adaptive control of pmsm systems with chaotic nature using lyapunov stability based feedback...

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International Journal of Innovative Computing, Information and Control ICIC International c °2009 ISSN 1349-4198 Volume 5, Number 2, February 2009 pp. 479—488 ADAPTIVE CONTROL OF PMSM SYSTEMS WITH CHAOTIC NATURE USING LYAPUNOV STABILITY BASED FEEDBACK LINEARIZATION Hyun Cheol Cho 1 , Kwon Soon Lee 1 and M. Sami Fadali 2 1 Department of Electrical Engineering Dong-A University 840 Saha-Gu, Hadan 2-Dong, Busan 604-714, Korea [email protected]; [email protected] 2 Department of Electrical Engineering University of Nevada Reno, NV 89557, USA [email protected] Received November 2007; revised April 2008 Abstract. Chaos in motor systems is undesirable in real-time implementation because it results in motor speed oscillations changes in steady-state torque. This paper presents an adaptive control approach for time-varying permanent-magnet synchronous motor (PMSM) systems with chaotic behavior. We consider bounded perturbations in the sys- tem parameters. First, we transform the nonlinear PMSM model to derive a nominal linear control strategy. Then, we design an auxiliary control to compensate for real-time control errors due to parameter changes using Lyapunov stability theory. We numeri- cally simulate our PMSM controller and demonstrate its eciency and reliability when compared to traditional controllers. Keywords: Adaptive control, PMSM, Chaos, Feedback linearization, Lyapunov stabil- ity 1. Introduction. Chaotic behavior of nonlinear motor systems can occur for certain ranges of their parameter values. Chaos yields unacceptable variations in output torque and oscillations in the motor speed. Consequently, we need control strategies to prevent chaos for satisfactory control performance in real-time implementations. Several strategies to reduce or eliminate chaos in motor systems have been proposed in the literature [1-5]. The most popular method for mitigating chaotic behavior in motor systems is due to Ott-Grebogi-Yorke (OGY) [2]. The method is robust in theory but a critical drawback is that it rarely yields a feasible parameter set in practical implementa- tion. In [1], the authors described bifurcation and chaos in PMSMs and its control. They used entrainment and migration control with the external torque as the manipulated vari- able to derive an exogenous input. Generally, using the torque as a manipulated variable is problematic because it imposes limitations in determining the initial conditions and the target. Ren et al. studied time-delay feedback control (TDFC) of chaos in PMSM [5] in which the direct axis and the quadrature axis stator voltages are used as manipulated variables without an exogenous force. In practice, it is dicult to estimate time delay for TDFC with a given target. More recently, nonlinear feedback control was utilized to overcome the disadvantages of TDFC [6]. The authors used the stator voltages as con- trol inputs with an approximate linearized system model. In [7] the authors utilized an extended Kalman lter estimation for state variables and stator’s resistance of induction motors, and employed virtual noise signals for compensating chaotic modeling error. 479

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Chaos in motor systems is undesirable in real-time implementation becauseit results in motor speed oscillations changes in steady-state torque. This paper presentsan adaptive control approach for time-varying permanent-magnet synchronous motor(PMSM) systems with chaotic behavior. We consider bounded perturbations in the systemparameters. First, we transform the nonlinear PMSM model to derive a nominallinear control strategy. Then, we design an auxiliary control to compensate for real-timecontrol errors due to parameter changes using Lyapunov stability theory. We numericallysimulate our PMSM controller and demonstrate its efficiency and reliability whencompared to traditional controllers.

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Page 1: ADAPTIVE CONTROL OF PMSM SYSTEMS WITH CHAOTIC NATURE USING LYAPUNOV STABILITY BASED FEEDBACK LINEARIZATION

International Journal of InnovativeComputing, Information and Control ICIC International c°2009 ISSN 1349-4198Volume 5, Number 2, February 2009 pp. 479—488

ADAPTIVE CONTROL OF PMSM SYSTEMS WITH CHAOTICNATURE USING LYAPUNOV STABILITY BASED

FEEDBACK LINEARIZATION

Hyun Cheol Cho1, Kwon Soon Lee1 and M. Sami Fadali2

1Department of Electrical EngineeringDong-A University

840 Saha-Gu, Hadan 2-Dong, Busan 604-714, [email protected]; [email protected]

2Department of Electrical EngineeringUniversity of NevadaReno, NV 89557, USA

[email protected]

Received November 2007; revised April 2008

Abstract. Chaos in motor systems is undesirable in real-time implementation becauseit results in motor speed oscillations changes in steady-state torque. This paper presentsan adaptive control approach for time-varying permanent-magnet synchronous motor(PMSM) systems with chaotic behavior. We consider bounded perturbations in the sys-tem parameters. First, we transform the nonlinear PMSM model to derive a nominallinear control strategy. Then, we design an auxiliary control to compensate for real-timecontrol errors due to parameter changes using Lyapunov stability theory. We numeri-cally simulate our PMSM controller and demonstrate its efficiency and reliability whencompared to traditional controllers.Keywords: Adaptive control, PMSM, Chaos, Feedback linearization, Lyapunov stabil-ity

1. Introduction. Chaotic behavior of nonlinear motor systems can occur for certainranges of their parameter values. Chaos yields unacceptable variations in output torqueand oscillations in the motor speed. Consequently, we need control strategies to preventchaos for satisfactory control performance in real-time implementations.Several strategies to reduce or eliminate chaos in motor systems have been proposed in

the literature [1-5]. The most popular method for mitigating chaotic behavior in motorsystems is due to Ott-Grebogi-Yorke (OGY) [2]. The method is robust in theory but acritical drawback is that it rarely yields a feasible parameter set in practical implementa-tion. In [1], the authors described bifurcation and chaos in PMSMs and its control. Theyused entrainment and migration control with the external torque as the manipulated vari-able to derive an exogenous input. Generally, using the torque as a manipulated variableis problematic because it imposes limitations in determining the initial conditions andthe target. Ren et al. studied time-delay feedback control (TDFC) of chaos in PMSM [5]in which the direct axis and the quadrature axis stator voltages are used as manipulatedvariables without an exogenous force. In practice, it is difficult to estimate time delayfor TDFC with a given target. More recently, nonlinear feedback control was utilized toovercome the disadvantages of TDFC [6]. The authors used the stator voltages as con-trol inputs with an approximate linearized system model. In [7] the authors utilized anextended Kalman filter estimation for state variables and stator’s resistance of inductionmotors, and employed virtual noise signals for compensating chaotic modeling error.

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