Lyapunov Redesign of Piezo-Actuator for Positioning Control

A Lyapunov redesign control method is proposed in this work to improve the positioning of a Piezo-electrical actuator. This scheme is usually used with nonlinear systems that have matched disturbances. This actuator has a hysteric nonlinearity and it is canceled by modeling and inserting its inversion in the forward path. However, some of the nonlinearity remains and can be modeled as a matched disturbance. This is further reduced by feedback control. The suggested method fits well with this class of nonlinearity. Furthermore, the stability of the closed-loop system is established because a Lyapunov function is part of the controller design. Simulations are provided with different trajectories to verify the effectiveness of this scheme. We also compared the results of the proposed method with other different methods.