Characterization modeling and H∞ control of n-DOF Piezoelectric actuators : Application to a 3-DOF precise positioner

This paper deals with the characterization, the modeling and the closedloop control of multivariable piezoelectric actuators, with an application to a 3-DOF piezoelectric tube scanner, widely used in precise positioning. These actuators are typified by hysteresis and creep nonlinearities, badly damped oscillation and strong couplings between their axis. First, during the modeling, we propose to decouple the system and to use a linear model where the couplings and the two nonlinearities are integrated through an external fictive disturbance. From the obtained monovariable systems, monovariable H∞ controllers are calculated by using specifications based on model approximation. The experimental tests demonstrate the efficiency of the method to reject simultaneously the couplings, hysteresis, creep and badly damped oscillations. Furthermore, the bandwidth of the closed-loop and the open-loop systems are compared and the results show that the proposed control technique allows to achieve a convenient closed-loop bandwidth and precision for all the axis of the precise positioner.