Analysis And Chaos Control Of PMSM-2R Manipulator With Nonlinear Coupled

The coupling system of mechanical,electrical and hydraulic energy domains is the development trend in modern industry,among which the electromechanical coupling system is the most widely used.Electromechanical coupling systems are usually composed of mechanisms driven by motors.Both the subsystems are usually non-linear,and chaos can occur under certain conditions.Since there are many parameters in a coupled electromechanical system,and there exist complex interactions between motor subsystem and mechanical subsystem,between power flows and between the variables of system,the dynamics characteristics and changes of power flows are more complex than that in sole energy domain system.In this paper,the coupling system of two strong non-linear systems of PMSM-2R manipulator is taken as the subject,and its mathematical model is established by using bond graph theory.The dynamics characteristics and power flows of the coupling system are studied through the coupling power variables between subsystems by means of phase diagram,time domain diagram,power spectrum and the max Lyapunov exponent.A synchronization control method is proposed to control the chaotic motion of the coupled system.The main research work and conclusions of this paper are as follows:1.Based on the theory of power conservation-based bond graph,the bond graph model of the PMSM-2R manipulator nonlinear coupling system is established.Further using the derivation rules of the bond graph,the mathematical model of the coupled system is obtained.Based on these models,the power flows between the subsystems and that internal each subsystem are analyzed.2.In analysis of power flows,P₁ and P₂ represent the output power of the motor and output power of the end link in 2R manipulator respectively.The results show that as effort,the load torque T_L,varies,the motion state and power flow of P₁ will interchange between periodic motion and chaotic motion;and as the flow,the speed of the motorω,varies,the motion state mechanical subsystem and power flow of P₂ will interchange between periodic motion and chaotic motion.And the change of power flow is consistent with the that of system motion,that is,when the system motion is periodic or chaotic,the power flow is correspondingly periodic and chaotic.The motion states of system are determined by the values of system parameters.3.since the nonlinear coupling system of PMSM-2R manipulator is a multi-parameter variable system,regression analysis method is used to analyze the significant degree of the coupling between inductance parameters of motor,the lengths and masses of each link on the power flow of the whole system.It is found that,compared with other parameters and their coupling effects,the coupling effect between the direct-axis inductance and the quadrature-axis inductance of PMSM has the most significant effect on the power state of the system.Based on the results of regression analysis,the chaotic edge of direct-axis inductance and the quadrature-axis inductance of PMSM is plotted,and in it the values of the parameters which will cause the chaotic motion are depicted.4.The synchronization theory is applied to design a controller,with which the coupled subsystem is controlled to a stable periodic motion simultaneously.