Robust H^∞ Control of Hysteresis in a Piezoelectric Stack Actuator¹

This paper describes an H^∞ control method for controlling hysteresis in a piezoelectric stack actuator. The actuator used is a high-performance monolithic multilayer piezoelectric stack actuator. The proposed control method involves the use of a capacitor in series with the piezoelectric actuator to provide a measured output voltage which is proportional to the charge on the piezoelectric actuator. The controller is designed based on a model of the hysteresis nonlinearity constructed using experimental data. The parameters in the nonlinear model of the system are obtained from the measurements on the piezoelectric actuator circuit. Our focus in this paper is to develop a tracking controller based on a charge output of the piezoelectric actuator system and to reduce the hysteresis nonlinearity. The paper considers a robust H^∞ tracking controller to control the piezoelectric actuator based on an uncertain system model. Experimental results show that the hysteresis can be significantly reduced and the measured output can closely track a 5 Hz sawtooth reference input signal when the H^∞ controller is used.