimum values for these angles depends onmany factors such as load level, rotor speed and rotorposition and demands an accurate model of the motoritself.

The main problem of 8/6 4-phase SRM can be sum-marized in four main points, the first is an unconventionalnon-sinusoidal excitation to which the popular rotatingfield theory is no longer applicable, the second is highlynonlinear characteristics of the motor; third is the interac-tion between different phases at current commutation andthe forth is 4 phase vector transformation problem. It hasbeen realized only recently that due to parameter variationand drift, the phase inductance profile can significantlydiffer from the design data. [2]

This paper proposes a novel DTC scheme for 8/6, 4-phase switched reluctance motor in an attempt to resolvethe above problems by introducing a new control strategyconfiguration in the motor and new driving techniqueswith simulation.

II. DIRECT TORQUE CONTROL

A. Conventional DTC Methodfor AC machine

Direct torque control based on the theories of fieldoriented control. Field oriented control(Vector Control)uses space vector theory to optimally control magneticfield orientation and direct self control establishes aunique frequency of inverter operating given a specific dclink voltage and a specific stator flux level. The operatingprinciple of DTC is to select stator voltage vectors ac-cording to the differences between the reference torqueand stator flux linkage and the actual values. The princi-ples ofDTC in the ac machine can be derived by examin-ing the motor equations. The stator flux linkage vectorcan expressed as below equation.[8]

IVs= (v- i R)dt (1)While the electromagnetic torque T can be expressed asequation [2]

3 L'l -XT= p fs fr2 oTLSLr

(2)

B. New Control Schemefor SRM

In the switched reluctance motor, the motor phasesare driven by switched currents which are non-sinusoidaland expected normally highly nonlinear. Furthermore, thephase of the motor are excited completely independently

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of each other. Thus, conventional ac machine rotatingfield theory cannot be directly applied to the switchedreluctance motor. This combined with the motor's highlynonlinear magnetic and torque characteristics has beenone of the major problems in the widespread adoption ofswitched reluctance motor drives in industry. However,by re-examining the torque equation of the switched re-luctance motor, a new control technique can be foundwhich uses a similar philosophy as the conventional DTCof ac machines. As in conventional DTC, the controlscheme directly controls the amplitude of the flux andtorque within hysterisis bands. However, the motor phaseswitching strategy is based instead on the non-uniformtorque characteristics of the SR motor. To drive the newcontrol scheme for the SR motor, the non-uniform torquecharacteristics will firstly be examined. The motor torqueoutput can be found using the motors electromagneticequation.

v = Ri+ dqi(0,i) (3)

Where, Lff(O, i) =the nonlinear function of phase flux

linkage as a function of rotor position 0 and current i.Fig. 3 shows stator current versus flux linkages character-istics ofnormal switched reluctance motor.

x

(D

*Unaligned Position

0 Stator current

Fig. 1 Stator current vs. flux linkages characteristicslinearization

The nonlinear flux linkage term can be expanded intopartial fractions, thus the equation for power flow can bewritten as

vi= Ri2 +.i80 (O,i) di +8i(O,i) dOi= +1 ~ +1&(4

8i dt ao dtThus in a differential time dt, the differential electrical energydWe transferred from the source to the magnetic field and me-chanical power output can found. To find an expression forthe motor torque production the energy equation is firstwritten as

dWe = dWm + dWf (5)where dWm and dWf are the differential mechanical and

field energy respectively. The field energy can be separated intoits constituent components and from consideration of the storedfield energy it can be shown.

dWm = i Y -(OJ)dO _ W dO (6)

The instantaneous torque is defined by bellows.

T dWm (7)dO I

Thus by substituting equation (6) into equation (7) theexpression for instantaneous torque production of an SRmotor phase can be written as

T ai (O(,i) dWf (o dO

C. Classic Converter for Control SRM

Classic Converter have main distinctive featureswhich is various control strategy implemented, can con-trol with superposition current to adjacent phase, lowerrated voltage, higher capacity and have two switches perphase.

And so classic converter most wide spread to controlswitched reluctance motor. Fig.2 shows the classic con-verter.

+Vdc +Vdc +Vdc

(a)Positive Volts (b)Zero Volts (c)Negative Volts

Fig. 3 Switched reluctance motor Phase Voltage States

It is can be seen in Fig 3, each motor phase can have threepossible voltage states for a unidirectional current. Thevoltage state Sq for a given phase is defined as 1 whenboth switches in a motor phase are turned on. In this casepositive voltage is applied to the motor phase. When cur-rent is flowing and one device is turned off, a zero voltageloop occurs and the state sequence is defined as 0. Finally,when both device are turned off, there is no current or afreewheeling current flows through the upper diodes. Inthis case negative voltage is experienced by the motorphase and the state sequence is defined as negative volt-age.

One of the eight possible states in chosen at any onetime in order to keep the stator flux linkage and the motortorque within hysterisis bands. As in the conventionalDTC scheme, if the stator flux linkage lies in the k-th

525

"I

8)

zone, the magnitude of the flux can be increased by usingthe switching vectors v(k+1) and v(k-1) and can be de-creased by using the vectors v(k+2) and v(k+2). Hencewhenever the stator flux linkage reaches its upper limit inthe hysterisis band, it is reduced by applying voltage vec-tors which are directed toward the center of the flux vec-tor space and vice-versa.

The motoring torque is controlled by an accelerationor deceleration of the stator flux relative to the rotormovement. Hence, if an increase in torque is required,voltage vectors that advance the stator flux linkage in thedirection of rotation are selected. This corresponds to se-lection of vector v(k+1) and v(k+2) for a stator flux link-age in the k-th zone. If a decrease in torque is required,voltage vectors are applied which decelerate the statorflux linkage vector. This corresponds to the vectors v(k- 1)and v(k-2) in the zone k.Switching table for controlling the stator flux linkage andmotor torque can be defined as shown in Tablet .

Table 1 Switching Table for DTCTorque Increase Increase Decrease DecreaseFlux Inrease Decrease Increase Decrease

V(k+ 1) V(k- 1) V(k+2) V(k-2)

In order to control the flux and torque within the hystere-sis bands, the instantaneous torque and stator flux vectormagnitude must be known. In the SR motor voltages inthe motor are highly non-sinusoidal and thus more effec-tive insight may be gained by firstly finding the individualflux linkages of each phase using the voltage. In this casethe magnitude of the individual phase flux linkages varieswith time, but the direction is always along the stator poleaxis. Torque look up table estimated previous and storedprocessor for adjustable Dwell angle.

III. IMPLEMENTAION OF SRM DTC CONTROLLER

In this system the phase currents and voltages for eachphase are measured using voltage and current sensors andthe phase flux linkages are then calculated with below.

-* t < o o

Vs= f(Vs-Rs is)+ S0

Control switching table is used to select the voltagecommand based on the present zone of the flux linkagethat can be determined by the angle. It can be defined n-dimensional vector for 8/6, 4-phase switched reluctancemotor structure. For the first time, Considering 4phasemotor, vector number is four and so combination of vec-tor is zero with appear on rectangular plane. In real sys-tem arbitrary phase will be excited first to detect the ini-tial rotor position . Rotor position move to arbitraryaligned position. Therefore we solve this problem with letto initial value 45 degree on 4 phase. Fig. 5 shows thevector diagram with 4phase to 2 phase solution.

k yKx

- -k

K

Fig. 5 Definition of two frame reference axis

Then torque can be calculated using the componentsof the estimated flux and measured currents. In order tocontrol the torque using hysterisis bands DTC requires thefeedback and to calculate the instantaneous for feedbackwe can use bellows.

(9)

A. 4-phase to a -/ vector transform

Based on the principles, which is explained above, acontroller for the SR motor was developed in Fig. 5shows the overall block diagram of the developed DTCbased SR motor drive.

HyteresisComiara-

Torque .ref.

Fig. 4 Block diagram of proposed direct torque

control scheme

T = p(Aa I,8 - Ax3I a ) (I10)Where p is the number of pole pairs and the o-P sub-

script refer to transformation components in the stationaryframe of reference and the i is the stator current compo-nent. Fig. 6 shows the voltage vector relationship refer tothe flux and current reference frame.

Flux rotation direction

iss

ia k

Fig. 6 Voltage vector relationship

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0

c

=YA f(V-iARA)dt= [VDCAt - RAiAcdt + AO ]SA

The flux-linkage for phases B , C and D can be found byinspection.

Table 2 Important simulation parameter for DTC(1 1)Air-gap

Radius to the air-gap at the rotor

Radius to the outside rotor yoke

0.00025 [m]

0.041805 [m]

0.0311 [m]

B. Proposed Control Strategy for 4-phase SRM

-J

Radius to the outside rotor yoke

Shaft radius

Shaft radius

Number of phases

Hysterisis width

Maximum switching frequency

Fig. 7 Block diagram of direct torque control strategy

Fig. 7 shows the control proposed strategy block dia-gram of direct torque control. The adaptive motor modelis assuming that the mutual coupling between any phasesdue to individual short flux loops used is small and ne-

glecting iron losses, the voltage vector and torque equa-

tion can be rewritten equation (1)3@1 '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. .............................Fig. 8 Torque vs. rotor position characteristics wave-

forms

Fig.8 shows the applied torque versus rotor position

characteristics. This is original data for the torque lookup

table for control.

IV. SIMULATION RESULT

Proposed control algorithm Simulation executed with

Matlab Simulink produced by Mathwork co. Ltd. Motor

model coded by Matlab in-file function. Input voltage DC

link is the 150 [V] number of stator poles is 8 number

of rotor poles is 6 and torque producing angle is the 16

[degree]. Table 2 shows the other main parameter for di-

rect torque control simulation.

Fig. 9 shows output waveform for the A-phase currentwhich is controlled with top flat shape for optimal currentcharacteristics. Fig.10 shows output waveform of the 4phase voltage combination which is synchronous withcurrent waveform. Fig. 11 shows output waveform of thesensor-less position detection for rotor position control.Fig. 12 shows output waveform of the Torque generationwhich is depend on Dwell angle. Fig. 13 shows outputwaveform of the Speed characteristics

Fig.Savefo

X~ 1

XSU~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.

Fi.9Otu aeoso h -hs ufn

Fig. 10 Output waveform of the 4 phase Voltage

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0.0311 [m]

0.016565 [m]

0.016565

4

3 [A]

10 [kHz]

Fig. 11I Output waveform of the sensor-less positiondetection

-w

Fig. 12 Output waveform of the Torque generation

Fig. 12 Output waveform of the Speed characteristics

V. CONCLUSION

In this paper, a novel control strategy for the 8/6 SRmotor was derived form analysis of the torque characteris-tics of the motor. In this method, Torque is directly con-trolled through the control of the magnitude of the fluxlinkage and the change in speed of the stator flux vector.Although the strategy is based on the nonlinear character-istics of the motor torque output during operation, thestrategy does not require the nonlinear magnetizationcharacteristics to be used in the real time torque control.Furthermore, the scheme is not dependent on the accuracyof the estimated model parameters as no model calcula-

tion is required during operation. Hence this overcomesthe disadvantages and difficulties faced by conventionallinear or nonlinear controllers of the SR motor.

In the future we will implement this theory and resultto experiment and practice motor drive for switched reluc-tance motor torque control and other applications.

REFERENCES

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[2] Adrian David Cheok and Yusuke Fukuda " A NewTorque and Flux Control Method for Switched Re-luctance Motor Drives" IEEE Transaction on PowerElectronics. Vol. 17, No. 4 , July 2002, pp.543-557

[3] Tian-Hua Liu and Ching-Guo Chen " Implementa-tion of a Sensorless Switched Reluctance Drivewith Self-inductance Estimating Technique" IEEEtrans. Ind. Appl., pp. 508-512.

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[5] M. Ehsani, I, Husain, and A. B. Kulkami " Elimina-tion of discrete position sensor and current sensor inswitched reluctance motor drives" IEEE Trans. Ind.Appl., vol. 28, no. Jan/Feb. 1992, pp. 128-135

[6] Iqbal Husain, Mohanmmad S. Islam, "Observers forPosition and SpeedEstimations in Switched Reluc-tance Motors", Proceedings of the 40th IEEE con-ference on Decision and contorl, pp. 2217-2222,2001

[7] B.Fahimi,M., A. Emadi,M., "Robust Position Sensor-less Control of Switched Reluctance Motor Drivesover the Entire Speed Range", IEEE, pp. 282-288,2002

[8] Codrut,VISA, Gabriel ABBA, Francois LEONARD,"Speed Control of a Switched Reluctance Motor Us-ing Non-Linear Methods", 2002 IEEE SMC., 2002

[9] M.S. Islam, M.N.Anwar and I. Husain, " Design andControl of Switched Reluctance Motors for Wide-Speed-Range Operation", IEE Proc-Electr. PowerAppl., Vol.150, No.4, July 2003

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[12] Robert B. Inderka, Rik W. A. A.De Doncker"DITC-Direct Instantaneous Torque Control ofSwitched Reluctance Drives" IEEE Transactions onindustry applications, Vol. 39, No. 4 July/August2003, pp. 1046-1051

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