Modeling and analysis of chaotic behavior in switched reluctance motor drives

Abstract

In this paper, modeling and analysis of chaotic behavior in switched reluctance (SR) motor drives using voltage PWM regulation is presented. The key is to derive a PoincarP map that is based on the nonlinear flux linkage model. Its Jacobian matrix can be evaluated by solving the corresponding variational equation. Based on the Poinear4 map and its Jacobian matrix, the analysis of chaotic behavior is presented. Furthermore, bifurcation diagrams are also figured out. They facilitate to determine the stable range of various system parameters so as to avoid the occurrence of chaos. Both computer simulations and experimental measurements are given to verify the theoretical modeling and analysis. I. INTRODUCTJONIn recent years, switched reluctance (SR) motor drives have been recognized to have promising industrial applications. Their simplicity in both motor construction and power converter requircmcnt offers the prospect of low-cost fully controllable brushless motor drives [I]. Rccenrly. the research on SR motor drives has been focused on motor design, converter topology and control strategy. However, the itwestigation into the nonlinear dynamics, namely chaotic behavior, of SR motor drives has been surprisingly rare [2]. The major reason should be duc to the coniplexity of aiialytical formulation and high noiilinearities of SR motor drives.Chaos is a common phenomenon in power converters when they operate under feedback control [3]-[4]. Chaotic behavior in switching mode power supplies has been actively invcstigatcd for a number of years. Chaos in induction and brushless dc motor drivcs has also becn discussed [SI-[6]. Very recently, the nonlinear dynamics and chaotic behavior of industrial dc motor drives have been investigated, by using numerical simulation and analytical modeling [7]. It has been identified that the nonlinear dynamics of the dc motor drive system is mainly die to the switching nonlinearity caused by voltage PWM regulation. Although the SR motor drive using voltage PWM rcgulation operates like the dc motor drive. its nonlinear dynamics are much more complicated, hence more prone to chaos.The purpose of this paper is to develop the modeling of chaos in the SR motor drive, which includes the formulation of the system modeling, the derivation of the Poincari: map and its Jacobian matrix. Based on the Poincare map and its Jacobian inatnx, the analyses of periodic solutions and chaotic behavior are also discussed. In order to attain the insight of chaotic behavior, both time-domain waveforms and phaseplanc trajcctories arc investigated. Morcover. bifurcation diagrams are also figured out so as to dctcnnine stable regions ofthc system parameters.In Section 11, the system modeling of the SR motor drive using the voltage PWM regulation is presented. Thcn, the PoincarC map and its Jacobian matrix are derived in Section 111. Analysis of chaotic behavior and computer simulations are respectively discussed in Sections IV and V. Finally, experimental measurements are given to verify the theoretical modeling an...

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