The Chaos Model Of The Permanent-Magnet Synchronous Motor And Its Analysis And Control

In this paper, the chaotic phenomena in the permanent-magnet synchronous motor (PMSM) and its control are studied extensively. First of all, based on the chaos model of the PMSM being formulated, the center manifold theory and the method of normal forms are used to simplify the PMSM model. By its center manifold, analyses of the stability and bifurcation of the PMSM are carried on, and its normal form provides the simplest form for further theoretically studying.Secondly, in terms of Lyapunov stability theory, the Hopf bifurcation of the PMSM is studied, and the conditions that the system parameters must satisfy are derived so that the PMSM can exhibit different behavior, such as a limit cycle, Hopf bifurcation and chaos. Besides, the numerical algorithms for calculating Poincare map, Lyapunov exponents and capacity dimensions are also proposed for studying the chaotic characteristics of the PMSM.Thirdly, in the case of experiment, the methods of studying chaos in the PMSM are discussed. Using time series the space of phase of the PMSM is reconstructed, and its reconstructed space of phase has the same topological structure with the original one. The Poincare map, Lyapunov exponents and capacity dimensions are derived by time series.After doing the above works, the control and anti-control of chaos in PMSM are studied. The OGY method is reformulated and improved, and then used to stabilize the unstable periodic orbits embedded in the chaotic attractors in the PMSM. The entrainment and migration of the PMSM chaotic system are also studied. When chaos has been found to be useful and the PMSM system is originally nonchaotic or even stable, an anti-control of...