Neural Speed Controller Trained Online by Means of ... - IEEE Xplore

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Neural Speed Controller Trained Online by Means of Modified RPROP Algorithm Tomasz Pajchrowski, Krzysztof Zawirski, Senior Member, IEEE, and Krzysztof Nowopolski

Abstract—In this paper, the synthesis and the properties of the neural speed controller trained online are presented. The structure of the controller and the training algorithm are described. The resilient backpropagation (RPROP) algorithm was chosen for the training process of the artificial neural network (ANN). The algorithm was modified in order to improve controller operation. The specific properties of the controller, i.e., adaptation and auto-tuning, are illustrated by the results of both simulation and experimental research. An electric drive with permanent magnet synchronous motor (PMSM) was chosen for experimental research, due to its impressive dynamics. The obtained results indicate that the presented controller may be implemented in industrial applications. Index Terms—Adaptive control, artificial neural networks (ANNs), backpropagation, motor drives, permanent magnet motors.

I. I NTRODUCTION

I

N THE CURRENT age of development of new technology and industrial processes automation, there is a rising demand for the improved dynamics of adjustable-speed drives. This demand for higher dynamic properties causes that parameters of speed controllers applied in drives are tuned to obtain the highest possible drive dynamics [1]–[3]. Any controller with such precisely selected values of its parameters is very sensitive to even small changes in any of the parameters of the drive system transfer function. The moment of inertia is the parameter that is variable the most often in industrial systems, e.g., drives in industrial manipulators or in feeding mechanisms of lathes, drives of coiling and reeling machines, as well as in paper manufacturing machines. In most of these applications, the moment of inertia is dependent on the angular position of the drive system [4], [5]. In complex drive structures, the parameter of delay, occurring in controllers and power converters, is not constant. Also in the states of field weakening, the parameter of electromagnetic torque to motor current ratio may change. Hence, there is a strong demand for the design of controllers that are insensitive (or have limited sensitivity) to changes in the parameters listed above [6]. Finding proper methods and designing, a controller that ensures high quality of the final product, i.e., very good dynamic properties and high precision of control, is Manuscript received March 06, 2014; revised September 08, 2014, August 29, 2014, and May 17, 2014; accepted September 14, 2014. Date of publication September 22, 2014; date of current version March 27, 2015. Paper no. TII-14-0284. The authors are with the Institute of Control and Information Engineering, Poznan University of Technology, Poznan 60965, Poland (e-mail: tomasz. [email protected]; [email protected]; krzysztof. [email protected]). Digital Object Identifier 10.1109/TII.2014.2359620

a difficult task and many research centers around the world are focused in this field [7]–[10]. Proposed solutions are based on robust [11]–[13] or adaptive [14]–[16] controllers. Methods of computational intelligence, artificial neural networks (ANNs) in particular, are utilized in the implementation of these control structures. In papers [17] and [18], two different concepts of the adaptive neural controller are presented. The model-reference adaptive controller presented in [18] is trained using the difference (treated as an error) between the reference output signal of a model and the real output signal of an object. In paper [4], the idea of a neural controller with reference current feedback is described. An interesting proposal of a neural controller trained by its own control error is presented in [17]. Further development of this idea is presented in [16], although a deeper analysis of the results is necessary. In this paper, an improved solution of the neural speed controller is presented. It has been obtained through further theoretical and simulation research works, proven by experimental tests. Every stage of controller synthesis is described and the taken design decisions are illustrated with simulation research prepared in the MATLAB-Simulink environment. The new results comprise a modification of the structure of the neural speed controller and some modifications and supplements in the ANN online training algorithm. The obtained results of the controller operation and the interesting properties of the controller allow recommendation of its implementation in industrial applications. A permanent magnet synchronous motor (PMSM) drive was selected for research works due to its very good dynamic properties. The scheme of the PMSM drive is shown in Fig. 1. The drive is equipped with space vector control ensuring constant power angle δ = π/2, and therefore, the assumed current value in d-axis is equal to zero. The analyzed neural speed controller computes the reference q-axis current value, proportional to the reference value of electromagnetic torque of the motor. This paper is divided into six sections. Introduction to the problem of speed control in electric drive, using ANN, is described in Section I. In Section II, the assumed concept of neural controller and proposed ANN structure are discussed. In Section III, the modified resilient backpropagation (RPROP) algorithm of the online ANN training is presented. The problem of controller astaticism is discussed in Section IV. Section V, where the proper operation of the controller and appropriateness of the simulation research are proven by the experiment results, is followed by a conclusion.

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Fig. 3. Structure of PD controller with two degrees of freedom and integration realized by the training algorithm of ANN.

Fig. 1. Block diagram of speed control system of PMSM drive.

Fig. 4. Structure of ANN.

Fig. 2. Structure of PI-2DOF.

II. S TRUCTURE OF THE C ONTROLLER A. General Idea On the basis of many similar research works, as well as multiple recommendations that can be found in [1], [2], and [19], it can be assumed that the proportional–integral controller structure with two degrees of freedom (PI-2DOF) is sufficient for the majority of speed control systems of electrical drives. The structure of PI–2DOF is presented in Fig. 2. The possibility of independent optimization of the system response for changes in the reference value and the changes in the disturbance value (in the presented application: the load torque) is a well-known advantage of this structure. The approach proposed in this paper is a substitution of the linear PI controller by the online-trained neural controller. The two basic assumptions of the ANN training process are as follows: the training is unsupervised and no training pattern is used. ANN is simply trained in order to minimize the speed control error (Fig. 1). Therefore, the error function is defined as follows [21], [22]: E=

1 · (ωref − ω)2 . 2

(1)

The minimization of the error function (1) by online operation of the training algorithm is assured by continuous changes in the ANN weights, performed in each step of the algorithm operation, as far as function (1) reaches zero value. In any transient process, prompted by a change in the reference speed, the torque load, or the drive parameters, the error function (1), being a square of speed control error, increases its value and thus starts the training algorithm. It means that the controller is tuned in two cases. 1) The first, during responses to changes in the reference speed or the load torque (or any other distortion), can be treated as the auto-tuning process. 2) The second,

in response to the drive parameter variation, is the equivalent of the adaptation of its parameters. These properties allow classifications of this ANN controller as self-training. The controller tending to the complete elimination of the control error in steady states, possesses astatic properties, unless there are no integral elements included in its structure. These premises allow changing the controller structure from PI-2DOF to PD-2DOF (proportional-derivative) with integral operation realized by the ANN training algorithm, as shown in Fig. 3. B. Structure of ANN The time accessible for computations of the controller and the ANN training procedure is limited by a short pulse width modulation (PWM) period necessary to obtain the high dynamics of the controller. The selection of the simplest structure of ANN is implicated by these conditions. The period of 100 µs was selected as the system operation step. In order to design the proper architecture of the network, an incremental construction technique was applied. This technique is based on the network expansion, as long as the properties of the system are improving. The criterion of the system operation improvement is the minimization of the error function—for various trajectories, step changes in the load torque and variations in the drive system parameters values. The system operation was evaluated in the real conditions, including delays, nonlinearity of the drive system, and complex mechanical structure, but remaining possibly simple structure of the network. The network structure was obtained through trial and error. The structure was developed according to the procedures presented in [23] and [24]. Within the wide range of tested structures of ANN, satisfactory results were obtained for the relatively simple structure presented in Fig. 4. The amount of the modified weights of ANN is limited to 15. The two types of neuron activating functions tested were as follows: 1) hyperbolic tangent (tanh); and 2) linear function. The hyperbolic tangent function turned out to be better for proper

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where Δwij (k) is the weight update between the ith neuron and the jth input, done in the kth step of the training; ηij (k) is the training factor (i, j, k, as above); E(w(k)) is the ANN error, computed in the kth step. Factor ηij (k) is selected for each weight Δwij (k) individually and is modified in each training step, according to (3)

TABLE I R ESULTS O F T ESTS W ITH D IFFERENT ANN S TRUCTURES

⎧ ⎪ ⎨min (a · ηij (k − 1), ηmax ), if Sij (k) · Sij (k − 1) > 0 ηij (k) = max (b · ηij (k − 1), ηmin ), if Sij (k) · Sij (k − 1) < 0 ⎪ ⎩η (k − 1), other cases. ij (3)

B. Modification of RPROP Algorithm ANN controller operation. Different structures were evaluated using the criterion of integral of square error (ISE). The results of tests with different ANN structures are shown in Table I. III. ANN T RAINING A LGORITHM A. RPROP Algorithm The assumed conditions of the ANN training process impose specific requirements on the training algorithm. It is essential to choose a simple procedure, which allows high speed of realization and can be implemented in a microprocessor controller (equipped with a signal processor). Significant part of the applied ANN training methods is based on the calculation of the network error function gradient. Many of them include complex computations, which disparages their application in the systems performing real-time calculations, as it is in the presented system. In the control applications of the neural networks (also in this paper), the error function is related with error of the system. The most commonly known and simple method, belonging to this class, is the error backpropagation algorithm [26]. In this method, each weigh is updated proportionally to the values of a partial derivative of the error with respect to this weight. The coefficient of proportionality η is called the training factor. If the error function is characterized by many ravines, the EBP algorithm convergence is very slow. To improve training performance, an additional component called “momentum” is added to the weight update [27]. A similar approach, attaching the simple PD control to the gradient processing, is presented in [18]. In this method, the function gradient is not computed directly, which significantly increases the algorithm efficiency. Other method, where the accurate gradient computation is unnecessary, is RPROP algorithm [20]. Besides the high computational efficiency, the fast convergence is an important advantage. Taking this into consideration, the RPROP algorithm, developed by [20], was chosen for the training of ANN in the described research. The essential advantage of the RPROP algorithm is based on the process of the ANN weights update (ANN training), where only the sign of error function gradient, instead of the value of the error, is utilized. This modification of the ANN weight in the training process is done according to [20]   ∂E(w(k)) Δwij (k) = −ηij (k) · sign ∂wij = −ηij (k) · sign(Sij )

(2)

During versatile research, a problem with controller instability was noticed by the authors, and therefore an original modification of the RPROP algorithm is proposed. According to the assumed controller conception, the error function for the ANN training process is the error of the speed control e(t). This error is computed in each step of the controller operation for the assumed set of weights. Taking into consideration the calculation of the error in the subsequent steps of controller operation, the gradient of the ANN error function may be approximated using the following simple formula: Sij (k) =

e(k) − e(k − 1) Δe(k) = Δwij (k) wij (k) − wij (k − 1) + Δwx

(4)

where e(k), e(k − 1) is control error in steps k, k − 1 of the controller operation; wij (k), wij (k − 1) is weight between the ith neuron and the jth input in steps (k), (k − 1) of the controller operation; Δwx is a small value, introduced for protection against division by zero in case of stopped weight changes. The calculation of the function gradient in this simple way, on the basis of the already known values of control error e(k) and weights wij (k), is a departure from the main feature of the RPROP method. However, (4) allows to determine in a simple manner, the sign of the slope needed in (3) and (6) and utilized in the RPROP method. In the case, when the network weights are kept at constant values in the result of the ANN training algorithm operation, division by zero occurs in (4). Therefore, if the weights are constant, the very small value of Δwx is forced a priori to avoid division by zero and to enable to determine the sign of the slope, despite the inaccurate value of Sij (k). After analysis of rules of ηij factors change, determined by (3), in the RPROP algorithm, described in (3), it can be easily noticed that the condition of keeping a factor at a constant value is fulfilled if and only if Sij (k) · Sij (k − 1) = 0.

(5)

This state practically does not occur in the numerical computations being done by any microprocessor system processing physical measurement data. Therefore, the continuous modifications of the ηij factors do not lead to any constant value, but continuous changes are imposed. Second, more important effect of the impossibility of reaching the state described by (5) is the continuous change in the ANN weights (wij ). The training process is never stopped. In this approach, a problem of

PAJCHROWSKI et al.: NEURAL SPEED CONTROLLER TRAINED ONLINE BY MEANS OF MODIFIED RPROP ALGORITHM

controller instability, in the result of neural network overtraining, can be noticed. In order to avoid an improper operation of the controller, a modification of the RPROP algorithm is proposed. This modification, analyzed in many simulation and experimental tests for different conditions of the controller and the drive system operation, is based on the introduction of a tolerant band ΔS into the training conditions (3) and transforms them to form, shown at the bottom of the page (6). Introduction of ΔS is important not only due to stopping of the training factors but also, most of all, as a criterion of stopping of the network training, according to (7) shown at the bottom of the page, that protects against overtraining. Properly selected range of the tolerant band ΔS, found through trial and error on the basis of many tests with different input signals and various operating points, assured stable operation of the neural controller and limited the excessive increase in the ANN weights. The proper operation of the controller with the tolerant band, proven by a number of tests, turned out to be a satisfactory solution. Due to this fact, no limits of the weight values are applied. The influence of the tolerant band on the controller operation is illustrated with the exemplary waveforms presented in Fig. 5. One can see that the weights are increased by the controller without tolerant band (only selected weights are shown), and after a few cycles of the reference speed changes, the controller operation becomes unstable. In the same conditions, the operation of the controller with tolerant band remains stable. The block diagram of the ANN training algorithm, including the modifications mentioned above, is shown in Fig. 6. Obviously, introduction of the tolerant band may cause not only the optimal values of weights that are reached but also the suboptimal. Hence, insertion of ΔS is as a kind of compromise between training accuracy and stability. The influence of the training factor on the ANN training stability is discussed in Section III-C. Reaching the tolerant band does not mean that the training process is stopped permanently. Each change in the operating conditions of the system, i.e., change in the reference speed value or change in the disturbance value, causes growth of the control error e(k), what increases also the value of its gradient. As a result, the tolerant band is left and the ANN training process is restarted.

C. Selection of Algorithms Elements The selection of the operation period of the ANN training procedure is an essential issue in the algorithm design.

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Fig. 5. (a) System responses to sequence of step changes in reference value. (b) Current in axis q value (current limit 8 A). (c) Selected weights of the neural controller (with and without tolerant band).

The smallest possible training step is equal to one period of the speed controller operation. However, the microprocessor of the controller in some cases may be overloaded by repeating the procedure of ANN training. Due to this, the possibility to lengthen the training step time was also tested. The influence of the training period changes is illustrated best by the waveforms of the system responses to the step changes in the load torque, presented in Fig. 7. These waveforms of drive speed are characterized by different training step values (Tt ). Each of the Tt values is a multiple of controller operation step Ts (Tt = 2 · Ts , 4 · Ts , 6 · Ts ). The conclusion is as follows: if the training step is longer then the speed controller reaction is slower, thus, the adaptation is slower. The selected value of the training step needs to be a compromise between the adaptation dynamics and the computational capability of the microprocessor system. There are a few parameter values in the RPROP algorithm (3) that were arbitrarily proposed by its authors [16].

⎧ if Sij (k) · Sij (k − 1) > ΔS ⎨min (a · ηij (k − 1), ηmax ), if Sij (k) · Sij (k − 1) < −ΔS ηij (k) = max (b · ηij (k − 1), ηmin ), ⎩ if − ΔS ≤ Sij (k) · Sij (k − 1) ≤ ΔS. ηij (k − 1),

(6)

⎧ ⎨−ηij (k) · sign (Sij (k)), if Sij (k) · Sij (k − 1) > ΔS Δwij (k) = −ηij (k) · sign (Sij (k)), if Sij (k) · Sij (k − 1) < −ΔS ⎩ 0, if − ΔS ≤ Sij (k) · Sij (k − 1) ≤ ΔS.

(7)

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Fig. 8. Simulation step responses of speed for different values of a coefficient.

Fig. 6. Block diagram of modified ANN training procedure.

Fig. 9. System responses to step change in reference speed value, for different ηmax values.

Fig. 7. Simulation waveforms of responses to step changes in load torque for different training periods. Algorithm without the tolerant band.

These parameters are the coefficients of increase (a) and decrease (b) in the ηij factors and the maximum and minimum values of these factors (ηmax , ηmin ). These parameters have a strong influence on the values of the training factor, which is critical for stability of the ANN training process, so their influence was investigated within simulation research. During tests, it was noticed that the values of parameters a and b were selected properly, and the changes in these values have only a slight influence on the quality of the adaptive control. This small influence is demonstrated in Fig. 8, where the speed waveform is scaled-up. It is clearly visible in Fig. 8 that if the a coefficient is decreased (to 0.9a) then the overshoot in the response is limited, but the response time is extended. After increasing the coefficient (to 1.25a and 1.5a), an increase in the overshoot and response time are observed (with no influence on the settling time). However, all the differences are very small, less than 0.05%. Although it must be stressed that the further increase in the coefficient a leads to instability of the system. The selected value of 1.2 may be considered as close to optimum. Similarly, the b coefficient was tested. The conclusion is that the changes in the b coefficient have a slight influence on the process of the system adaptation. These values cannot be selected randomly. The presented selection of these

Fig. 10. System responses to step changes in load torque for different ηmin values. Algorithm without the tolerant band.

values, considering data accessible in the literature, is proper for this system. Investigations of selection of the training factor limits (ηmax , ηmin ) showed that if these parameter values are selected improperly, oscillations in the drive speed occur, as a result of the unstable training process. This observation is illustrated by the waveforms in Fig. 9, where responses to the step change in the reference speed are shown. Improperly selected values of the parameter ηmax (ηmax1 , ηmax3 ) lead to the occurrence of oscillations. The proper selection of the ηmin value is essential as well. The influence of this limitation values on the system response to a step change in the load torque is shown in Fig. 10. Larger values of ηmin (ηmin1 , ηmin3 ) lead to faster responses of the controller (faster process of the weight coefficients change), but oscillations of the rotational speed are generated. Smaller

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Fig. 12. Structure of ANN with additional integration. Fig. 11. Simulation waveforms of system responses to step changes in load torque for different widths of tolerant band (ΔS1 < ΔS2 < ΔS3 ).

values (ηmin3 ) result in slower reaction of the controller, but with smoother speed changes (smaller amplitude and frequency of oscillations). Taking into consideration, the strong influence of the training factor limitation on the stability of the training process, a variable limitation of ηij is assumed. The proper limitation values are defined as the following function of the control error:

Fig. 13. System responses to step changes in load torque for controller with and without additional integration.

ηmax (k) = ηmaxL + kηmax |e(k)|, where ηmaxL ≤ ηmax (k) ≤ ηmaxH ηmin (k) = ηminL + kηmin |e(k)|, where ηminL ≤ ηmin (k) ≤ ηminH

(8)

where ηmaxL , ηmaxH are the minimum and maximum values of the ηmax factor; ηminL , ηminH are the minimum and maximum values of the ηmax factor; kηmax , kηmin are slope coefficients. The functions (8) are stored in the memory of the microprocessor controller as two look-up tables.

IV. A STATICISM OF THE N EURAL C ONTROLLER According to the observations described in Section II-B, the controller astaticism is a result of some specific properties of the ANN training algorithm. It is confirmed by the results of tests of the system response to step change in the load torque for different training cycle periods, shown in Fig. 7. The introduction of the tolerant band ΔS in formulas (6) and (7), necessary for stable controller operation, is related with degradation of controller astaticism. The steady state control error is increased if the tolerant band is wider. This relation is shown in the results of the tests for different values of the tolerant bandwidth, presented in Fig. 11. For this reason, the introduction of an integral element to the controller structure is proposed, in order to obtain complete elimination of the steady state control error in the closed-loop system including the ANN controller with the tolerant band. This new controller structure is shown in Fig. 12. The integral gain is changed during the ANN training process like a regular network weight. The results of operation of this controller are shown in Fig. 13. It is illustrated with the presented system responses to step changes in the load torque that the speed control error is eliminated only by the controller with additional

Fig. 14. Laboratory stand diagram.

integrating element, in contrast to the controller with tolerant band, but without integration. V. R ESULTS OF E XPERIMENTAL R ESEARCH A. Laboratory Stand Description The laboratory system utilized for verification of simulation research results is shown in Fig. 14. All the mentioned algorithms and procedures were implemented in the digital signal processor ADSP-21060. The high efficiency of this microprocessor unit allowed processing all the measurements, control and training algorithms within 100 µs sampling period. The same period is selected for the PWM inverter operation. In order to make the results of simulation and experimental

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Fig. 15. Experimental waveforms of system response to step change in load torque for different ANN training periods. Controller with integral module.

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Fig. 17. Experimental waveforms of speed control system step responses and changes in selected weights for two different initial values of weight: random and zero.

Fig. 16. Experimental waveforms of system response to step change in load torque for different widths of tolerant band (ΔS1 < ΔS2 < ΔS3 ). Controller without integral module.

research comparable, the authors made efforts to transfer all the conditions and parameters of the laboratory stand into its precise computer model. Thus, the results of the experiments and simulation are very convergent. The parameters of the drive system are presented in Appendix.

B. Selected Results of Laboratory Experiments In order to evaluate the reliability of the results of simulation with the simplified model, many experimental tests were carried out. The influence of the training period and the influence of the tolerant band to speed error caused by the step change in load torque were investigated. The results are presented in Figs. 15 and 16. Comparing the waveforms in Fig. 6 with those in Fig. 15 as well as Fig. 11 with Fig. 16, a close similarity can be noticed. In Fig. 15, the elimination of the steady state control error is presented as the effect of the addition of the integration module. The effects of the controller tuning by ANN training may be observed in Fig. 17. The system responses to a series of step changes in reference speed are presented in this figure. The two following cases are compared: 1) with zero initial values of weights and 2) with random initial values. For both these initial states, after the first-step adequate weights values are selected by the ANN training process, so the overshoot is

Fig. 18. Responses of drive system with minimum and maximum moment of inertia to load torque step changes, with PI and ANN controller.

much smaller in the next-step responses. The effects of the ANN training process may be observed even more precisely by tracking the values of exemplary weights, shown in this figure. The properties of appropriate ANN training and tuning of the controller parameters are clearly proven. If the initial transient process with large overshoot is unacceptable for the drive, a special start-up procedure with stopped drive shaft, described in [12], is recommended. Another solution is to store the weights of the controller that has been already tuned and to start the controller operation with the stored values. The adaptive abilities of the controller may be evaluated by an analysis of responses to step changes in load torque at two extreme moment of inertia values: Jmin and Jmax = 7 · Jmin , shown in Fig. 18. The parameters of the PI controller were selected so as to obtain robustness to the changes in the parameters of the object, according to the original method described in [25]. The maximum dynamic speed control errors, caused by the step change

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A PPENDIX TABLE II DATA O F I NVESTIGATED D RIVE

Fig. 19. Experimental system responses to step change in reference speed for controller without integration, with limited output signal: with continuous training (1) and with training stopped if system is in limitation (2).

in the load torque, for both minimum and maximum value of J, are similar for both of the controllers. However, the settling time is 2.5 times longer for the PI controller (ts = 200 ms) than for the neural controller (ts = 80 ms). Moreover, for the minimum value of the moment of inertia, oscillations in the response to the step changes in the load are caused by the PI controller. It shall be emphasized that the parameters of the compared PI controller are tuned in a specific way. If a standard method, e.g., symmetry criterion, was applied, the results would be much worse. The output signal of the controller is limited, so the reference motor torque (and reference current id ) is limited as well. If the state of limitation is reached, the speed control system becomes open; hence, the ANN training process shall be stopped. System responses to the reference speed step change, with controller output reaching limitation, are presented in Fig. 19. The two following cases are shown: 1) continuous training process; and 2) ANN training stopped if the system operates within the limits. It is visible in the presented waveforms that without stopping ANN training in limitation, the overshoot in system response is noticeably larger.

VI. C ONCLUSION The proposed conception of the neural self-training controller (trained online) possesses two valuable properties: 1) auto-tuning; and 2) adaptation of its parameters. The controller tunes its parameters not only for changes in object parameters but also during all transient processes caused by changes in the reference signal or the load torque, tending to minimize the speed control error. The assumed controller structure and the training algorithm allow the implementation available in the signal processors with sampling period equal to 100 µs. The controller may be applied to electric drives with as good dynamic as these with PMSM. The described modifications of the original RPROP training algorithm are necessary for appropriate controller operation. These proposed original modifications may prove their usefulness also in other ANN applications. The impressive static and dynamic properties of the neural controller allow for consideration of its implementation in industrial drives.

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Tomasz Pajchrowski received the M.Sc. and Ph.D. degrees in automatic control of electrical drives from the Poznan University of Technology (PUT), Poznan, Poland, in 1999 and 2005, respectively. Currently, he is an Assistant Professor with the Electrical Engineering Faculty, PUT. He is an author and coauthor of over 60 scientific papers. His research interests include the application of the control theory and nonlinear, adaptive, and robust control system to the controlled electrical drives.

Krzysztof Zawirski (SM’05) received the Ph.D. degree in electrical engineering and the D.Sc. (habilitation) degree from the Poznan University of Technology (PUT), Poznan, Poland, in 1979 and 1993, respectively. Currently, he is a Full Professor and Head of the Group of Power Electronics and Motion Control, PUT. From 1991 to 1994 and from 1996 to 1997, he was a Visiting Professor with Universidade da Beira Interior, Covilhã, Portugal. He is an author and coauthor of over 170 scientific papers, a textbook, two books, and two monographs. His research interests include control of synchronous permanent magnet motors and switched reluctance motors, where control systems, the nonlinear, adaptive, and robust control algorithms, as well as computational intelligence methods are applied. Dr. Zawirski is a Member of European Power Electronics and Drives (EPE), and a Member of the International Steering Committees of a few European conferences. He was a General Chairman of the 13th Power Electronics and Motion Control Conference EPE-(PEMC)’2008, which was held in Pozna´n in September 2008.

Krzysztof Nowopolski received the M.Sc. degree in automatic control from the Poznan University of Technology (PUT), Poznan, Poland, in 2012. Currently, he is an Assistant with the Institute of Control and Information Engineering, PUT. His research interests include design of machine intelligence algorithms, and implementation of models and control structures of electrical drive in field programmable gate array devices.