The Study Of Controlling Chaos Of A Permanent Magnet Synchronous Motor

With the development of permanent magnetic materials and a reduction of its price, the use of the permanent magnet synchronous motor (PMSM) is becoming more and more widespread. The PMSM, however, is a nonlinear system with multi-variable and significant coupling. It can exhibit a variety of chaotic or limit cycle phenomenon under some choices of system parameters and external inputs. Chaos is an important part of the nonlinear field and an extremely active research front. As a specific mode of motion of the nonlinear dynamical system, chaos is ubiquitous and extremely complicated. Chaos of the PMSM has a strong impact on the process of production. Therefore, chaos analysis of the PMSM is of great practical significance.In this paper, first, the mathematical model of the PMSM under the synchronization reference frame is obtained according to the circuit philosophy and coordinate transformation. And then the chaotic model with two parameters is derived by affine transformation and time scaling. Its chaotic characteristics are analysed with respect to the phase trajectory, Lyapunov exponent, center manifold, the bifurcation diagram, the Poincare map and power spectrum. The results show that the PMSM has rich nonlinear characteristics.Second, the values of state variables are restricted to the allowable operating voltage range of circuit elements under the eligible scaling. Then a corresponding mimic channel is designed with the of circuit design software based on the basic circuit element such as integration circuit and operational circuit of differential ratio. When the results of circuit simulation and numerical simulation are the consistent, the actual analogue circuit is designed and the results are the same as simulation results. Once again, the realization of the circuit shows that the PMSM has rich nonlinear characteristics.Finally, several algorithms have been given such as the algorithm of state feedback control, the algorithm of delay feedback control, the control algorithm of differential geometry and the algorithm of adaptive control. When these algorithms apply to the PMSM control system, they are qualified with excellent control effect.