Optimal turn-off angle control in the face ofautomatic turn-on angle control forswitched-reluctance motors

Y. Sozer and D.A. Torrey

Abstract: A new approach to the automatic control of excitation parameters for theswitched-reluctance motor (SRM) is presented. The excitation parameters include the turn-onangle, the turn-off angle and the magnitude of the phase current. The objective is to develop aneasily implementable control algorithm that automatically maintains the most efficient excitationangles in producing the required current to produce the electromagnetic torque. The control algor-ithm determining the turn-on and turn-off angles supports the most efficient operation of the motordrive system. The turn-on angle and turn-off angle controllers work independently and harmo-niously with the speed controller. The turn-on angle controller consists of two pieces: the firstpiece of the control technique monitors the position of the first peak of the phase current (up)and seeks to align this position with the angle where the inductance begins to increase (um). Thesecond piece of the controller monitors the peak phase current and advances the turn-on angle ifthe commanded reference current cannot be produced by the controller. The first piece of the con-troller tends to be active below base speed of the SRM, where phase currents can be built easily bythe inverter and up is relatively independent of um. The second piece of the controller is activeabove base speed, where the peak of the phase currents tends to naturally occur at um regardlessof the current amplitude. The two pieces of the controller naturally exchange responsibility as aresult of a change in command or operating point. The turn-off angle controller works independentof the turn-on angle controller. Through modelling of an experimental SRM and extensive simu-lation, it is seen that the optimal-efficiency turn-off angles can be characterised as a function ofpeak phase current and motor speed. Accordingly, the optimal-efficiency turn-off angle is deter-mined from an analytic curve fit. It has been shown that a curve fit using only four optimisedpoints gives very close estimation to the most efficient turn-off angle at any given operatingpoint. The SRM, inverter and control system are modelled in Simulink to demonstrate the operationof the system. The modelling is based on the finite element data that include spatial nonlinearitiesand magnetic saturation. The control technique is then applied to an experimental SRM system.Experimental operation documents that the technique provides for efficient operation of theSRM system through tuning the controller at only four operating points.

1 Introduction

The switched-reluctance motor (SRM) is under develop-ment for variable-speed applications where the inherentcharacteristics of the SRM make commercial sense. Todate, these applications include sourcing aerospace powersystems [1], starter/alternators for hybrid vehicles [2–4]and wind turbine applications [5]. The aerospace andautomotive applications are generally characterised byhigh-speed operations. The wind energy application ischaracterised by low-speed, high-torque operations.Standard references on the SRM are [6, 7], and controlof the SRM is discussed in [8]. This work builds on thediscussion presented in [8].The SRM produces torque through excitation that is

synchronised to rotor position. The excitation is generally

# The Institution of Engineering and Technology 2007

doi:10.1049/iet-epa:20060412

Paper first received 19th October 2006 and in revised form 5th January 2007

The authors are with the Advanced Energy Conversion, LLC, Suite 500, 10Hermes Road, Malta, NY 12020, USA

E-mail: yilmaz@advancedenergyconversion.com

IET Electr. Power Appl., 2007, 1, (3), pp. 395–401

described by three excitation parameters: the turn-onangle uon, the turn-off angle uoff and the reference currentIref. A control algorithm would typically use the sameexcitation parameters for each phase, implemented withthe spatial shift consistent with the symmetrically displacedphase structure. Control of the excitation angles results ineither positive net torque for motoring or negative nettorque for generating. Although there are similaritiesbetween motor control and generator control, there arealso substantial differences. This work focuses on motorcontrol.

Efficient operation of the SRM, or any motor drive, isalways of importance. Inefficiency leads to larger size,increased weight and increased energy consumption. Inorder to maximise SRM efficiency, the average torque toRMS phase current, Tavg/Iphrms, is maximised. Mechanicaloutput is proportional to the average output torque Tavg andelectrical input is proportional to the RMS phase currentIphrms. The optimisation is intended to increase the efficiencyof the motor, which is the ratio of the output power to theinput power. The ratio of Tavg/Iphrms captures our intendedgoal of providing the required electromechanical outputwith the minimum electrical input.

395

A closed loop control for excitation angles for the SRMhas been proposed to get the most efficient operation overthe entire operating region. This approach is an alternativeto the self-tuning approach to optimisation of excitation par-ameters [9, 10]. The automatic turn-on angle control algor-ithm in the face constant conduction angle is presented bySozer et al. [8]; this work builds on our previous work byadding automatic control of the turn-off angle to maximisedrive efficiency. The turn-on angle is driven by closed loopcontrol. It automatically adjusts the turn-on angle using theplace of first peak of the phase current and its magnitude.Optimal turn-off angle control in the face of automaticallyadjusted turn-on angles is the focus of the paper. The algor-ithm produces the turn-off angle based on experimentalcharacterisation at only four operating points, representingall combinations of low-speed, high speed, low-phasecurrent and high-phase current. The method does not needmachine modelling or extensive simulations during real-time implementation. Because these operating points canbe characterised experimentally, it is not necessary tocharacterise them analytically. The algorithm is easy toimplement and does not need look-up tables for excitationparameters. Implementation of the algorithm is demon-strated in simulation and experiment for a four-phase SRM.

2 Control algorithm

The objectives of the algorithm are best explained throughconsideration of the linear inductance profile for the SRMshown in Fig. 1. The minimum inductance region isdefined by the angular interval over which the rotor polesdo not overlap the stator poles. The maximum inductanceregion is defined by the angular interval over which thereis complete overlap between the stator and rotor poles.The regions of increasing and decreasing inductance corre-spond to varying overlap between the stator and rotor poles.

For operation of the SRM as a motor, phase current mustbe present in the phase winding as the inductance is increas-ing in the direction of rotation. For operation of the SRM asa generator, phase current must be present in the phasewinding as the inductance is decreasing in the directionof rotation. The polarity of current is immaterial, so it isassumed that the phase current is always positive. Theturn-on angle is the electrical position where the motorphase is excited, on the other hand the turn-off angle isthe electrical angle where the phase for that cycle isturned off. The placement of the excitation angles isextremely important in producing the amount of torqueefficiently at any operating point. As long as continuousconduction of the phases is prevented during each electricalcycle, the turn-on and turn-off angles can be controlledseparately.

2.1 Turn-on angle control

If one were to examine the static torque curve for a typicalSRM, it would be observed that the maximum torque for a

Fig. 1 Linear inductance profile of the SRM showing ug and um

396

given amount of current occurs as the rotor begins to moveout of the minimum inductance position. This observationsuggests that maximum torque per ampere is producedupon leaving the minimum inductance position. Iron per-meance causes torque production to fall off as overlapbetween the stator and rotor poles increases. In applicationswhere average torque is of primary importance, it is import-ant to make the most of the region near the unaligned pos-ition. Because it takes time to build the phase currents, wemust anticipate the arrival of the torque productionregion. We must therefore turn on the phase windingsbefore the angle marked um in Fig. 1 so that the current isat Iref when the rotor reaches um.The conventional approach to determining uon is to work

backward from um

uon ¼ um �LminIrefv

Vdc

(1)

where Lmin is the minimum inductance, Vdc the dc busvoltage, v the rotor speed and Iref the chopping level.Equation (1) assumes that the inductance is constantduring the region [ug, um]. The inductance can be a functionof the phase current, rotor position and temperature. At lowspeed, this method can give reasonable performance unlessuon becomes less than ug. For operation over a wide speedrange, (1) starts to break down as back emf voltagebecomes more prominent. It is desired to have closed loopcontrol that provides the turn-on angle making first peakof the phase current at um without the need of accuratemotor parameters and measurement of the dc bus voltage.The proposed closed loop control algorithm continuously

monitors the position of the first peak of the phase current(up). The turn-on is advanced or retarded automaticallyaccording to the error between up and um. This piece ofthe controller successfully places up at um. Above basespeed, the peak current naturally tends to occur near um.At these speeds, uon has little impact on up but significantimpact on the magnitude of the current at up.In order to show the behaviour of the phase current at

different operating points, the 16/12 four-phase SRMdesigned for a 1-kW, 12-V automotive application is mod-elled using finite element data which include spatial andmagnetic nonlinear effects. The model is based on a pre-viously developed analytical model of the SRM which sum-marises the terminal magnetisation characteristics of theSRM [11].The SRM is simulated at 2500 rpm with two different

turn-on angles. For each of the turn-on angles, up occursapproximately at the same place with different current mag-nitudes. This phenomenon can be observed in Fig. 2. Toreflect this effect, the algorithm forces the peak phasecurrent to match the commanded phase current.Feed-forward control of uon using (1) is used to speed con-vergence to the correct value of uon.If the controller is in current regulation mode, Ip occurs

close to Iref and so the error between Ip and Iref does nothave any effect on the command for uon. Below basespeed, the piece of the controller responsible for keepingup at um effectively works to achieve the control objective.At high speed, if the controller is in voltage control modeup naturally occurs at um. The piece of the controller respon-sible for forcing Ip to track Iref effectively works to advancethe turn-on angle to keep Ip close to Iref. If the referencecurrent or the motor speed is reduced, the drive enters intocurrent regulation mode and up occurs before um. Thepiece of the controller responsible for forcing up ¼ umbecomes active and brings up to um by retarding uon.

IET Electr. Power Appl., Vol. 1, No. 3, May 2007

2.2 Turn-off angle control

Once the phase current has been established after turning onthe excitation, the excitation needs to be turned off at theoptimum place to produce the maximum amount of torquewith a minimum electrical input for a given peak phasecurrent. From the turn-on control, the optimum turn-onangle is obtained at each operating point. For a givenspeed, the peak phase current and the turn-on angle fromthe turn-on angle controller have been simulated for everypossible turn-off angle. The simulations are based on theSRM model described in the turn-on angle controlsection. The simulations are performed at 500 rpmincrements between 500 and 3000 rpm and every 25 Abetween 25 and 150 A of peak phase current.Fig. 3 shows the motor torque, RMS phase current and

torque per RMS phase current against turn-off angles for1000 rpm motor speed, 75 A peak motor phase currentand a fixed turn-on angle found from turn-on anglecontrol. The torque per RMS phase current is peaking at333.6 electrical degrees. Extending the turn-off anglefurther enables us to produce more torque at the expenseof increased RMS current. At this operating point using333.6 electrical degrees, 3.67 N m can be produced whichrequires 44.97 A of RMS phase current. Extending theturn-off angle to 342 electric degree enables us to produce3.76 N m which requires 47.3 A of RMS phase current.By keeping the turn-off angle at 333.6 electrical degrees,

Fig. 3 Motor torque, RMS phase current and torque per RMSphase current versus turn-off angle at 1000 rpm, 75 A

Fig. 2 Phase currents at 2500 rpm with different turn-on angles

IET Electr. Power Appl., Vol. 1, No. 3, May 2007

the reference current level needs to be increased to 76.1 Ato obtain 3.76 N m which requires 45.7 A of RMS phasecurrent. It can be concluded from this test that it is moreefficient to increase reference current rather than extendthe turn-off angle beyond most efficient turn-off angle.

Simulations are extended and performed at every500 rpm between 500 and 3000 rpm and every 25 A ofpeak phase current between 25 and 150 A. For a givenspeed and peak phase current, turn-on angles from theturn-on angle controller with all possible turn-off anglesare tested. Among all the simulated data, the optimumturn-off angles are selected for a given speed and peakphase current. The criterion is to find the turn-off anglehaving the maximum torque per RMS phase current ratiofor a given speed and peak phase current. Fig. 4 showsthe optimal turn-off angles as a function of speed andpeak phase current.

As indicated in Fig. 4, the optimum turn-off angles are afunction of operating speed and peak phase current level.The optimum turn-off angles can be represented analy-tically as

uoff ¼ k1vIref þ k2vþ k3ffiffiffiffiffiffiIref

pþ k4 ð2Þ

where v is the rotor speed, Iref the reference peak phasecurrent and k1, k2, k3 and k4 are curve-fit parameters. Forour simulation work, the curve-fit parameters are based ona least-squares fit to the collection of optimal turn-offangles over all operating points found based on thesimulation.

For our experimental work, the curve-fit parameters arebased on the optimised data for four operating points repre-senting all combinations of low speed, high speed, lowcurrent and high current. The curve fitting for the exper-imental turn-off angles is based on the experimentallyoptimised turn-off angles. The optimisation procedure isdescribed in Section 4.

Fig. 5 shows the optimised turn-off angles versus simu-lation number. A total of 36 simulations were performedwith six points at every speed. The points at each speedare for peak phase current increments of 25 A from 25 to150 A. The curve fit of the turn-off angles using all dataand data from only four operating points are presented inFig. 5. It is apparent that the curve fit using only four datapoints gives results that are close to the actual optimisedturn-off angles using all data points.

Fig. 4 Optimal-efficiency turn-off angles as a function of speedand peak phase current

397

For our simulation work, the curve-fit parameters arebased on a least-squares fit to the collection of optimalturn-off angles over all operating points found based onthe simulation. The curve fitting for the experimentalturn-off angles is based on the experimentally optimisedturn-off angles. The optimisation procedure is described inSection 4.

On the basis of the curve fitting of the optimised turn-offangles, an equation for the specific motor to obtain theturn-off angle based on the motor speed and peak phasecurrent has been used. The combination of the turn-onangle control and turn-off angle control is coupled torealise an efficient closed-loop excitation angle controllerfor the SRM. The outer speed controller commands thepeak reference current. On the basis of the speed andthe peak reference current, the curve-fit portion producesthe turn-off angle. The maximum turn-on angle is calculatedbased on the turn-off angle and the maximum available con-duction angle. The turn-on angle controller tries to producethe commanded phase current when forcing the first peak ofthe phase current up to occur at um. The control of uon anduoff is summarised in Fig. 6.

3 Verification through simulation

The algorithms motivated in Section 2 were implemented insimulation to confirm proper operation before being exper-imentally implemented on the physical system. The SRM towhich the simulation is applied is a 16/12 four-phase SRMdesigned for a 1-kW, 12-V automotive application. Table 1

Fig. 5 Optimal efficiency turn-off angles versus simulationnumber for different speed and phase current levels along withthe comparison of the curve fits using all of the optimizedturn-off angles and using only four points from the optimised data

Fig. 6 Algorithm used to automatically adjust the excitationangles

398

gives the parameters of the SRM used in this work. TheSRM magnetics are modelled analytically based on datacollected through finite element analysis. The overallcontrol algorithm is shown in Fig. 7.Fig. 8 shows the result of the angle control technique for

125 A reference current and varying speed profile. Fig. 9shows the simulation results of the implemented controltechnique at 2500 rpm where the reference current ischanged from 25 to 140 A at 0.3 s. These figures show theturn-on controller properly placing the peak current at um

Fig. 7 The overall control algorithm of the SRM including anglecontroller

Fig. 8 Simulation results of the implemented control techniquewith 125 A reference current with a varying speed profile

Table 1: Specifications for the experimental SRM

Quantity Value Units

rated power 1000 W

base speed 1500 rpm

maximum speed 3000 rpm

dc voltage 12 V

number of rotor poles 12

number of stator poles 16

number of phases 4

aligned phase inductance 0.228 mH

unaligned phase inductance 0.0226 mH

ug 142 8 (electrical)

um 218 8 (electrical)

IET Electr. Power Appl., Vol. 1, No. 3, May 2007

and producing the required peak current. The turn-offcontroller also properly adjusts the turn-off angle for theoperating speed and peak phase current level. To theextent that uon and uoff correspond to the control parametersthat are required for peak efficiency, the required torque isproduced with the highest efficiency possible.In order to show the sensitivity of the optimal-efficiency

control, motor operation is tested outside the estimatedranges. Optimisations are performed at 250 rpm with 75 Apeak current and 4000 rpm with 75 A peak current and com-pared with turn-off control algorithm output. Fig. 10 showsthe optimisation at 250 rpm and Fig. 11 shows the optimis-ation at 4000 rpm. The model calculated the turn-off angleas 317 electrical degrees compared to optimisation, whichgives 307 electrical degrees at 250 rpm with 75 A peakphase current. Optimisation at 4000 rpm with 75 A peakphase current gives 342 electrical degrees as opposed tomodel calculates the turn-off angle as 336 electricaldegrees. There is a slight error in estimating the optimumefficiency turn-off angle if the system is run out of theintended operating range. Operation outside the intendedduty can be anticipated through judicious choice of thefour operating points used for optimisation.

Fig. 9 Simulation results of the implemented control techniquewith 2500 rpm motor speed and the current reference is changedfrom 25 to 140 A at 0.03 s.

Fig. 10 Motor torque, RMS phase current, and torque per RMSphase current versus turn-off angle at 250 rpm, 75 A

IET Electr. Power Appl., Vol. 1, No. 3, May 2007

4 Experimental results

The performance of the controller is experimentally verifiedthrough a 16/12 four-phase SRM designed for a 1-kW,12-V automotive application. The control algorithm ofSection 2 is implemented using an Analog DevicesADMC401 digital signal processor (DSP). The SRM iscoupled to a hysteresis brake, which acts as a controllablemechanical load. A resolver with resolver-to-digital conver-ter circuitry provides 12-bit position information to theDSP. A 12-V battery provides dc power to the inverter.Fig. 12 shows the block diagram of the experimental setup.

The speed controller of the SRM and the proposedturn-on angle controller is implemented first. The optimis-ation of the turn-off angle is performed at four operatingpoints representing all combinations of low and highspeed with low- and high-phase current. For a giventurn-on angle, the peak phase current and motor speed forall possible turn-off angles are tested. At each operatingpoint, torque output, RMS phase current and turn-offangle are recorded. Fig. 13 shows the variation in torqueper RMS phase current with turn-off angle at four operatingpoints. The turn-off angles of interest are those that maxi-mise the torque per RMS phase current ratio. Having themost efficient excitation angles for four operating points,the turn-off angles have been determined for any givenpoint using (2). Fig. 14 shows the curve fit of the turn-offangles using the experimentally optimised data. The opti-mised turn-off angles versus number of experiment areshown for a given speed. Fig. 15 shows the dependence ofturn-off angles on speed and power using experimental data.

Having the curve-fit parameters for turn-off angles, theturn-off angle controller is integrated into the overallsystem controller. Table 2 provides the parameters used inthe system controller. Using the block diagram of the com-plete control system given in Fig. 7, the turn-off angle con-troller is tested in the experimental system. Fig. 16 showsthe response of the experimental system where the speedis changed from 500 to 2500 rpm with a 3 Nm load.Fig. 17 shows the motor phase currents at 500 rpm,2500 rpm and during transients. The closed-loop turn-oncontroller effectively works and makes both up ¼ um andIp ¼ Iref at every speed. The turn-off controller immediatelyadjusts the turn-off angle to the change in commanded oper-ating point. Both controllers work harmoniously with thespeed controller to produce desired torque with theminimum RMS phase current possible. The commanded

Fig. 11 Motor torque, RMS phase current, and torque per RMSphase current versus turn-off angle at 4000 rpm, 75 A

399

Fig. 12 Block diagram of the experimental setup

Fig. 13 Variation in torque per RMS phase current with turn-offangle at four operating points determined experimentally

Fig. 14 Experimentally determined optimal-efficiency turn-offangles at four operating points and curve fit using the data fromthe four optimal points

The horizontal axis represents the operating point number

400

Fig. 15 Curve fit of the experimentally determined optimal-efficiency turn-off angles at four operating points versus motorspeed and peak phase current

Table 2: Parameters for the controllers of Fig. 6

Quantity Value Units

Kpu 0.033

KpI 1.899 8/A (electrical)

ucond 178 8(electrical)

k1 28.106e-5 8s/A (electrical)

k2 21.397e-2 8s (electrical)

k3 29.278e-l 8/ffiffiffiffiA

p(electrical)

k4 3.556e2 8 (electrical)

proportional gain 0

integral gain 78 s21

IET Electr. Power Appl., Vol. 1, No. 3, May 2007

turn-on and turn-off angles are 200 and 320 electricaldegrees, respectively, at 500 rpm as shown in Fig. 16. Theactual turn-on and turn-off angles are 210 and 330 electricaldegrees, respectively, at 500 rpm as shown in Fig. 17.The discrepancy is because of implementation errorsin the experimental system such as resolution in the pulse-width modulation (PWM) outputs or resolver-to-digitalconverters.For lower speeds and power levels, there is some devi-

ation between the optimised turn-off angles and the anglespredicted by the curve fit. This is a reflection of the incon-sistency in the optimal-efficiency turn-off angles deter-mined through simulation. However, it is known thatsmall changes in excitation parameters will not cause asignificant change in the achieved efficiency because ofthe general nature of the SRM. Further, at lowerspeeds and power levels there are more combinations ofexcitation parameters that support a particular operatingpoint. Nonetheless, the trend in turn-off angle is consistent

Fig. 16 Response of the experimental system where the set speedis changed from 500 to 2500 rpm with a 3 N m load

Fig. 17 Motor phase currents at 500 rpm, 2500 rpm and duringthe transient from 500 to 2500 rpm with a 3 Nm load

IET Electr. Power Appl., Vol. 1, No. 3, May 2007

with (2) even for a curve fit based on only four operatingpoints, and that the curve fit improves as speed and powerlevels increase.

5 Summary

The behaviour of switched-reluctance motor efficiency ischaracterised in terms of operating speed, torque productionand excitation angles. An efficient, easily implementedcontrol algorithm for excitation angles is developed. Thenew approach provides for automatic turn-on angle adjust-ment without the need for motor parameters or self-tuningtechniques. The algorithm monitors the peak phasecurrent and where the peak current occurs. It places the pos-ition of the first peak of phase current at umin order to maxi-mise the torque per Ampere produced by the SRM. Thecontroller also ensures that the peak phase current is equalto the reference current. It is shown that turn-off anglesare a function of peak phase current level and speed, sothey can be represented through a curve-fitting function.The turn-off angles are easily optimised by determiningthe optimal-efficiency excitation parameters at only fouroperating points.

The overall system is simulated with the SRM modelbased on finite element data. The control technique is thenimplemented on an experimental system as part of aoverall speed controller. The new technique provides easyimplementation of the control technique. The results ofthe experimental tests show that the new control techniqueprovides an efficient SRM controller that is easy toimplement.

6 References

1 MacMinn, S.R., and Sember, J.W.: ‘Control of a switched-reluctanceaircraft starter-generator over a very wide speed range’. Proc. of theIntersociety Energy Conversion Engineering Conf., 1989,pp. 631–638

2 Kokernak, J.M., Torrey, D.A., and Kaplan, M.: ‘A switched reluctancestarter/alternator for hybrid electric vehicles’. Power ElectronicsProc. (PCIM Conference), 1999, pp. 74–80

3 Mese, E., Sozer, Y., Kokernak, J.M., and Torrey, D.A.: ‘Optimalexcitation of a high speed switched reluctance generator’. Proc.IEEE Applied Power Electronics Conf., 2000, pp. 362–368

4 Besbes, M., Gabsi, M., Hoang, E., Lecrivain, M., Grioni, B., andPlasse, C.: ‘SRM design for starter-alternator system’. Proc. Int.Conf. on Electric Machines, 2000, pp. 1931–1935

5 Torrey, D.A.: ‘Variable-reluctance generators in wind-energysystems’. Proc. of the IEEE Power Electronics Specialists Conf.,1993, pp. 561–567

6 Lawrenson, P.J., et al.: ‘Variable-speed switched reluctance motors’,IEE Proc., 1980, 127, pt. B, (4), pp. 253–265

7 Miller, T.J.E.: ‘Switched reluctance motors and their control’ (OxfordUniversity Press, 1993)

8 Sozer, Y., Torrey, D.A., and Mese, E.: ‘Automatic control ofexcitation parameters for switched-reluctance motor drives’, IEEETrans. Power Electronics, 2003, 18, (2), pp. 594–603

9 Fahimi, B., Suresli, G., Johnson, J.P., Ehsani, M., Arefeen, M., andPanahi, I.: ‘Self-tuning control of switched reluctance motors foroptimized torque per Ampere at all operating points’, Proc. IEEEApplied Power Electronics Conf., 1998, pp. 778–783

10 Russa, K., Husain, I., and Elbuluk, M.: ‘A self-tuning controller forswitched reluctance motors’, IEEE Trans. Power Electronics, 2000,15, pp. 545–552

11 Torrey, D.A., and Lang, J.H.: ‘Modelling a nonlinearvariable-reluctance motor drive’, IEE Proc., 1990, 137, pt. B,pp. 315–326

401