Discrete Sliding-Mode Tracking Control of High-Displacement Piezoelectric Actuator Systems

We consider the modeling and control of a high-displacement piezoelectric actuator system (HDPAS). An HDPAS includes a multilayer LVPZT bender actuator (MLBA) and a low-pass filter. The MLBA is subject to hysteresis, bending modes, measurement noise, and external disturbance. Because the spillover associated with a reduced-order model of the MLBA has been known to have the potential to cause the instability of the closed-loop system, a low-pass filter is applied to reduce its effect. To obtain an acceptable model for the HDPAS, a band-limited input and its corresponding output are fed into a recursive least-squares parameter estimation scheme. The resulting model is then used for a controller design, which includes three features. First, a dead-beat to its filtered switching surface is achieved. Second, the $H∞$ norm of the sensitivity function between the filtered switching surface and the output disturbance is simultaneously minimized to attenuate the effect of output disturbance. Third, a switching control based on Lyapunov redesign is used to further improve the tracking accuracy. To demonstrate the effectiveness of the proposed control, the experimental results of the HDPAS by using the proposed control are compared with those by a proportional integral differential (PID) control.