ann-pm-mot

1836 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 49, NO. 4, JULY/AUGUST 2013

Intelligent Speed Control of Interior PermanentMagnet Motor Drives Using a Single

Untrained Artificial NeuronCasey B. Butt and M. Azizur Rahman, Life Fellow, IEEE

AbstractThis paper presents an intelligent speed controller forthe interior permanent magnet synchronous motor based on a sin-gle artificial neuron. Traditional artificial neural network-basedmotor controllers require extensive offline training, which is bothtime consuming and requires extensive knowledge of motor be-havior for the specific drive system. In addition, drive behavioris unpredictable when parameters outside the training set are en-countered. The proposed drive system overcomes these limitationsby requiring no offline training, is robust under varying operatingparameters, and is easily adaptable to various drive systems. Driveefficacy is verified in simulation as well as experimentally.

Index TermsArtificial neural network (ANN), intelligentcontrol, interior permanent magnet motor, interior permanentmagnet synchronous motor (IPMSM), motor control.

I. INTRODUCTION

THE INTERIOR permanent magnet synchronous motor(IPMSM) in speed-controlled high performance drive ap-plications is required to quickly achieve command speed andmaintain that operating point with maximum accuracy andminimal perturbation despite the occurrence of sudden and un-known disturbances. Conventionally, proportional-integral (PI)and proportional-integral-derivative (PID) speed controllershave been utilized to meet these control challenges. However,the operation of the IPMSM is strongly affected by rotormagnetic saliency, saturation, and armature reaction effects[1], making the dq-axis reactance parameters change over theoperating range and rendering conventional fixed-gain PI andPID controllers very sensitive to parameter variations [2][4].

Researchers have used controllers based on fuzzy logic,sliding mode, traditional artificial neural network (ANN), andgenetic algorithm to address these issues [8][13]. Each ofthese controllers, however, has its own performance and/orimplementation shortcomings.

This paper presents an ANN-based controller for the IPMSMdrive which precisely and accurately follows command speeds,with insensitivity to load and parameter variations, yet requires

Manuscript received August 23, 2011; revised March 2, 2012, June 1, 2012,and August 16, 2012; accepted October 18, 2012. Date of publication April 12,2013; date of current version July 15, 2013. Paper 2011-IACC-465.R3, pre-sented at the 2011 IEEE International Electric Machines and Drives Confer-ence, Niagara Falls, ON, Canada, May 1518, and approved for publicationin the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the IndustrialAutomation and Control Committee of the IEEE Industry Applications Society.

The authors are with the Faculty of Engineering and Applied Science,Memorial University of Newfoundland, St. Johns, NL A1B 3X5, Canada(e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/TIA.2013.2257973

minimal offline training. The system is simplified to a singleartificial neuron (SAN) to minimize complexity and computa-tional capacity requirements. Speed error and comparison of theSANs output command torque to a calculated reference torqueare used conditionally at each iteration to adaptively modify theSAN parameters to minimize speed error and ensure stability.An approximation of the maximum torque per ampere (MTPA)mode of operation is incorporated, resulting in increased effi-ciency up to base speed.

The proposed IPMSM drive system has been implementedusing a dSPACE digital signal processor (DSP) controller boardwith a 1-hp IPMSM. The indirect vector control scheme of theIPMSM drive has been employed [14]. Experimental results areprovided to confirm the efficacy of the drive system.

II. IPMSM DYNAMICS

Adopting the conventional practice of neglecting iron losses,the mathematical model of an IPMSM drive can be describedby the following equations in a synchronously rotating rotordq reference frame as:[vqvd

]= rs

[iqid

]+

[pLq PrLd

PrLq pLd] [

iqid

]+

[Prf

0

](1)

Te =TL +Bmr + Jmpr (2)

Te =3P

2[f iq + (Ld Lq)idiq] (3)

wherevd, vq d- and q-axis stator voltages;id, iq d- and q-axis stator currents;Ld, Lq d- and q-axis stator inductances;rs stator per-phase resistance;r rotor speed in angular frequency;Te, TL electromagnetic and load torques;Jm moment of inertia of the motor and load;Bm friction coefficient of the motor;P number of poles of the motor;p differential operator (= d/dt);f rotor magnetic flux linking the stator.

III. CURRENT CONTROL ALGORITHM

The torque equation, (3), indicates that there exists a non-linear relationship between the electrical torque and d- and

0093-9994/$31.00 2013 IEEE

BUTT AND RAHMAN: INTELLIGENT SPEED CONTROL OF INTERIOR PERMANENT MAGNET MOTOR DRIVES 1837

q-axis currents. In order to incorporate this nonlinearity in apractical IPMSM drive, an approximation of the control tech-nique known as the MTPA mode is derived. MTPA providesthe maximum motor torque with the minimum possible statorcurrent [15][19].

A. MTPA Mode

The maximum torque per unit current can be achieved bydifferentiating (3) with respect to q-axis current iq and settingthe resulting equation to zero, which gives

id =f

2(Lq Ld)

2f

4 (Lq Ld)2+ i2q. (4)

Substituting (4) into (3), one can get a nonlinear relationshipbetween iq and Te as

Te=3P

2

f iqf iq

2(LdLq)

2f i

2q

4(LqLd)2 +i4q

.

(5)In real time, the implementation of the drive system becomes

potentially undefined and computationally burdensome withexpressions (4) and (5). To address this, the d- and q-axiscurrents are obtained by expanding the square root term of (4)via a Taylor series expansion about zero, giving

id = 0.11825i2q . (6)

Numerical values of (6) are obtained by using the parametersof Motor A found in the Appendix. By substituting (6) into (3),the following relationship can be obtained:

iq = 1.06157Te. (7)

As this derivation involves a series approximation and theassumption that the involved motor parameters remain constant,(6) and (7) are used to achieve approximate MTPA control ofthe IPMSM [20].

The block diagram in Fig. 1 shows the control scheme of themotor drive. The command torque T e is obtained from a SAN-based speed controller. Then, using (7), the reference q-axiscurrent iq is computed from T e . Subsequently, the referenced-axis current id is calculated using (6). The correspondingthree-phase currents are determined by vector rotation. A hys-teresis current controller compares the reference three-phasecurrents with actual currents and generates gate signals for thetransistorized inverter.

IV. DESIGN OF SAN CONTROLLER FOR IPMSM

A. SAN Control Principle

The dynamic model of the IPMSM can be rewritten from (1)and (2) as

Lqpiq + PrLdid = vq rsiq Prf (8)pr =(Te TL Bmr)/Jm. (9)

Fig. 1. Block diagram of the SAN-based IPMSM drive.

The load will be considered as having unknown nonlinearmechanical characteristics and can be modeled using the fol-lowing equation as [2]:

TL = A2r +Br + C (10)

where A, B, and C are arbitrary constants. To make the controltask easier, the equations of the IPMSM are expressed as asingle-input/single-output system by combining (9) and (10) incontinuous time domain form as

Jmdrdt

= Te (Bm +B)r A2r C. (11)

A small incrementTe inTe causes a small incrementr inr

Jmd(r +r)

dt= (Te +Te)

(Bm +B)(r +r)A(r +r)2 C. (12)Subtracting (11) from (12) gives

Jmd(r)

dt= Te (Bm +B + 2Ar)(r)A(r)2.

(13)By replacing all the continuous quantities of (13) by theirfinite differences, the discrete-time small signal model of thesimplified IPMSM with nonlinear load can be given as

Te(n) =Jmts

e(n)

+ (Bm +B + 2Ar(n))r(n) +A {r(n)}2 . (14)Hence,

T e (n) =

discrete

Te(n) = f (e(n),r(n), r(n)) (15)

where e(n) = r(n)r(n 1) is the change of speederror, r(n) = e(n) =

r(n) r(n) is the present sample

of speed error, r(n 1) is the past sample of speed error,r(n) is the present sample of actual speed, r(n) is the presentsample of command speed, ts is the sampling time interval, andf denotes the nonlinear function. Equation (15) indicates that,in order for the SAN-based speed controller to produce accurate


torque commands under nonlinear loading, its inputs need bethe speed command r(n), speed error r(n), and change ofspeed error e(n).

Thus, the purpose of using the SAN speed controller is toobtain the command torque by mapping the nonlinear func-tional relationship between the command electrical torque T eand the rotor command speed r, speed error e(n), and changein speed error e(n), with no reliance on knowledge of motorparameters.

B. Reference Command TorqueEquation (2) can be rearranged and discretized to give

TL(n) = Te(n) Jmpr(n)Bmr(n). (16)Jm and Bm are known; r(n), the present sample of rotorspeed, can be obtained from a position sensor mounted tothe rotor shaft; and pr(n) = (r(n) r(n 1))/ts is thechange in rotor speed over the sampling period. This meansthat load torque TL(n), at the present sample, can be calculateddirectly from (16) if Te(n) is known at that sampling instant.Te(n) can be calculated from (3) as

Te(n) =3P

2[f iq(n) + (Ld Lq)id(n)iq(n)] . (17)

irq(n) and ird(n) can be calculated via Parks equation andreference frame transformation from samples of ia(n), ib(n),and ic(n) taken by current sensors. P and f are known, andLd and Lq must be assumed to have constant known values.

With the current sample value of TL now having been cal-culated, (2) can be utilized to calculate the reference commandtorque as follows:

T ref(n) = Jmpr(n) +Bmr(n) + TL(n) (18)where pr = (r(n) r(n))/ts is the current sample valueof speed error divided by the sampling time, r(n) is the currentsample of command speed, and r(n) is the current sample ofrotor speed.

This value of command torque is calculated with the as-sumption that Ld and Lq have constant known values. Thatassumption is, of course, incorrect. Using the actual inductancecurves of our test motor indicates that this Tref commandmay vary from the correct torque value by up to 42% at themost extreme cases. This command torque serves merely as areference for the real-time training of the SAN and to set boundsto assure drive stability, however, and for these purposes, it issufficient.

C. SAN-Based Speed Controller for IPMSM DriveTo minimize computational burden, a single feedforward

neuron structure is employed, with the command torque beingthe only output of the SAN controller. The inputs to the SAN arethe present sample of command speed r(n), present sample ofspeed error e(n) = r(n) r(n), and present sample of thechange of speed error e(n) = r(n)r(n 1). Neu-ron output ranges from -1 to 1 via a tan-sigmoid transfer func-tion, so this value is multiplied by the maximum peak torque

Fig. 2. SAN for IPMSM drive.

Fig. 3. Simulated response of SAN controller-based IPMSM drive to188.5-rad/s speed command at no external load.

rating of the motor to obtain the actual torque command. Dueto space limitations, the equations of the ANN structure are notincluded herethey are based directly on conventional feedfor-ward ANN methods. The SAN structure is illustrated in Fig. 2.

From this command torque, the MTPA approximation is usedto obtain the appropriate q- and d-axis command currents, iqand id, respectively, to produce the desired motor speed. Phasecommand currents, ia, ib, and ic, are then calculated via theinverse Park transform and applied to the motor through thevoltage source inverter via a hysteresis controller.

In order to provide adaptive control, the weights and biasof the SAN are updated, by back propagation, whenever thespeed error exceeds an appropriately chosen threshold. If thisthreshold is not exceeded, the weights and bias will be usedagain in the following iteration. The speed error itself, e(n) =r(n) r(n), is used for back-propagation updating.

In addition, at each sample, torque error eT (n) = T ref(n)T SAN(n) is used for SAN retraining if eT (n) exceeds a tol-erance value. If retraining is not successful within a specifiednumber of back-propagation iterations (to fix a maximum limiton the computing time that retraining can take), then T ref(n) isused to generate motor currents at that sample. Bounding T SANby comparison to an approximate torque command ensuresthat the SAN does not cause the drive to become unstable,and specifying the back-propagation iteration count allows thecontrol algorithm to be adjusted for the capabilities of theprocessing power at hand. In addition, this also allows the SANto produce its own initial weights and bias, as well as adjustthose weights and bias on a per-sample basis, meaning that nooffline training is required.


Fig. 4. Simulated response of SAN drive, with T ref disabled, to 188.5-rad/sstart-up speed command and sudden application of full load (0 2 Nm)at 2 s.

As an example of the training process, Fig. 3 shows thesimulated speed response of the SAN drive under no externalload to a rated command speed of 188.5 rad/s. The speed errortolerance was set at 0.1 rad/s, the torque error tolerance wasset to 42% as explained earlier, and ten torque error retrainingiterations were allowed at each sample. Under these conditions,the weights and bias of the SAN settled to W1 = 0.6286,W2 = 1.5458, W3 = 1.0276, and B = 0.4652. At the finalsample, the command torque value was T SAN = 0.5098 N m.The learning rates of the SAN were tuned manually so that theSAN could train itself within the 42% torque error boundary forall but four of the samples, where T ref was used as commandtorque. As the sampling rate was 5 kHz, this indicates that theSAN successfully provided the torque command for 4996 of the5000 total torque commands issued.

To illustrate the contribution of the reference torque com-mand T ref as a boundary for the SAN, Fig. 4 shows thesimulated response of the drive at start-up and under full load(2 N m) application with T ref disabled. The drive does reachand maintain command speed based on speed error trainingalone, but with significant oscillation and load sensitivity.

Each iteration of the combined speed- and Tref -basedtraining of the SAN-based controller imposes 50 mult./div.,37 add./sub., and 16 exponential operations. This is a significantincrease in computational burden as compared to a singleiteration of a conventional PID controller but only occurs whenretraining is necessary. During trained operation, a total of 17operations are required by the SAN. In real-world implemen-tation on the laboratory equipment, the SAN-based drive wasfound to perform best at a maximum sampling rate of 5 kHz,whereas a typical PID-based controller could be sampled at10 kHz. A more complex four-neuron-based ANN controllerrequired the sampling frequency to be lowered to 1 kHz anddid not produce acceptable real-world results due to this.

V. LABORATORY IMPLEMENTATION

The complete drive system has been implemented in thelaboratory with a 1-hp IPMSM using a dSPACE DS1102 DSPcontroller board. The actual motor currents are measured byHall-effect sensors and fed to the DSP board through an A/D

Fig. 5. Simulated response of SAN-based IPMSM drive to sudden applicationof load (0 2 N m) at a command speed of 188.5 rad/s. (a) Speed,(b) a phase current, (c) q-axis current, and (d) d-axis current.


Fig. 6. Simulated response of PID-based IPMSM drive to sudden applicationof load (0 2 N m) at a command speed of 188.5 rad/s. (a) Speed,(b) a phase current, (c) q-axis current, and (d) d-axis current.

Fig. 7. (a) Simulated SAN controller with sudden parameter change (Rs 2Rs and Ld 0.5Ld) under nonlinear load. (b) Simulated start-up responsesof SAN drive to rated speed command (188.5 rad/s) with inertia changes.Dashed line = Jm, and solid line = 1.5Jm.

converter. As the motor neutral is isolated, only two phasecurrents are fed back, and the other phase current is calculatedfrom them. Three-phase reference currents are generated uti-lizing the reference q- and d-axis currents and rotor positionangle obtained through an encoder mounted on the shaft of themotor. Computed three-phase reference currents are convertedto upper and lower hysteresis limits by adding and subtract-ing a preselected percentage band. Actual motor currents arecompared to these hysteresis current limits, and pulse-widthmodulated gate-drive signals are generated accordingly.

All computations involving the SAN, the generation of ref-erence currents and, consequently, gate-drive signals for theinverter, are done in the ANSI C programming language viaa PC. The program is compiled using the Texas Instruments Ccompiler and downloaded to the DS1102 controller board viadSPACE software. The sampling frequency is set at 5 kHz.

VI. RESULTS AND DISCUSSION

Prior to implementation, the complete SAN-based drive sys-tem, including provisions for iron losses in the motor, was sim-ulated using Matlab/Simulink software. A PID-based controllerwas tuned and implemented to serve as a baseline comparison.PID tuning was roughed out via the ZieglerNichols method


Fig. 8. (a) Simulated PID controller with sudden parameter change (Rs 2Rs and Ld 0.5Ld) under nonlinear load. (b) Simulated start-up responsesof PID drive to rated speed command (188.5 rad/s) with inertia changes.Dashed line = Jm, and solid line = 1.5Jm.

and then adjusted manually for best performance. Kp, Ki, andKd were tuned to balance the overshoot and loading responsewith the settling time, and the back calculation method wasimplemented as an antiwindup strategy. Simulated and exper-imental results from both drives are presented in this section.

Fig. 5 shows the simulated speed, a phase, and q- andd-axis current responses of the SAN-based IPMSM drive atstart-up and to a step increase in load from 0 to 2 N m for arated command speed of 188.5 rad/s. The speed disturbance dueto the load application is almost indiscernible at this resolution.The increase in phase current draw due to the sudden torquerequirement increase is obvious. The q-axis current increaseswith load to produce the required additional torque, and thed-axis current increases slightly in the negative direction to takeadvantage of the reluctance component of the torque equation,as per the MTPA scheme.

Fig. 6 shows the simulated speed, a phase, and q- andd-axis current responses of the PID controller-based IPMSMdrive at start-up and to a step increase in load from 0 to 2 N mfor a rated command speed of 188.5 rad/s. Unlike the SAN-based controller case, the speed disturbance due to the loadapplication is more dramatic. The increase in current draw dueto the sudden torque requirement increase is similarly obvious,although it ramps more gradually as compared to the SAN case.

Fig. 9. Experimental response of SAN-based IPMSM drive to sudden changesof command speed at light load (90 188.5 130 rad/). (a) Speed and(b) a phase current.

The q-axis current increases with load to produce the requiredadditional torque, and the d-axis current increases slightly in thenegative direction, as per the MTPA scheme. These responsesshow slower reaction times than the SAN case.

Fig. 7(a) and (b) shows the simulated SAN-based drivesspeed responses to sudden parameter changes (Rs to 2Rs andLd to 0.5Ld) under nonlinear loading (TL = 2/35532.25)and to inertia changes under no load at start-up with ratedspeed command (Jm increased to 1.5Jm). The SAN-baseddrives speed response appears unaffected by these Rs and Ldvariations under nonlinear load. The inertia increase reducesthe acceleration of the motor at start-up but has little effectotherwise.

Fig. 8(a) and (b) shows the simulated PID-based drivesspeed responses to sudden parameter changes (Rs to 2Rs andLd to 0.5Ld) under nonlinear loading (TL = 2/35532.25) andto inertia changes under no load at start-up with rated speedcommand (Jm increased to 1.5Jm). The PID-based drivesspeed response shows some sensitivity to these Rs and Ldvariations under nonlinear load, although the command speedis maintained. The inertia increase reduces the acceleration ofthe motor at start-up and also increases overshoot.

Fig. 9(a) and (b) shows the experimental speed and currentresponses of the SAN-based IPMSM drive to step changesof the command speed at light load. The drive reaches andmaintains command speeds quickly and accurately during thestep increase and step decrease of the command speed. Thephase current magnitude does not appear to change significantlywith motor speed (as load torque is constant). The currentfrequency, however, increases and decreases appropriately withchanging command/motor speed.


Fig. 10. Experimental response of SAN-based IPMSM drive to sudden ap-plication of full load (0 2 N m) at rated speed (188.5 rad/s). (a) Speed,(b) a phase current, (c) q-axis current, and (d) d-axis current.

Fig. 10 shows the experimental speed, a phase, and q- andd-axis current responses of the SAN drive to sudden applicationof full load (0 2 N m) at rated speed (188.5 rad/s). Althoughspeed disturbance due to loading is not visible at this resolution,the increased phase current amplitude with the application ofload is apparent. Likewise, q- and d-axis currents respond,particularly iq , with increases in magnitude to meet the addi-tional torque demand.

Fig. 11. Experimental start-up responses of SAN drive to rated speed com-mand (235.6 rad/s) with inertia changes.

Fig. 12. Experimental response of PID-based IPMSM drive to (a) start-upspeed command of rated speed (188.5 rad/s) and (b) sudden application of fullload at rated speed.

Fig. 11 shows the start-up response of the SAN drive to rotorinertia changes. Because the original laboratory motor did notpractically allow inertial adjustments, an alternate test motorwas used for these results (see Motor B in the Appendix).The increased inertia decreases the drives acceleration to basespeed (235.6 rad/s) but has little visible effect otherwise. TheMTPA equations (6) and (7) and Tref were adjusted in accor-dance with Motor B, but the SANs learning parameters werenot deliberately retuned to accommodate this motor.

For comparison and confirmation of simulation results,Fig. 12 shows the experimental speed responses of the PID-based drive (Motor A) to (a) start-up speed command of ratedspeed (188.5 rad/s) and (b) sudden application of full loadat rated speed. As in the simulation, the PID-based driveaccurately achieves command speed with moderate overshootbut characteristically experiences temporary disturbance whenpresented with sudden load incursion.


VII. CONCLUSIONThese results indicate that the SAN-based controller with

real-time training offers excellent speed response and load han-dling for high-performance IPMSM drives. A high performancestandard is achieved despite a minimum level of complexityand computational burden as compared to other intelligence-based adaptive controllers. A new approach to the use ofartificial intelligence for motor drives has been presented, inwhich the often cumbersome task of offline training has beensidestepped by enabling the drive to train itself in real timeduring operation.

The SAN-based real-time control strategy can be a goodchoice to provide adaptive control of the IPMSM drive withoutnecessitating high processor power or extensive offline training.On the very modest PC-based system used for experimentalwork (dSPACE ds1102 controller board in a PII 300-MHzPC with 128-MB RAM), the SAN-based controller achieveda sampling frequency of 5 kHz. With greater computing power,better accuracy and precision of speed and current responseswould be expected.

APPENDIXMOTOR PARAMETERS

Motor A: 3 , 1 hp, 208 V, 60 Hz, P = 2, Ld = 0.04244 H,Lq = 0.07957 H, rs = 1.93 , Jm = 0.003 kg m2,Bm = 0.0008 N m/rad/s, and f = 0.314 V/rad/s.

Motor B: 3 , 2 hp, 245 V, 112.5 Hz, P = 6, Ld =0.005432 H, Lq = 0.008582 H, rs = 2.90 , Jm =0.000449 kg m2, Bm = 0.000119 N m/rad/s, andf = 0.042935 V/rad/s.

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Casey B. Butt received the B.Sc. degree in physicsand the B.Eng., M.Eng., and Ph.D. degrees in elec-trical engineering from the Memorial University ofNewfoundland, St. Johns, NL, Canada, in 1995,2002, 2003, and 2007, respectively.

In 2007, he joined the hybrid electric vehicle divi-sion of General Motors Company, Detroit, MI, USA.His research interests are in the areas of electricmachines and intelligent control systems.

M. Azizur Rahman (M66SM73F88LF07)was born in Santahar, Bangladesh, on January 9,1941. He received the B.Sc. degree in electrical engi-neering from the Bangladesh University of Engineer-ing and Technology, Dhaka, Bangladesh, in 1962,the M.A.Sc. degree in electrical engineering fromthe University of Toronto, Toronto, ON, Canada, in1965, and the Ph.D. degree in electrical engineer-ing from Carleton University, Ottawa, ON, Canada,in 1968.

He is currently a Professor and University Re-search Professor at the Memorial University of Newfoundland, St. Johns,NL, Canada. He has published over 700 papers, 178 IEEE TRANSACTIONSpapers, and two books, is the holder of 11 patents, and contributed ten chaptersfor research and academic publications. His current research interests arein machines, intelligent controls, power systems, digital protection, powerelectronics, and wireless communication.

Prof. Rahman is a Registered Professional Engineer in the Provinces ofNewfoundland and Labrador, Canada. He is a Fellow of the Institution ofEngineering and Technology, U.K., a Fellow of the Engineering Instituteof Canada, a Fellow of the Canadian Academy of Engineering, and a LifeFellow of the Institution of Engineers, Bangladesh. He was the recipient ofthe following awards: the IEEE Notable Service Award in 1987, IEEE IndustryApplication Societys Outstanding Achievement Award in 1992, IEEE CanadaOutstanding Engineering Educators Medal in 1996, IEEE Third MillenniumMedal in 2000, IEEE Cyril Veinott Electromechanical Energy ConversionAward in 2003, IEEE William E. Newell Power Electronics Award in 2004,IEEE Dr.-Ing. Eugene Mittelmann Achievement Award in 2007, IEEE RichardH. Kaufmann Technical Field Award in 2007, and IEEE Power and EnergySociety Distinguished Service Award in 2008.

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