Bifurcation Mechanism And Chaos Of Permanent Magnet Synchronous Motor Research On Control Strategy

Permanent magnet synchronous motor has been widely used in power transmission,electric vehicles,aerospace and other speed control systems because of its simple structure,small weight and high output power.However,the permanent magnet synchronous motor(PMSM)will appear chaotic behavior under certain working conditions and parameters,and the chaotic behavior in the system is one of the reasons leading to the instability of the motor during normal operation.Aiming at the bifurcation behavior of the system,this paper will study the bifurcation behavior of the equilibrium point of the system under other external input conditions on the basis of zero external input,and further study the preconditions for the system to produce chaos.Aiming at the chaotic behavior of the system,this paper introduces the finite time control theory and designs a finite time controller to control the chaotic behavior of the system.The simulation results show that the state variables of the system can converge to the expected value more quickly after adding the finite time controller.In this paper,the bifurcation characteristics and finite time control of PMSM chaotic system are studied.1)Firstly,it introduces the background of the research and the development of chaos theory.Secondly,the development and research status of bifurcation theory are introduced.It is specifically explained that with the change of bifurcation parameters,the equilibrium state of the system will change,and even the topological structure will change,which will eventually lead to chaos.Finally,the research of chaos control,the application direction of chaos control,some methods of controlling chaos of PMSM and the development of finite time control are introduced.2)Secondly,the basic characteristics of system bifurcation are studied.It is shown that the generation of Hopf bifurcation is an important condition for the chaotic behavior of the system.The equilibrium point of the system will appear static bifurcation,Hopf bifurcation,period doubling bifurcation and chaotic behavior with the change of bifurcation parameters.Secondly,the basic characteristics and related concepts of chaos are studied,including its internal randomness,boundedness,sensitivity to initial value and small disturbance,phase space,attractor and strange attractor.Then the judgment conditions of chaotic behavior are studied,including phase space observation method and Lyapunov exponent method.Finally,the coordinate transformation of permanent magnet synchronous motor is studied,and the chaotic model of the motor is deduced,which provides conditions for analyzing the chaotic behavior of the system.3)Firstly,the equilibrium point of the chaotic system of permanent magnet synchronous motor(PMSM)with external inputu_d=u_q=T_L=0 is analyzed.By constructing the Jacobian matrix of the system,the equilibrium points of the system are analyzed in turn,and the eigenvalues are solved.The real part of the eigenvalue is compared with the size of 0 to judge whether the system is bifurcated.The external input u_d≠0,u_q=T_L=0 of the system is also analyzed The method is the same as the first case.Secondly,in the case of different bifurcation parameters,the trajectory of the system solution is simulated and analyzed.Finally,we judge whether the system has chaos by judging whether the value of Lyapunov exponent is greater than 0,and simulate the Lyapunov exponent of the system with different parameters.4)Fourth,according to the chaos phenomenon in the third chapter,the controller is designed and analyzed.Firstly,the non finite time controller is designed to control the chaotic system;Secondly,according to the finite time control theory,the finite time controller is designed.In order to make the system run stably in the predetermined trajectory under both control conditions,the expected value of the system is assumed,the coordinates of the system are transformed,and the transformed error system is obtained.The stability of the system is verified by constructing the Lyapunov function of the system,The simulation results show that the state variables of the system can converge to the expected value more quickly after the finite time control is added.