Implementation of a neural network to adaptively identify and control ...

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 34, NO. 3, MAY/JUNE 1998

Implementation of a Neural Network to Adaptively Identify and Control VSI-Fed Induction Motor Stator Currents Bruce Burton, Associate Member, IEEE, Ronald G. Harley, Fellow, IEEE, Gregory Diana, Member, IEEE, and James L. Rodgerson

Abstract— This paper presents a prototype hardware implementation of a continually online trained artificial neural network (ANN) to adaptively identify the electrical dynamics of an induction machine and control its stator currents from a pulsewidth modulated voltage-source inverter. A singletransputer-based hardware platform is described, and the effects of computational speed limitations on the controller bandwidth are discussed. Captured results are compared with simulation results to practically verify the success of the adaptive neural network identification and control scheme. Index Terms—Current control, hardware implementation, induction motors, neural networks.

I. INTRODUCTION

Fig. 1. Adaptive ANN induction motor control scheme.

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HE most common system identification and control and other, general, applications of artificial neural networks (ANN’s) involve the offline training of arbitrarily large (many hidden layers and many nodes in each layer) feedforward sigmoidal ANN’s using the backpropagation training algorithm [1]. This offline training is done using large amounts of data, taken directly from the process to be identified and controlled, which must include fairly densely spaced data points on the extreme boundaries of system operation. Comparatively sparse data points may be used to represent system behavior within these boundaries, as ANN’s have inherently good generalization (interpolation) capabilities, but generally exhibit unacceptably poor performance outside (extrapolation) of the operating conditions over which they have been trained. Disadvantages of this offline training approach are that the amount of system data, training time, and ANN size are not only dependent on system complexity, but also the range of operating conditions involved. Offline-trained systems are also prone to degraded performance or even failure should Paper MSDAD 97–12, presented at the 1994 Industry Applications Society Annual Meeting, Denver, CO, October 2–7, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Industrial Automation and Control Committee of the IEEE Industry Applications Society. This work was supported in part by the University of Natal and in part by the Foundation for Research and Development (FRD) in South Africa. Manuscript released for publication September 20, 1997. B. Burton, R. G. Harley, and G. Diana are with the Department of Electrical Engineering, University of Natal, Durban, 4001 South Africa (email: [email protected]; [email protected]; [email protected]). J. L. Rodgerson is with the Department of Electrical and Electronic Engineering, Manukau Institute of Technology, Manukau City, Auckland, New Zealand (e-mail: [email protected]). Publisher Item Identifier S 0093-9994(98)03622-6.

unforeseen circumstances force the system out of the range of operating conditions over which the ANN has been trained. This paper describes the prototype hardware implementation of the current controller of the theoretically proposed adaptive ANN induction motor control scheme of [2], shown in Fig. 1. One of the most attractive features of the proposed scheme is that it remains adaptive throughout operation, which gives it the ability to track parameter variations under all operating conditions. Adaptive current control (i.e., calculating control so as to force the actual stator current to track voltage the desired current ) is achieved directly from the output of a continually online-trained ANN model of the voltage-fed motor, using a simple algebraic control equation. Adaptive speed control (i.e., calculating the desired current so as to produce the necessary torque to force the actual shaft/rotor speed to track the desired speed ) is achieved by continually training an ANN model of the current-controlled motor and using this model for continual training of an ANN speed controller. Since training is done online, it is imperative that the ANN size and the execution time of the ANN output calculation and training algorithm be minimized, in order to allow implementation on modest hardware, while maintaining the desired sampling rate. The ANN current control scheme in Fig. 1 thus presents the greatest challenge in terms of practical implementation, since the required current-loop sampling rate is typically an order of magnitude higher than that of the speed loop. Results are presented which verify the practical operation of the theoretically proposed ANN current identification and control method on a single-T800-transputer-based high-speed

0093–9994/98$10.00  1998 IEEE

BURTON et al.: NEURAL NETWORK TO IDENTIFY AND CONTROL STATOR CURRENTS

programmable digital controller [3] developed previously for motion control applications using traditional controllers for motor currents and speed. The limitations of this hardware restrict the bandwidth of the online ANN identifier and controller, which are computationally much more burdensome than traditional controllers. Nevertheless, the results demonstrate the truly adaptive nature of the ANN-based controller and its excellent tracking ability and robustness. The theory of the current-loop ANN identifier and controller are considered; the practical implementation requires certain modifications and the implications thereof are discussed in some detail and illustrated with simulated and captured practical results. Sigmoidal feedforward neural networks and the fundamentals of the backpropagation training algorithm are introduced and their application in the adaptive induction motor current identification and control strategy is outlined. The singleT800-transputer-based hardware platform used is also briefly described, and the effect of its computational limitations upon ANN performance is evaluated.

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Fig. 2. Function approximation ANN training scheme.

II. SIGMOIDAL FEEDFORWARD ANNS Backpropagation-trained sigmoidal feedforward ANN’s (commonly known as backpropagation ANN’s) are the most common ANN’s in practical use, with applications ranging from financial market prediction to medical test analysis; their widespread use continues to add to empirical proof of their usefulness and reliability. A. Backpropagation versus Other ANN Types Following the suggestions for further work cited in [2], this investigation first considered the use of radial basis function ANN’s and recurrent ANN’s as alternative network types, but found that backpropagation ANN’s were best suited in this instance. This is due to the comparatively low computational overhead involved in the implementation of continual online backpropagation training on a digital processor and resulting higher speeds of execution. The theory of backpropagation ANN’s and the issues of continual online training are considered in more detail in [4]. B. Fundamentals of the Backpropagation Algorithm It has been shown [5] that a sigmoidal ANN, with sufficient neurons in a single hidden layer, may be trained to identify and approximate any desired continuous vector mapping function over a specified range. Fig. 2 shows how this ANN is trained to . The objective of training approximate a desired function is to modify weight matrices and so as to minimize the difference between the desired function output and the ANN output over a specified range of . This difference is called the ANN output or training error . The backpropagation training algorithm is simply a set of equations representing least-mean-square parameter (weight) optimization, as applied to the ANN function . The algorithm derives its name from the fact that these equations through the ANN appear to backpropagate the output error structure to obtain the weight updates.

Fig. 3. Adaptive current control law using a continually online-trained ANN model of the voltage-fed induction motor.

Where is not time varying, training is stopped once is sufficiently low over the desired range. However, continual online training is required where the ANN function is required to adaptively approximate or track functions which are time varying, such as the desired functions of the voltagefed and current-controlled induction motor models and the speed controller of Fig. 1. The accuracy with which ANN’s are able to track timevarying functions depends not only on the number of hidden neurons, but also on the rate at which the weights are updated, i.e., the sampling rate. Thus, the number of hidden neurons must be large enough for good accuracy, but also small enough that the ANN computations can be completed within a sufficiently small sampling period. III. ONLINE IDENTIFICATION AND CONTROL OF INDUCTION MOTOR STATOR CURRENTS USING ANNS Fig. 3 shows an expanded view of the ANN current identifier and controller of Fig. 1. The pulsewidth modulation (PWM) and inverter blocks from Fig. 1 are omitted in Fig. 3, since the MATLAB simulations of this paper assume an ideal voltage source; this assumption is usually valid if the PWM frequency is high enough for the inverter to produce nearsmooth sinusoidal motor currents. A. The Electromagnetic Model of the Voltage-Fed Induction Machine The discrete-time nonlinear autoregressive moving average with exogenous inputs (NARMAX) model of the electromagnetic dynamics of the voltage-fed induction machine is

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introduced in [2]. The advantage of the NARMAX model is that it is in input/output form and may thus be identified by an ANN, as described in Section II. In the stationary two-axis reference frame, the NARMAX model is defined as

(1) Equation (1) therefore defines the stator currents which will flow in the motor at the next sampling instant as some nonlinear function of present sampling instant values and previous sampling instant values of , electrical rotor speed , and input stator voltages . Parameter is called the voltage constant and represents the direct effect of the control voltage applied at the present sampling instant on the currents which will flow in the motor at the next sampling instant; it is due to this direct effect that a simple algebraic current control equation may be derived, as is a function shown in Section III-C. The nominal value of of motor parameters and sampling rate; this function is derived in [2]. Function is time varying because it is determined by motor inductances (which vary rapidly due to unmodeled saturation effects) and resistances (which vary slowly due to unmodeled thermal effects and rapidly due to the unmodeled skin effect associated with alternating currents). B. Identification of the Stator Currents A backpropagation network with function is continually trained to adaptively approximate the time-varying function and voltage constant of (1) to give the ANN estimated one-step-ahead predicted stator currents as [2]:

(2) The error vector used to train this ANN model of the voltagefed motor can be obtained by delaying the ANN estimate of what the stator currents will be at the next sampling instant by one sampling period and subtracting this from the actual (measured) stator currents flowing in the machine, i.e., . However, this error is calculated differently when the ANN model is used in conjunction with the stator current control equation, as explained in the next section. C. Control of the Stator Currents The objective of a stator current controller is to force the actual stator currents in the machine to follow a desired . It is proposed in [2] that should be current vector derived from the output of a first-order reference model. This model represents the desired stator current dynamic response

of the machine (usually a fast, critically damped response) and is implemented in the synchronously rotating two-axis reference frame, as shown in Fig. 3, where is the desired electrical frequency of rotation. This avoids the phase delays which would be introduced if the reference model reference frame. The were implemented in the stationary effect of this reference model on the controller performance is investigated in Section IV. Because of the direct influence [evident in (1)] of the stator on the voltages applied at the present sampling instant stator currents at the next sampling instant , there always exists a control voltage which will force these currents , where is defined to equal the desired value in (3), shown at the bottom of the page. This algebraic current control equation can be implemented directly using the output of the ANN identifier function and estimated voltage constant in place of and such that is now defined in (4), shown at the bottom of the page. in Now, substituting the right-hand side of (4) for (2), shows that when control equation (4) is used to calculate . Thus, the ANN identifier training error of when the Section III-B is calculated as identifier is used to implement control equation (4), as shown in Fig. 3. IV. PRACTICAL IMPLEMENTATION This section considers the various practical issues of digitally implementing the algorithm of Fig. 3 and (4). A. Practical Computation Time Delays The control equation (4) and algorithm depicted in Fig. 3 assumes that the feedforward or output calculation of the ANN is instantaneous. In other words, it assumes that the is evaluated as the ANN inputs are sampled function is output at the same instant. This is clearly and that output will be not practically realizable. At best, the delayed by the total length of time taken for the following to be completed: 1) A/D conversions; 2) abc line currents to transform; 3) decoding of rotor speed from the shaft encoder; calculation; 4) ANN output and 5) output of the command to the PWM; 6) PWM switching output calculation; 7) actual PWM switching signal output. Steps 1)–7) represent approximately half of the computations that must be completed within one sampling period, which means that a delay of up to half a sampling period can

(3) (4)


Fig. 4. Block diagram of the controller and other drive components.

occur from the time that the ANN inputs are sampled and the corresponding stator voltage command takes effect. The backpropagation training algorithm and ANN weight modifications take up the other half of the sampling period. A safety margin must also be left to allow for worst case datadependent calculation times. Simulation results have shown that the stability and tracking ability of the controller are not significantly degraded, due to a delay of up to one whole sampling period in the final execution of the stator voltage command. All simulation and captured results presented in this paper have been obtained by forcing the delay in the execution of stator voltage commands to be one whole sampling period. B. Achievable Sampling Rate In addition to the unavoidable computational delays described above, the achievable sampling rate depends on the following: 1) amount of computation time required to execute the entire algorithm; 2) efficiency of the controller algorithm software implementation; 3) raw digital processing power, I/O, and overall speed of the hardware platform used; 4) degree of parallelism offered by the digital processing components and exploited in the software implementation. For the purposes of this paper, only points 1) and 2) are considered, since the target hardware is an existing, singletransputer-based, controller hardware platform. Using this platform means that higher sampling rates may only be achieved by cutting down on the amount of computation as far as possible, without affecting the controller stability or significantly degrading its tracking performance. The main factors to consider in this regard are the number of hidden nodes in the ANN and the estimation of parameter . The number of hidden nodes is heuristically determined in [2] to be 12. While simulations showed that this number could be reduced to eight without significant degradation in controller performance, this number was left at 12 to allow for the introduction of the PWM in the physical system. In the simulations, it was assumed (as in the control equation (4) and block diagram of Fig. 3) that the PWM and IGBT inverter combination would produce ideal (commanded) stator voltages. In practice, high switching frequencies result in fairly accurate, but not ideal, voltage inversion, and the full 12 hidden nodes were included to allow the ANN to identify

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and compensate for any voltage distortion. Simulations, of the same kind as those presented in Section IV, showed the controller response to be less sensitive to noise and more damped for static values of approximately equal to 5 than . Fixing also had no marked effect on the confor troller’s ability to track parameter variations in the machine. A final sampling rate of 500 Hz was achieved with an ANN of eight inputs, 12 hidden nodes, and two outputs, and a fixed . The issues of raw computational power and hardware and software parallelism and efficiency, raised in points 1)–4) are reported on in more detail in [4] and [6]. C. A Single-Transputer-Based Controller Platform The controller platform [3] is shown in Fig. 4; it uses a 25MHz INMOS T800 transputer. The T800 implements reduced instruction set computing (RISC) and incorporates a 32-b integer processor, which runs in parallel with a 64-b floating point unit (FPU) on a single chip, with 4 kB of on-chip RAM, configurable for high-speed code and/or data access. The FPU enables high-speed implementation of all controller arithmetic in normal floating-point precision. The controller platform incorporates auxiliary synchronous state machines and I/O including the following to reduce I/O computing overheads on the main processor: 1) decoding of rotor position from a shaft encoder; 2) high-speed simultaneous sampling of up to 16 analog channels and 12-b A/D conversions; 3) PWM space vector modulation application specific integrated circuit (ASIC) and associated protocol drivers; 4) 16-b digital I/O ports. The T800 was programmed using the INMOS ANSI C TOOLSET [7] and an IBM PC host. D. Electrical System Hardware A 220-V 3-kW wound-rotor induction motor was supplied by a PWM-controlled insulated gate bipolar transistor (IGBT) voltage-source inverter fed from a battery bank of 275 V. A commercially available space vector modulation PWM ASIC, embedded in the controller hardware platform, was line voltage commands, from the ANN used to translate controller, into corresponding space vector modulation inverter switching signals. A switching frequency of 4 kHz was used and synchronous sampling of the machine rotor speed and stator currents at 500 Hz was ensured. V. SIMULATED

AND

CAPTURED RESULTS

A. Initial Conditions As mentioned in Sections IV-A and B, all simulated and captured results presented in this paper are obtained using a backpropagation ANN of eight inputs, 12 hidden neurons, and two outputs. Execution (by the PWM ASIC) of the ANN controller stator voltage commands ( in Fig. 3) is deliberately delayed by one whole sampling period. A detuned, fixed , equal to 5 times its nominal value [3], is used to make the system more damped to compensate for this delay. All of the ANN inputs are scaled to lie roughly in the range [ 1,

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(a)

(b)

(c)

(d)

3 Fig. 5. (a) Simulated desired (i s 3 ) and actual (is ) stator current, with reference model. (b) Simulated desired (is ) and actual (is ) stator current, with reference model. (c) Simulated actual stator voltage (vs ) and current (i ) , with reference model. (d) Simulated actual stator voltage (vs ) and s current (is ), with reference model.

1]. The ANN inputs and outputs are expressed as per unit (PU) values, as a convenient method of scaling. Linear output neurons (not sigmoidal) are used to allow both positive and negative instantaneous controller outputs of more than 1 PU in magnitude. All simulated and captured results are obtained with random initial ANN weights set by a software pseudorandom number generator, and there is no commissioning or pretraining period, as specified in [2]. The results are thus conclusive proof of the excellent adaptability and ease of commissioning of this type of ANN controller, within the bandwidth limitations of the controller hardware. B. Simulation Method The system in Fig. 3 is simulated in MATLAB. The ANN controller is modeled as a discrete process and the induction machine is modeled in continuous time in the reference

frame. The effects of the PWM and inverter switching (Fig. 1) are not modeled. C. Types of Disturbance While the motor is at standstill, the values of and are held at zero until s, when they are stepped up to some fixed values. In the rest of this paper, this moment is referred to as the moment of switch-on. In the synchronously rotating reference frame, constant values of and translate into the constant magnitudes of the three-phase stator currents, while translates into the constant frequency the constant value of of these currents. The to transformation in Fig. 3 transforms the desired currents in the synchronously rotating reference frame to in the stationary reference frame; constant values for therefore become sinusoids with frequency .


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(a)

(b)

(c)

(d)

3 Fig. 6. (a) Captured desired (i s 3 ) and actual (is ) stator current, with reference model. (b) Captured desired (is ) and actual (is ) stator current, with ) , with reference model. (d) Captured actual stator voltage (vs ) and current reference model. (c) Captured actual stator voltage (vs ) and current (i s (is ), with reference model.

Fig. 5(a) illustrates how starts from zero at s. At s, the magnitude of are stepped down, while is stepped up; this translates into decreasing their magnitudes, but increasing their frequency. Furthermore, at s, the magnitudes step up to larger than before , as well), while steps down to lower (magnitude of is not raised than before. In the results presented here, above 3 rad/s because the maximum sampling rate is 500 Hz; this, in turn, is fixed by the time (between samples) needed to carry out all the computations in the software implementation of Fig. 3. and (vector ) form The desired values of the inputs to the ANN current control scheme. The correct operation of the ANN can be evaluated by comparing these values with the actual currents. Moreover, desired the correct operation can be judged by considering both the results from a simulation of Fig. 3, as well as those from the practical implementation. For example, Fig. 5(a) contains the

and the simulated actual . The same simulated desired in Fig. 5(b) and and in Fig. 5(c) and (d). applies to D. Results The results of two case studies are presented. In Case Study are passed through a reference 1, the step changes in model with a time constant of 200 ms, in order to practically verify the simulated results of [2]. 1) Case Study 1—Part A: The simulated results (for Fig. 3) appear in Fig. 5(a) and show how the changes in are not instantaneous (due to the 200-ms the desired differs from time constant); it also shows that the actual the desired for only a short period (about 200 ms) after switch-on. Thereafter, this simulated adaptive ANN controller is able to identify the induction motor and control the actual to be almost identical to the desired value. This is a particularly important result, since the ANN has had no commissioning or pretraining prior to switch-on, but it starts at switch-on with

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(a)

(b)

(c)

(d)

3 Fig. 7. (a) Simulated desired (i s 3 ) and actual (is ) stator current, without reference model. (b) Simulated desired (is ) and actual (is ) stator current, without reference model. (c) Simulated actual stator voltage (vs ) and current (i ) , without reference model. (d) Simulated actual stator voltage (vs ) s and current (is ), without reference model.

random values of weights and its training algorithm is able to adjust these weights to their correct values within 200 ms. Moreover, when the magnitude and frequency of the desired changes at s and again at s, the ANN tracks these changes very well. in Fig. 5(b) display a similar The simulated results for in Fig. 5(a), except that the initial behavior to those of and actual is smaller, difference between desired at switch-on is less than the because the change in desired change in desired . Fig. 5(c) and (d) illustrates the waveforms applied by the ANN to the motor in order to ensure and . the desired waveforms of 2) Case Study 1—Part B: The simulated results of Fig. 5 are to be compared with the captured results of Fig. 6. Fig. 6(a) confirms that the untrained practical ANN controller very quickly at switch-on identifies and controls the actual to follow the desired current. The same applies to in Fig. 6(b).

The captured actual currents in Fig. 6(a) and (b) do, however, have small distortions which are not present in the simulated actual currents in Fig. 5(a) and (b). These distortions in actual currents are at regular 60 intervals and are caused by the PWM voltages from the inverter. At the edges of any train of PWM pulses making up a half cycle of voltage, the pulses become narrow and disappear completely once the minimum on-time command from the SVM algorithm is reached. The fundamental of this PWM voltage waveform thus suffers from crossover distortion and, for a three-phase system, this crossover distortion occurs at 60 intervals. These distortions, in turn, cause distortions in each of the phase currents at 60 intervals. These distortions, together with other measurement noise present in the captured currents, propagate through the controller and provide the practical ANN with more identification information. High-frequency measurement noise at switchon enables faster training and thus a smaller discrepancy


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(a)

(b)

(c)

(d)

3 Fig. 8. (a) Captured desired (i s 3 ) and actual (is ) stator current, without reference model. (b) Captured desired (is ) and actual (is ) stator current, without reference model. (c) Captured actual stator voltage (vs ) and current (is ), without reference model. (d) Captured actual stator voltage (vs ) and current (i s ), without reference model.

between desired and actual currents immediately after switchon. Including measurement noise into the simulation confirms improved training and reduces the amount of current overshoot at switch-on in Fig. 5(a) and (b) to levels comparable with those in Fig. 6(a) and (b). The 60 distortions in current represent a sixth harmonic component, even during steady operation. The ANN quickly learns to issue distorted voltage commands to try to compensate for these distortions in the currents. The results of Figs. 5 and 6 show that the ANN-based identification and control algorithms proposed earlier [2] have been successfully implemented to control motor phase currents rad/s. at frequencies of up to 3) Case Study 2—Part A: The objective of this case study is to determine whether the reference model (Fig. 3) with its 200-ms time constant, as used in Case Study 1, is really necessary. The tests of Case Study 1 are, therefore, repeated with the reference model removed, and the results which

appear in Figs. 7 and 8 are to be compared with those in Figs. 5 and 6, respectively. The simulated current overshoot at switch-on is greater without the reference model [compare Fig. 5(a) with Fig. 7(a)], because the 200-ms time constant of the reference at switch-on, thus model slows down the rate of rise in giving the ANN slightly more time to identify the motor before being able to control the currents. Nevertheless, one can conclude that the first-order reference model in Fig. 3 is unnecessary. Although not shown here, the results of further investigations have shown that the overshoot at switch-on is also related reduces to the parameter ; for example, an increase in the amount of overshoot. 4) Case Study 2—Part B: The simulated results of Fig. 7 are to be compared with the captured results of Fig. 8. In general, the respective results in these two figures agree as well as they did in Case Study 1 (Figs. 5 and 6). Removal of

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the 200-ms delay reference model has no noticeable impact on the ANN’s practical performance, not even on the effect of the crossover distortions. 5) Case Study 3: The results of Case Study 2 were exof the tended by increasing the value of the frequency currents. At the increased frequencies, the simulated results display a similar response to those in Fig. 7, but the captured results show signs of growing instability in the actual currents, and the ANN hunts wildly when the frequency exceeds 8 rad/s. The instability is caused by the sixth harmonic distortion, which the ANN attempts to compensate for. Methods of overcoming this limitation are, at present, being investigated and point to an increased sampling rate and/or larger number of nodes in the ANN. In either case, higher speeds of computation will be required.

[6] R. G. Harley, M. J. van der Westhuizen, D. C. Levy, and D. R. Woodward, “Optimising Multirate motion control algorithms on parallel processors by static scheduling,” in Conf. Rec. IEEE-IAS Annu. Meeting, Denver, CO, Oct. 1994, pp. 1872–1878. [7] The INMOS ANSI C Toolset User & Reference Manuals, INMOS Ltd., Bristol, U.K., 1990.

Bruce Burton (S’94–A’95) was born in Johannesburg, South Africa, in 1971. He received the B.Sc. Eng. degree in electronic engineering in 1992 and the M.Sc. Eng. degree in electrical engineering in 1995 from the University of Natal, Durban, South Africa, where he is currently working toward the Ph.D. degree in the Motion Control Research Group. His research interests include artificial intelligence, control systems, electrical drives, and digital controller hardware.

VI. CONCLUSION A scheme for adaptive identification and control of induction motor currents and shaft speed using continually online-trained ANN’s was first proposed in [2]. This paper has presented the first work on the real-time implementation of this scheme; it presents a prototype hardware implementation of the ANN current controller and shows practical results which confirm the true self commissioning and adaptive current responses seen in the simulations of [2]. Without any knowledge of the motor’s electrical circuits, or any pretraining whatsoever, the prototype ANN of this paper quickly identifies the electromagnetic system and then tracks low-frequency desired currents. In order to track full-frequency desired currents, the 500-Hz sampling rate of the prototype ANN current controller must be increased by an order of magnitude. Continuing research is aimed at increasing the speed of execution of the ANN current identifier/controller algorithm and subsequently implementing the ANN speed identifier/controller of [2]. ACKNOWLEDGMENT The authors gratefully acknowledge the technical support of D. Woodward on the transputer controller. REFERENCES [1] D. Hammerstrom, “Neural networks at work,” IEEE Spectrum, vol. 30, pp. 26–32, June 1993. [2] M. T. Wishart and R. G. Harley, “Identification and control of induction machines using artificial neural networks,” in Conf. Rec. IEEE-IAS Annu. Meeting, Toronto, Ont., Canada, Oct. 1993, pp. 703–709. [3] G. Diana, B. Hao, R. G. Harley, D. R. Woodward, and D. C. Levy, “Implementing field oriented control of a voltage fed current regulated induction motor on a single transputer,” in Conf. Rec. IEEE-IAS Annu. Meeting, Denver, CO, Oct. 1994, pp. 750–755. [4] B. Burton and R. G. Harley, “Reducing the computational demands of continually online trained artificial neural networks for system identification and control of fast processes,” in Conf. Rec. IEEE-IAS Annu. Meeting, Denver, CO, Oct. 1994, pp. 1836–1843. [5] G. Cybenko, “Approximations by superpositions of a sigmoidal function,” in Mathematics of Control, Signals and Systems, vol. 2. Surrey, U.K.: Springer–Verlag, 1989, pp. 303–314.

Ronald G. Harley (M’77–SM’86–F’92) received the M.Sc. Eng. degree from the University of Pretoria, Pretoria, South Africa, in 1965 and the Ph.D. degree from Imperial College, London, U.K., in 1969. In 1971, he was appointed Professor of Electrical Machines and Control at the University of Natal, Durban, South Africa. He was a Visiting Professor at Iowa State University of Science and Technology, Ames, in 1977, Clemson University, Clemson, SC, in 1987, and Georgia Institute of Technology, Atlanta, in 1994. His areas of research include power system dynamics, electrical machines, power electronics, and control of ac variable-speed drives. Dr. Harley is a member of the IEEE Power Electronics and IEEE Industry Applications Societies. He is also a Fellow of the Institution of Electrical Engineers, U.K., and the South African Institute of Electrical Engineers.

Gregory Diana (S’91–M’91) received the B.Sc. Eng. degree from the University of Natal, Durban, South Africa, in 1982. He is presently a Senior Lecturer in the Department of Electrical Engineering, University of Natal. His interests lie in the application of advanced and intelligent control in the areas of variablespeed drives, power quality, industrial processes, and pinch technology for the investigation and development of energy-efficient demand-side management measures to achieve more effective use of existing power system technology.

James L. Rodgerson received the B.Sc. Eng. degree in electrical engineering from the University of Natal, Durban, South Africa, in 1971. He subsequently joined the Department of Electrical Engineering, University of Natal. During his 24 years of service, he was made responsible for the control systems stream and became an Associate Professor. In 1996, he joined the Electrical and Electronic Engineering Department, Manukau Institute of Technology, Auckland, New Zealand, where he is presently Group Manager of the Electrical Group. Most of his work has been directed toward the provision of quality education, including the development of MATLAB-based software for the education of students in the fundamentals of direct digital control.