| With the development of AC servo technology,permanent magnet synchronous motor(PMSM)is widely used in high-precision servo control because of its simple structure,small size,high efficiency and reliable operation.Friction is a kind of external disturbance existing in almost all servo systems,which is an important reason affecting the low-speed performance of servo systems.It is of great significance to analyze the friction characteristics and study the corresponding compensation methods.Firstly,the mathematical model of the system is established to analyze the influence of position sensor and differential velocity calculation on the system,as well as the nonlinear phenomenon caused by friction under common working conditions.Then the static and dynamic characteristics of friction are analyzed,and the effect of each characteristic in the system is studied.Aiming at the possible stick slip motion of the system at low speed,the system is equivalent to a mass spring damping system,the Stribeck function is linearized,and the conditions of stick slip are qualitatively analyzed and quantitatively calculated by using dimensionless method and phase plane method,so as to provide theoretical basis for eliminating low speed creep.In order to reduce the tracking error and improve the control accuracy,a modelbased friction compensation method is studied.The generalized Maxwell-slip(GMS)friction model is used to identify the parameters of pre sliding and sliding states.Considering that the fixed friction compensation can not deal with the problem of time-varying parameters,a piecewise adaptive control algorithm is proposed.The traditional adaptive control rate is designed based on the principle of deterministic equivalence,and the output error is integrated to estimate the parameters,which will reduce the closed-loop performance of the system.In order to improve the robustness of the control system,the adaptive law is designed according to the principle of immersion and invariance(I&I),and the global stability of the control method is proved by Lyapunov theorem.When the friction stiffness is large,the compensation method of feedforward control can not realize the complete decoupling of friction.To solve this problem,this paper proposes a nonlinear PID(NPID)control algorithm to suppress friction disturbance.Based on GMS model and gain scheduling technology,when the system is subjected to elastic friction,the integral control with high gain is adopted.When the system is subjected to plastic friction and sliding friction,the feedforward compensation combined with low gain feedback control is adopted.Based on the basic characteristics of friction,this method can improve the dynamic response of the system and reduce the tracking error while ensuring the global stability of the system.Finally,the experimental platform of PMSM low-speed servo based on STM32 microcontroller is built.Several important characteristics of friction are tested and friction parameters are identified.Compared with traditional PID control,fixed friction compensation and nonlinear PID control algorithm,the effectiveness of the proposed algorithm is verified under various conditions. |
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