Model-independent Nonlinear Control For Piezoelectric Actuator

Piezoelectric ceramic actuator is widely used in all kinds of ultra-precision motion control workplaces because of its advantages of high positioning resolution,fast response speed,small volume,light weight and low cost,and can provide high-precision nano-scale motion.However,the nonlinear hysteresis effect of piezoelectric ceramic actuators will lead to large positioning error of the system,limit the ultra-precision micron-scale movement of the system,and even cause instability of the system.In order to reduce the influence of nonlinear hysteresis effect on piezoelectric ceramic actuator system and improve the accuracy of piezoelectric ceramic actuator in practical application,it is necessary to suppress the nonlinear hysteresis effect to achieve precise control.However,it is difficult to obtain the accurate model of piezoelectric actuator system and nonlinear hysteresis effect,so it is of great practical significance to design a controller that is not based on piezoelectric actuator model and achieve higher control accuracy.In order to suppress the nonlinear hysteresis effect and realize the precise control of the piezoelectric actuator system,three model-free kinds of nonlinear controllers without reference to piezoelectric actuator and hyteresis models are proposed in this thesis.Firstly,to fascilitate the control design and analysis,the piezoelectric actuator system model is transformed appropriately.Then,a model-independent sliding mode nonlinear PID(NPID)control method without involvement of piezoelectric actuator system model and hysteresis model is proposed.Subsequently,a finite-time nonlinear continuous PID(FPID)controller which is not based on piezoelectric ceramic actuator system model and hysteresis model is proposed,which further shortens the transition process of the system.Finally,an inputconstrained nonlinear saturated PID(SPID)controller which is not based on piezoelectric ceramic actuator system model and hysteresis model is proposed,which solves the effect of actuator saturation on the system control performance in practical applications.By applying Lyapunov stability theory and nonlinear system homogeneity technique,it is proved that the resulted three closed-loop systems has global asymptotic stability and finite-time boundedness,respectively.Using Matlab software,numerical simulation and comparisons with the control methods in the literatures are performed to show the effectiveness and improved performance of the proposed approaches.The proposed three control methods all have the advantages of not based on system model for controller design and easy engineering implementation.It provides a simple control strategy for fast and accurate position control and trajectory tracking of a large class of piezoelectric ceramic actuator systems.In particular,the finally proposed SPID control has a well-defined upper limit.By selecting the controller parameters that meet certain conditions,the saturation of the driver can be effectively avoided,and the motion control problem when the input of the piezoelectric ceramic actuator system is limited can be solved.