Trajectory tracking of large-displacement piezoelectric actuators using a nonlinear observer-based variable structure control

The trajectory tracking of a large-displacement piezoelectric actuator (LDPA) using a nonlinear observer-based variable structure control (VSC) was developed. A mechanism of amplification using a double lever was first designed, fabricated, and tested. Subsequently, a nonlinear model for the LDPA was verified by sinusoidal response and system knowledge. Because not all of the states of the nonlinear model were available, a nonlinear state observer was employed to estimate the state (e.g., velocity, hysteresis, excitation force, and its derivative). For tracking the trajectory dominant by a specific frequency, the reference model with desired amplitude and phase features was designed. The proposed control scheme contained a feedback linearization with variable structure controller, a reference model to assign the desired dynamics, and a nonlinear state observer to estimate the unavailable state. The VSC included the following two parts: equivalent control and switching control. The equivalent control using the signals from observer and reference model was constructed to obtain the desired control behavior. Due to the existence of hysteresis, disturbance, and estimation error, the tracking performance was often deprived. In this situation, the switching control was employed to ameliorate the robust performance. The stability of the overall system was then verified by Lyapunov stability theory so that the ultimately bounded tracking was accomplished. Experiments of the LDPA were carried out to verify the usefulness of the proposed control.