High Precision Discrete Sliding Mode Control Method For Piezoelectric Linear Motor

With the continuous advancement of science and technology,the demand for high-precision positioning systems in many technical fields is increasing.In bioengineering,medical engineering,integrated circuits,aerospace,optical fiber transmission,etc.,the demand for micro-and nano-level precision positioning and drive control technology is extremely urgent.Piezoelectric linear motor is a friction-coupled piezoelectric actuator that uses the inverse piezoelectric effect to convert electrical energy into mechanical energy.Through the friction between mechanical structures,the reciprocating motion of the elastic body is converted into the linear motion of the controlled object.At the same time,it has the characteristics of easy integration and miniaturization.The piezoelectric linear motor motion platform is a complex system with characteristics such as nonlinearity,easy resonance,rate correlation and hysteresis.The current control research mostly stays at the level of open loop,PID,etc.,and there is an urgent need for advanced and effective control strategies to achieve high Accurate trajectory tracking needs.This article first introduces the characteristics and classification of piezoelectric linear motors,and then summarizes the achievements of different scholars at home and abroad in the structural design and control schemes of this research object.The research in this paper is mainly divided into two aspects: one is to conduct open-loop characteristic test analysis,expected trajectory planning,and mathematical model identification of piezoelectric linear motors,and then to design a series correction link that can improve the dynamic performance of the system;the other is based on the identification Model,design an effective closed-loop controller so that the motor platform can achieve nanometer-level precision trajectory tracking.This article first conducts an open-loop characteristic test and analysis on the piezoelectric linear motor motion platform,and has an in-depth understanding of the motor’s mechanical stroke,operating mechanism and its own characteristics.In order to obtain the mathematical model of the motor to facilitate the design of the controller,a closed-loop frequency sweeping scheme with higher identification accuracy is selected to sweep the controlled object to obtain the amplitude-phase characteristic curve in the frequency domain,and the transfer function of the system is obtained through the amplitude-phase analysis.Then design a series correction feedback controller to improve the problem of low system bandwidth and poor dynamic performance.However,the series correction belongs to linear control,and the nonlinear suppression ability of the system is not strong.In order to solve the shortcomings of the series correction in the trajectory tracking experiment,such as poor steady-state and dynamic performance,this paper is based on the corrected system,and the selected structure is simple and robust.The robust PI-type discrete sliding mode surface design is based on a series-corrected discrete sliding mode controller(DSMC),and a Lyapunov function is constructed to prove the stability of the system.Finally,the design is verified on the built piezoelectric linear motor motion platform The effectiveness of the method,through trajectory tracking comparison experiments with traditional PID,series correction,etc.,verify that the tracking effect of the proposed controller is significantly better than traditional PID and series correction feedback control.Because DSMC chooses linear PI sliding mode surface,the trajectory tracking control of nonlinear system still has the problems of overshoot and large steady-state error.Therefore,this paper selects the nonlinear second-order terminal sliding mode surface with global convergence and less chattering phenomenon,and introduces a low-pass filter to improve the sliding mode surface,and designs a second-order terminal discrete sliding mode surface based on the low-pass filter.Mode controller(2-TDSMC).In addition,the stability of the system is proved based on the Lyapunov stability theorem.Different expected trajectory tracking experiments show that,compared with DSMC,the designed 2-TDSMC greatly reduces the overshoot and adjustment time of point-to-point single-step round-trip trajectory tracking,and the error index is reduced by a little when tracking the third-order S-curve trajectory.Times more.It proves that the proposed controller has a good effect on a precision motion platform with a piezoelectric linear motor as the core,and has certain application value.