THE POSSIBILITY of achieving high-performance goals

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007 671 Sliding Mode Neuro-Adaptive Control of Electric Drives Andon Venelinov Topalov, Member, IEEE, Giuseppe Leonardo Cascella, Member, IEEE, Vincenzo Giordano, Francesco Cupertino, and Okyay Kaynak, Fellow, IEEE Abstract An innovative variable-structure-systems-based approach for online training of neural network (NN) controllers as applied to the speed control of electric drives is presented. The proposed learning algorithm establishes an inner sliding motion in terms of the controller parameters, leading the command error towards zero. The outer sliding motion concerns the controlled electric drive, the state tracking error vector of which is simultaneously forced towards the origin of the phase space. The equivalence between the two sliding motions is demonstrated. In order to evaluate the performance of the proposed control scheme and its practical feasibility in industrial settings, experimental tests have been carried out with electric motor drives. Crucial problems such as adaptability, computational costs, and robustness are discussed. Experimental results illustrate that the proposed NN-based speed controller possesses a remarkable learning capability to control electric drives, virtually without requiring a priori knowledge of the plant dynamics and laborious startup procedures. Index Terms Adaptive control, electric drives, neural networks (NNs), variable structure systems. I. INTRODUCTION THE POSSIBILITY of achieving high-performance goals when controlling dynamic systems is usually directly related to the degree of the model accuracy that can be achieved. In those applications where the knowledge of the system to be controlled is fragmentary or obtainable only in a costly way through complex offline experiments, artificial neural networks (NNs) can be an effective instrument to learn from input output data and efficiently catch information about the most appropriate control action to apply [1]. However, the application of NNs in feedback control systems requires the study of their properties such as stability and robustness to environmental disturbances and structural uncertainties before drawing conclusions about the performances of the overall Manuscript received July 9, 2004. Abstract published on the Internet November 30, 2006. The work of A. V. Topalov was supported in part by the Bogazici University Research Fund Project 03A202 and in part by the TUBITAK Project 100E042. The work of O. Kaynak was supported by the Ministry of Education and Science of Bulgaria Research Fund Project BY-TH-108/2005. A. V. Topalov is with the Control Systems Department, Technical University of Sofia, 4000 Plovdiv, Bulgaria (e-mail: topalov@tu-plovdiv.bg). G. L. Cascella, V. Giordano, and F. Cupertino are with the Dipartimento di Elettrotecnica ed Elettronica, Politecnico di Bari, via Re David 200-70125 Bari, Italy (e-mail: cascella@deemail.poliba.it; cupertino@deemail.poliba.it; giordano@ deemail.poliba.it). O. Kaynak is with the Department of Electrical and Electronic Engineering, Mechatronics Research and Application Center, Bogazici University, Bebek, 34342 Istanbul, Turkey (e-mail: okyay.kaynak@boun.edu.tr). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2006.888930 system [2], [3]. Moreover, in neuro-adaptive systems, in order to compensate for the existing variable and unpredictable disturbances and changes in the plant parameters, robust and fast online learning of the neural controller is a key issue. It is, therefore, essential to provide a tuning mechanism that guarantees stability and ensures high speed of convergence and robustness. Gradient-based learning methods have been frequently used in NN-based control applications [4] [7], but they can very often lead to suboptimal performances in terms of the convergence speed, robustness, and computational burden. Furthermore, the stability of the learning process is not guaranteed. Recently, variable structure systems (VSSs)-based algorithms have been proposed for online tuning of NNs. Implementations on several NN and fuzzy inference system models have appeared in the literature [8] [15], showing very interesting properties and proving to be faster and more robust than the traditional techniques. One of the first studies on adaptive learning in simple network architectures known as adaptive linear elements (ADALINEs) is due to Ramirez et al. [8], in which the inverse dynamics of a Kapitsa pendulum is identified by assuming constant bounds for uncertainties. Yu et al. [9] extend the results of [8] by introducing adaptive uncertainty bound dynamics and focus on the same example as the application, the drawback of the strategy being the existence of noise on the measured variables. In another paper [10], the existence of a relation between the sliding surface for the plant to be controlled and the zero learning error level of the parameters of the ADALINE neurocontroller is discussed and the control applications of the method considered in [8] and [9] are studied with constant uncertainty bounds. Differently from [8] [10], the sliding mode algorithms proposed in [11] and [12] are for online training of multilayer NNs. As is well known, multilayer feedforward networks structures (MFNNs) are commonly used for online modeling, identification, and adaptive control purposes in case variations in process dynamics or in disturbance characteristics are present. They do not have the limited approximation capabilities of the early proposed Perceptron and ADALINE networks [16]. In the approach presented in [11], separate sliding surfaces are defined for each network layer, taking into account the learning error variable and its time derivative. In [12], the ideas developed in [8] are further extended to allow online learning in MFNNs, with one sliding surface being defined using only the learning error, which makes it computationally simpler and suitable for real-time applications. The online learning capabilities of these algorithms in applications demanding adaptation to constantly changing environmental parameters, such as adaptive real-time control, are investigated in [13] [15]. 0278-0046/$25.00 2007 IEEE

672 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007 Although the results presented in [12] are quite encouraging, they have been obtained through simulation analysis only. The main goal of this work is to prove experimentally the effectiveness of the proposed approach for online training of MFNN-based controllers in nonlinear feedback control systems. The initial results obtained in [10], on the relation between the sliding surface for the plant to be controlled and the zero learning error level of an ADALINE neurocontroller, have been also extended and proved to be valid for the MFNN-based controller case. The control application studied is the speed control of a permanent magnet synchronous motor (PMSM). In industrial applications, PMSM drives are widely used, due to their inherent features such as versatility, ruggedness, and precision. However, in some applications, when uncertainties and disturbances are appreciable, traditional control techniques are not able to guarantee optimal performances or can require a considerably time-consuming and plant-dependent design stage. This has recently motivated a considerable amount of research in the field of NNs-based control of electric drives, in order to exploit the property of NNs to learn complex nonlinear mappings [4] [6], [17], [18]. In industrial settings, the most widely used controller is still the proportional-integral-derivative (PID) one and the spread of neural controllers for electric drives is contingent on the satisfaction of some critical requirements. Apart from guaranteeing good performance in a wide range of operating conditions, the computational burden presented by the neural controller should be low enough to allow its implementation on low-cost microcontrollers. Furthermore, even in the presence of a fragmentary knowledge of the plant parameters, the startup procedure (choice of the learning rate, number of the neurons and the network layers, inputs and outputs, as well as the desired NN output) should be fast, straightforward, and as general as possible, i.e., applicable for different motors and drives, and thus reducing the necessary installation time, with remarkable and captivating cost savings. Starting from these considerations, the experimental part of this work is carried out aiming at three main objectives. First, it investigates the feasibility of the proposed VSS-based learning algorithm in control problems, verifying its potentialities from a practical point of view, in terms of robustness and stability. Second, the design of the MFNNs-based controller is conducted to reach an optimal tradeoff between performance and complexity, since a simple control architecture would result in lowcost microcontroller implementations and in a faster and easier design stage for industrial practitioners. Finally, it is studied whether the same controller, despite its simplicity, is able to guarantee good performances in different operational conditions by automatically adapting its parameters. The main body of this paper contains five sections. Section II gives the definitions and the formulation of the problem in the framework of the applied VSS-based learning algorithm and the proposed neuro-adaptive control scheme. Section III introduces the equivalency constraints on the sliding control performance for the plant and sliding mode learning performance for the controller. Section IV presents the experimental application of the proposed speed control scheme to PMSM drives. Finally, Section V summarizes the results of this investigation and discusses further improvements. Fig. 1. Block diagram of the sliding mode neuro-adaptive control system. II. BASIC ASSUMPTIONS AND PROBLEM FORMULATION Consider a MFNN-based controller where the vector of the time-varying input signals is augmented by the bias term. Let states for the nonlinear, differentiable, activation function of the neurons in the hidden layer and its time derivative is considered bounded. denotes the vector of the output signals from the neurons in the hidden layer and is the vector representing the time-varying output signals of the neurons in the hidden layer before applying the activation functions (the vector of the net input signals). The neuron in the output layer is considered with a linear activation function and is the scalar signal of the controller output. The matrix of the connections weights for the neurons in the hidden layer is denoted by, where each element means the weight of the connection of the neuron from its input. is the vector of connections weights between the neurons in the hidden layer and the output node. Both and are considered augmented by including bias weight components. The output signal of the th neuron from the hidden layer and the output signal of the controller can be defined as The MFNN-based controller is assumed to operate within an adaptive control scheme, the general structure of which is presented in Fig. 1, [10]. It has to be noted that although, for simplicity, the controller in Fig. 1 is depicted as having two inputs only, depending on the design strategy implemented, it may have more inputs. A VSS-based learning algorithm is applied to the controller. The sliding surface for the system under control and the zero adaptive learning error level for the MFNN-based controller are defined as and, respectively, with being a constant determining the slope of the sliding surface. The desired control input, which is generally unknown, is denoted with. The sliding manifold for the system to be controlled is adopted as a first-order mode based on the assumption that the dynamics of the system under control (the electric drive) can be modeled using second-order differential equation [20], [21]. (1) (2)

TOPALOV et al.: SLIDING MODE NEURO-ADAPTIVE CONTROL OF ELECTRIC DRIVES 673 The input vector of the MFNN-based controller and its time derivative are assumed to be bounded, i.e., and with and being known positive constants. Due to the physical constraints, it is also assumed that the magnitude of all vectors row constituting the matrix and the elements of the vector are bounded, i.e., and for some known constants and, where. The desired control input and its time derivative are considered also as bounded signals, i.e.,,, where and are positive constants. Definition 2.1: A sliding motion is said to exist on a sliding surface, after a hitting time if the condition is satisfied for all in some nontrivial semi-open subinterval of time of the form. Theorem 2.1: If the adaptation law for the controller parameters and is chosen, respectively, as (5) where,, is the derivative of the neurons activation function, and corresponds to its maximum value. The inequality (5) means that the controlled trajectories of the learning error level converge to zero in a stable manner. It will now be shown that such a convergence takes place in finite time. Let us consider the differential equation that is satisfied by the controlled learning error trajectories which is as follows: (3) with being sufficiently large positive constant satisfying then, given an arbitrary initial condition, the learning error converges to zero in a finite-time estimated by (4) and a sliding motion is sustained on for all. Proof 2.1: Consider as a Lyapunov function candidate. Then, differentiating yields For any, the solution of this equation, with initial condition at satisfies (6) (7) At time, the solution takes zero value, and therefore (8)

674 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007 By multiplying both sides of the equation with, the estimate of in (4) can be obtained using the inequality (9) III. RELATION BETWEEN THE SLIDING MODE CONTROL OF THE PLANT AND SLIDING MODE LEARNING OF THE NEURAL CONTROLLER The differential relation between the sliding line and the zero adaptive learning error level may be specified by the following general equation: Obviously, for all times sliding mode controller gain (9), taking into account the chosen in (3), it follows from (5) that: (11) The values of the integers and characterizing the relation are difficult to obtain if the system dynamics is unknown. If assumed that then, qualitatively, this means that if the value of tends to zero, goes to zero too. On the physical level, the controlled system will achieve perfect tracking because the controller produces the desired control inputs or vice versa. It will also be true that if the learning error vector is getting away from the origin, that is begins to increase in magnitude, the corresponding divergent behavior in will take place or vice versa. Let us then analyze the following three conditions that the function must satisfy [10]. 1) Region Condition: The desired control input must drive the state tracking error of the controlled plant to the sliding manifold. This means that as the control input approaches its desired value for the current conditions, the plant state tracking error vector is driven toward the sliding manifold (12) (10) The two equivalent limits and their consequences can be rewritten as follows: (13) and a sliding motion exists on for. As it has been already mentioned, the desired control input signal is generally unavailable and this consists the main problem in applying directly the presented learning algorithm to the MFNN-based controller. If the command error is not available, cannot be constructed. To overcome this difficulty several different approaches can be implemented. 1) A forward NN plant predictive model may be used, as in [13] and [14], to calculate the predicted command error named as the virtual error of the control input. 2) The well-known feedback-error-learning approach which is based on the parallel work of a neural, plus a secondary proportional plus derivative (PD) controller offers another possibility which has been investigated in [15]. The PD controller is provided both as an ordinary feedback controller to guarantee global asymptotic stability in compact space and as an inverse reference model of the response of the system under control. 3) Different approach, which is characterized with a decrease of the computational burden and is based on an existing relation between the and, has been initially proposed in [10] for training of ADALINE neural controllers. The third approach is further extended and applied to the sliding mode learning of the MFNN-based controller in this investigation. From the above statements it follows that following condition: (14) must satisfy the (15) After analyzing the signs of and on the different sides of line, it follows also that the relation must satisfy the requirement (16) 2) Compatibility Condition: The tracking performance of the feedback control system can be analyzed by introducing the following Lyapunov function candidate: (17) It is to be noted that a similar Lyapunov function has been introduced for the controller performance evaluation. Evidently, only the choice of a relation leading to a simultaneous minimization of both Lyapunov functions introduced can

TOPALOV et al.: SLIDING MODE NEURO-ADAPTIVE CONTROL OF ELECTRIC DRIVES 675 be considered suitable since, otherwise at least one of the design objectives will be violated. 3) Invertibility Condition: Let us consider a family of lines drawn in accordance with the equation for different. Obviously, the tracking error vector will fall onto one of these subsets of the phase space at each instant of time. However, based on the relation between and, each line from this family corresponds to a different situation entailing different values. It may be also concluded that simultaneously with the increase of the amplitude of, the magnitude of must also increase, because of the increasing distance to the sliding line. Consequently, the relation must be invertible, or for. The above three conditions clearly specify that, in order to achieve simultaneous minimization of the two quadratic functions and, the relation must be such to perform a mapping between their horizontal axes. Theorem 3.1: If the adaptation strategy for the adjustable parameters of the MFNN-based controller is selected as in equation (3), choosing any continuous, monotonically increasing function to serve as a relation, satisfying the conditions 3.1 3.3, will ensure the negative definiteness of the time derivative of the Lyapunov function in (17). Proof 3.1: Evaluating the time derivative of the Lyapunov function in (17) yields TABLE I PMSM NAMEPLATE In the above, the invertibility condition is used to rewrite the argument of the Lyapunov function. The partial derivative is positive due to the monotonically increasing behavior of the relation, and since is defined on the first and the third quadrants of versus coordinate system. Evidently from (18), an equivalence between the sliding mode control of the plant and the sliding mode adaptive learning inside the MFNN-based controller will have place. The obtained result means that, assuming the sliding mode control task is achievable, using the adaptation law of (3) together with relation, satisfying the conditions 3.1 3.3 enforces the desired reaching mode followed by a sliding regime for the system under control. It is straightforward to prove that the hitting occurs in finite time (see Proof 2.1). IV. EXPERIMENTAL RESULTS (18) In this section, results from experimental studies are presented aiming to prove the performance of the MFNN-based control structure with sliding mode learning as a speed controller for electric motor drives in the presence of very demanding nonlinear disturbances. The experimental setup is made up of a 350 W three-phase PMSM (whose nameplate data are presented in Table I), a threephase inverter, and a dspace DS1103 controller board which has been designed for rapid prototyping of real-time control systems and is fully programmable in Matlab/Simulink environment through real-time workshop (RTW). The speed sensor is an incremental encoder, while two Hall-effect transducers are used for current feedback. The speed controller has been implemented with a Simulink block diagram using a sampling time of 0.2 ms. The dspace code generator compiles the Simulink program and the real-time executable code is then downloaded to the DSP memory. During motor operation, the DSP receives the feedback from the encoder and commands the appropriate control action to the inverter. The code of the implemented MFNNbased speed controller takes up a very small part of the DSP memory and can be, therefore, simply embedded in an industrial drive without any extra hardware. The design of user friendly control panels and virtual instruments for online monitoring and parameter tuning has been realized with Control Desk.

676 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007 control replaces the corrective one when the system is inside this layer. Since when applying the second method a finite steady-state error would always exist, most of the approaches use the saturation or the sigmoid function to replace the sign function. In order to reduce the chattering effect in the sliding mode, the function in (20) has been used in this investigation instead of the sign function in the dynamic strategy described in (3) (20) Fig. 2. Control architecture for vector control strategy. In this study, a three-layer feedforward NN with one hidden layer of hyperbolic tangent neurons and a linear scalar output layer is employed. The input of the neural controller has been chosen to be identical to a conventional PD controller. In this perspective, no biases are used so that the output depends on the chosen inputs only. In order to show that the existence of a priori knowledge about the NN configuration is not essential, every experiment has been carried out with all the network weights initialized to random values. Several tests have been conducted to choose the parameters of the neural controller, i.e., number of neurons in the hidden layer and the design parameter, aiming at reaching the simplest configuration to alleviate the computational costs and to shorten the design stage. Thanks to the remarkable speed of learning of the proposed algorithm, even only one hidden neuron is enough to guarantee good results. The parameter has been chosen with a trial and error procedure, but there is no need for fine tuning. It is sufficient to gradually increment it to increase the dynamic response of the network until rotor speed oscillations start appearing. As a general rule of thumb, if the feedback error is big, the network should adapt more quickly so a higher value of is needed, whereas if oscillations around the set-point arise, the network is adapting too fast and the value of should be reduced. Based on the tracking error, first the value of is evaluated and this quantity is passed through the function to get the value of, which is used in the dynamic adjustment mechanism. In evaluating the value of the quantity, the slope parameter of the switching line has been set to 40. As the relation, the following selection is made parallel to the conditions discussed in the third section (19) The adopted relation has been previously successfully applied in [7] and [10]. It is well-known that sliding mode control suffers from high-frequency oscillations in the control input, which are called chattering. Chattering is undesired because it may excite the high-frequency response of the system. The common methods to eliminate the chattering are usually classified into two groups [19]: 1) Using a saturation function to replace the sign function. 2) Inserting a boundary layer so an equivalent A. Speed Control of a PMSM In Fig. 2, the block diagram of a vector controlled PMSM is shown. The structure of the control scheme is based on the dynamic equations of the motor in the rotor flux reference frame ( ) [20]. The flux and the torque of the motor are separately controlled by the references and. For the PMSM, the zero-direct-axis-current strategy is used to operate up to the rated speed [21]. In this condition, the PMSM behaves like a DC motor in which the main flux is provided by the permanent magnets and the armature current corresponds to [20]. The electromagnetic torque produced is given by, where is the torque constant. The MFNN-based speed controller using the speed and acceleration feedbacks and together with their references and, is in charge to give the reference that forces actual speed to the reference one. The stator current references, set to zero and, are directly impressed by the action of the built-in control of the inverter that uses as feedbacks the rotor position, and the stator currents and. B. Low- and High-Speed Test The experimental setup used for all the experiments is shown in Fig. 3. Fig. 4 shows the speed and torque response in p.u. to this test. In order to provide a nonlinear disturbance, a second controlled PMSM motor is mechanically coupled to the first. The second PMSM is torque-controlled by a standard PI-based control system, and the torque-load reference is chosen equal to (21) where is the rotor speed, and are the rated speed and torque (Table I), and finally, is initially set equal to 1.1. It means that when the motor operates at the rated speed, the load torque will be 10% more than the rated torque. The idea is to stress the motor and its controller with a nonlinear varying load that slightly exceeds the normal working conditions. At s, the speed reference is set to 20% of the rated speed. After a short-time interval equal to 0.015 s, in which the NN parameters are initially adapted and the static friction is overcome, the speed starts changing. After the first steady-state, at s, a second speed command is given to reach the rated speed. As the speed response shows (Fig. 4), the overshoots, the transients, and the ripple in steady-state are negligible, proving that the controller ensures high rate of convergence of the rotor speed to the reference speed despite the changing operating conditions.

TOPALOV et al.: SLIDING MODE NEURO-ADAPTIVE CONTROL OF ELECTRIC DRIVES 677 Fig. 6. Speed and torque response to the speed-reversal test with k =1:1. Fig. 3. Experimental setup. Fig. 4. Speed and torque response of the vector-controlled PMSM. Fig. 7. Speed and torque response to the speed-reversal test with k =1:6. Fig. 5. Phase space behavior. Fig. 4 also highlights a satisfactory behavior of the motor in terms of torque response. Both the two speed steps do not cause large oscillations of the torque. After the smooth peak between 0.15 and 0.22 s (first transient), the torque is close to zero due to the very low torque-load at low speed (see (21)). The motor performances are also satisfactory in response to the second step input, despite a 10% extra load during the steady-state. In order to analyze into details the behavior of the control system, Fig. 5 shows the trajectory of the state in the plane with during the same experiment of Fig. 4 together with the sliding line. For sake of clarity, just the second transient is reported and both error and its derivative are expressed in per unit. Before the speed step, between 0.65 and 0.75 s, the system is in steady-state and both error and its derivative are close to zero, and the working point is indicated with (1) in Fig. 5. Due to the applied step input, the error increases, its derivative has a pulse, and after a sampling period the point moves to (2). Then, the acceleration (and the absolute value of the speed error) increases and reaches its maximum value in s (point (3) in Fig. 5). From now on the state moves towards the sliding line with maximum acceleration and reaches it in (4). From sto s the state moves on the sliding line until the speed reaches the set-point. Note that the time needed to reach the sliding line is limited by the maximum acceleration of the drive. C. Speed Reversal Test This subsection shows the results given by the proposed control to two reversal speed tests, in order to again evaluate the neural controller in very demanding conditions.

678 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 1, FEBRUARY 2007 The speed and torque responses to the first test are shown in Fig. 6. While the motor is at the rated speed, after 0.15 s, the full-speed reversal is commanded, i.e., plus/minus rated speed. The speed reversal is repeated at s. It has to be noted that the reversals are performed with the nonlinear disturbance previously used, (21) with. As shown in Fig. 6, the motor operates the reversal in about 0.3 s with negligible overshoot and ripple; moreover, the motor crosses the zero-speed condition without being influenced by static friction. Also, this demanding test does not cause oscillation in the torque response. In order to further prove the effectiveness of the proposed solution, the speed reversal test has been repeated with a greater torque load, specifically (21) with. It means that when the motor operates at the rated speed the load torque is 60% more than the rated torque. In spite of this very demanding nonlinear load, the reversals are well performed, as shown in Fig. 7. The authors underline that this work aims at experimentally validating the theory discussed above. It means that, at the present stage of our research, a PI-based control system after a time-consuming calibration can be optimized to outperform our neural controller, but this supposes that the motor parameters, as well as the load, are known. On the contrary, the proposed neural controller does not use any a priori knowledge of the plant, consequently, it can also be used with different motors and different operating conditions without any tuning. V. CONCLUSION This paper discusses the main characteristics and the potentialities of a MFNN-based controller, perpetually trained online with an algorithm based on the VSS theory. Its performance has been evaluated in the speed control of electric drives. The experimental results obtained indicate that the proposed NN-based controller possess a number of interesting features, namely: good performances in several operating conditions without requiring any information about the parameters of the electric drive; high speed of convergence of the algorithm that does not need an initial setup stage before being applied to the actual system; no need for a priori knowledge of the desired output of the NN for the adaptation process; possibility of implementation on low-cost microcontrollers; no skilled operator required for the tuning and maintenance stage. REFERENCES [1] K. S. Narendra and K. Parthasarathy, Identification and control of dynamical systems using neural networks, IEEE Trans. Neural Netw., vol. 1, no. 1, pp. 4 27, Mar. 1990. [2] M. O. Efe and O. Kaynak, Stabilizing and robustifying the learning mechanisms of artificial neural networks in control engineering applications, Int. J. Intell. Syst., vol. 15, no. 5, pp. 365 388, 2000. 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Yu, Neuro-sliding mode control with its applications to seesaw systems, IEEE Trans. Neural Networks, vol. 15, no. 1, pp. 124 134, Jan. 2004. [8] H. Sira-Ramirez and E. Colina-Morles, A sliding mode strategy for adaptive learning in adalines, IEEE Trans..Circuits and Syst.-I: Fundamental Theory and Appl., vol. 42, no. 12, pp. 1001 1012, Dec. 1995. [9] X. Yu, M. Zhihong, and S. M. M. Rahman, Adaptive sliding mode approach for learning in a feedforward neural network, Neural Comput. Appl., vol. 7, pp. 289 294, 1998. [10] M. O. Efe, O. Kaynak, and X. Yu, Sliding mode control of a three degrees of freedom anthropoid robot by driving the controller parameters to an equivalent regime, ASME J. Dynamic Syst., Measur. Control, vol. 122, pp. 632 640, Dec. 2000. [11] G. G. Parma, B. R. Menezes, and A. P. Braga, Sliding mode algorithm for training multilayer artificial neural networks, Electron. Lett., vol. 34, no. 1, pp. 97 98, 1998. [12] N. G. Shakev, A. V. Topalov, and O. Kaynak, Sliding mode algorithm for on-line learning in analog multilayer feedforward neural networks, in Artificial Neural Networks and Neural Information Processing, Kaynak, Ed. et al. Berlin, Germany: Springer-Verlag, 2003, Lecture Notes in Computer Science, pp. 1064 1072. [13] A. V. Topalov and O. Kaynak, Online learning in adaptive neurocontrol schemes with a sliding mode algorithm, IEEE Trans. Syst., Man and Cybern. Part B, vol. 31, no. 3, pp. 445 450, Jun. 2001. [14], Neural network modeling and control of cement mills using a variable structure systems theory based on-line learning mechanism, J. Process Control, vol. 14, no. 5, pp. 581 589, 2004. [15], Neural network closed-loop control using sliding mode feedback-error-learning, in Neural Information ProcessingN. R. Pal, Ed. et al. Berlin, Germany: Springer-Verlag, 2004, vol. 3316, Lecture Notes in Computer Science, pp. 269 274. [16] M. L. Minsky and S. A. Pappert, Perceptrons. Cambridge, MA: MIT Press, 1969. [17] A. Rubaai, R. Kotaru, and D. M. Kankam, A continually online-trained neural network controller for brushless DC motor drives, IEEE Trans. Ind. Appl., vol. 36, no. 2, pp. 475 483, Mar./Apr. 2000. [18] Y. Yi, D. M. Vilathgamuwa, and M. A. Rahman, Implementation of an artificial-neural-network-based real-time adaptive controller for an interior permanent-magnet motor drive, IEEE Trans. Ind. Appl., vol. 39, no. 1, pp. 96 104, Jan./Feb. 2003. [19] J. Slotine and W. Li, Applied Nonlinear Control. Englewood Cliffs, NJ: Prentice-Hall, 1991. [20] W. Leonhard, Control of Electrical Drives. Berlin, Germany: Springer Verlag, 1985. [21] R. Krishnan, Electric Motor Drives: Modeling Analysis and Control. Englewood Cliffs, NJ: Prentice-Hall, 2001. Andon Venelinov Topalov (M 02) received the M.Sc. degree in control engineering from the Faculty of Information Systems, Technologies and Automation, Moscow State University of Civil Engineering (MGGU), Moscow, Russia, in 1979 and the Ph.D. degree in control engineering from the Department of Automation and Remote Control, Moscow State Mining University (MGSU), Moscow, in 1984. From 1985 to 1986, he was a Research Fellow in the Research Institute for Electronic Equipment, ZZU AD, Plovdiv, Bulgaria. In 1986, he joined the Department of Control Systems, Technical University of Sofia, Plovdiv, where he is presently an Associate Professor. He has held long-term visiting Professor/Scholar positions at various institutions in South Korea, Turkey, Mexico, Greece, Belgium, U.K., and Germany. He has coauthored one book and authored or coauthored more than 70 research papers in conference proceedings and journals. His current research interests are in the fields of intelligent control and robotics.

TOPALOV et al.: SLIDING MODE NEURO-ADAPTIVE CONTROL OF ELECTRIC DRIVES 679 Giuseppe Leonardo Cascella (S 96 M 96) was born in Bari, Italy, in September 1975. He received the Laurea degree (Honors) and the Ph.D. degree in electrical engineering from the Technical University of Bari, Bari, Italy, in 2001 and 2005, respectively. In 2003, he was awarded the Marie Curie Fellowship at the School of Electrical and Electronic Engineering, University of Nottingham, Nottingham, U.K., where he worked for one year on the research project Self-Commissioning of Electric Drives with Genetic Algorithms. Currently, he is Research Assistant with the Converters, Electrical Machines and Drives Research Group, Technical University of Bari, and his main interests include modeling and control of electromechanical systems and machine vision. Francesco Cupertino was born in Italy in December 1972. He received the Laurea degree and the Ph.D. degree in electrical engineering from the Technical University of Bari, Bari, Italy, in 1997 and 2001, respectively. From 1999 to 2000, he was with the PEMC Research Group, University of Nottingham, Nottingham, U.K. Since July 2002, he has been an Assistant Professor at the Department of Electrical and Electronic Engineerin, Technical University of Bari. He teaches several courses in electrical drives at the Technical University of Bari. He is the author or coauthor of more than 50 scientific papers on these topics. His main research interests cover the intelligent motion control and fault diagnosis of electrical machines. He is the author or coauthor of more than 50 scientific papers on these topics. Vincenzo Giordano was born in Bari, Italy, in 1977. He received the M.S. degree (Honors) in electrical engineering and the Ph.D. degree in control engineering from the Polytechnic of Bari, Bari, in 2001 and 2005, respectively. In 2004, he was a Visiting Ph.D. student with the Automation and Robotics Research Institute, University of Texas, Arlington, under the supervision of Prof. F. Lewis. In 2005, he was a Visiting Researcher with the Singapore Institute of Manufacturing Technology, Singapore. As a Ph.D. student, he was co-responsible for the organization and startup of the Robotics Laboratory at the Polytechnic of Bari. He has published more than 20 international journal and conference papers. His research interests include intelligent control techniques applied to industrial automation, robotics, and discrete-event systems. Okyay Kaynak (SM 90-F 03) received the B.Sc. degree with (First Class Honors) and the Ph.D. degree in electronic and electrical engineering from the University of Birmingham, Birmingham, U.K., in 1969 and 1972, respectively. From 1972 to 1979, he held various positions within the industry. In 1979, he joined the Department of Electrical and Electronics Engineering, Bogazici University, Istanbul, Turkey, where he is presently a Full Professor. He has served as the Chairman of the Computer Engineering and the Electrical and Electronic Engineering Departments and as the Director of the Biomedical Engineering Institute, Bogazici University. Currently, he is the UNESCO Chair on Mechatronics and the Director of the Mechatronics Research and Application Centre. He has held long-term (near to or more than a year) Visiting Professor/Scholar positions at various institutions in Japan, Germany, the U.S., and Singapore. His current research interests are in the fields of intelligent control and mechatronics. He has authored three books and edited five and authored or coauthored more than 200 papers that have appeared in various journals and conference proceedings. Dr. Kaynak has served as the President of the IEEE Industrial Electronics Society (2002 2003) and as an Associate Editor of both the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS and the IEEE TRANSACTIONS ON NEURAL NETWORKS. He is now the Editor-in-Chief of the IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS. Additionally, he is on the Editorial or Advisory Boards of a number of scholarly journals.