Modeling and control of piezoelectric stack actuators with hysteresis

Abstract

Piezoelectric actuators are popularly applied as actuators in high precision systems due to their small displacement resolution, fast response and simple construction. However, the hysteresis nonlinear behavior limits the dynamic modeling and tracking control of piezoelectric actuators. This thesis studies a dynamic model of a moving stage driven by piezoelectric stack actuator. The Bouc-Wen model is introduced and analyzed to express the nonlinear hysteresis term of the piezoelectric stack actuator, where the values of the parameters of the model have been taken from a previous work. The simulated results using MATLAB/Simulink demonstrate the existence of the hysteresis phenomenon between the input voltage and the output displacement of the piezoelectric stack actuator, and validate the correctness of the model. Moreover, a Luenberger observer is designed to estimate the hysteresis nonlinearity of the system, and then combined with the voltage input signal to form a Luenberger-based feedforward controller to control the displacement of the system. Furthermore, a Proportional-Integral-Derivative (PID) feedback controller is integrated with the feedforward controller to achieve more accurate output displacement, where the gains of the PID controller are optimized using Particle Swarm Optimization. Several performance index formulas have been studied to get the best solution of the PID’s gains. An Integral Time Squared Error plus Absolute Error performance index formula has been proposed to achieve zero overshoot and steady-state error. The simulated results accomplished using MATLAB/Simulink show the ability of the designed controllers to vastly reduce the amount of error of the output displacement and the response time of the system.