Finite-Time Control for Piezoelectric Actuators With a High-Order Terminal Sliding Mode Enhanced Hysteresis Observer

Xin Che,Rui Xu,Ping Jia,Dapeng Tian

doi:10.1109/access.2020.3044188

Abstract

Piezoelectric actuators (PZTs) are essential elements in high-precision systems. However, the hysteresis nonlinearity introduced by PZTs degrades the control accuracy. In this paper, a high-order terminal sliding mode enhanced hysteresis observer is designed, which compensates the error between the Bouc-Wen model and the actual hysteresis. Subsequently, a novel terminal sliding mode control (TSMC) is proposed. Unlike the conventional TSMC, the novel TSMC method makes the tracking error in the sliding mode converge to the origin within a finite time regardless of the initial conditions, which improves the performance of conventional TSMC. The stability of the proposed control method is verified through the Lyapunov theory. Finally, simulations and experiments are implemented to validate the effectiveness of the proposed control method. Experimental results demonstrate that the proposed method has a more superior performance than conventional TSMC.

Highlights

P IEZOELECTRIC actuators (PZTs) have become one of the key components in various precision engineering applications, such as atomic force microscopy [1], tilting mirrors [2], biological micromanipulation [3], and highprecision manufacturing machines [4]
A high-order terminal sliding mode enhanced hysteresis observer which compensates the error between the hysteresis model and the actual hysteresis is devised in this paper to improve the control accuracy of the PZT system
The chattering of high-order terminal sliding mode is reduced using an integral function; 2) A novel terminal sliding mode surface is proposed, which can provide a finite-time convergence, and makes the tracking error in the sliding mode converge to the origin within a maximum settling time regardless of the initial conditions; 3) The stability of the combined controller is analyzed using the Lyapunov stability theory; and the tracking performance of the resulting control system as compared to that of the conventional terminal sliding mode control (TSMC) and the novel TSMC is demonstrated by experimental investigations on a PZT driven tip/tilt platform

Summary

INTRODUCTION

P IEZOELECTRIC actuators (PZTs) have become one of the key components in various precision engineering applications, such as atomic force microscopy [1], tilting mirrors [2], biological micromanipulation [3], and highprecision manufacturing machines [4]. A high-order terminal sliding mode enhanced hysteresis observer which compensates the error between the hysteresis model and the actual hysteresis is devised in this paper to improve the control accuracy of the PZT system. The chattering of high-order terminal sliding mode is reduced using an integral function; 2) A novel terminal sliding mode surface is proposed, which can provide a finite-time convergence, and makes the tracking error in the sliding mode converge to the origin within a maximum settling time regardless of the initial conditions; 3) The stability of the combined controller is analyzed using the Lyapunov stability theory; and the tracking performance of the resulting control system as compared to that of the conventional TSMC and the novel TSMC is demonstrated by experimental investigations on a PZT driven tip/tilt platform.

CONVENTIONAL TSMC DESIGN

HYSTERESIS OBSERVER DESIGN

NOVEL TSMC DESIGN

SIMULATION RESULTS

CONCLUSION AND FUTURE WORKS