Model Reference Adaptive Control of Piezoelectric Actuators with Stochastic Disturbances under Gain Adjustment

Piezoelectric actuators have the characteristic of high displacement resolution and are widely used as actuators in precision positioning systems. However, due to the effects of hysteresis nonlinearity, creep, and stochastic disturbance on piezoelectric actuators, the stability and positioning accuracy of the output are difficult to achieve. In this research, a new model reference adaptive control method is proposed for controlling the output displacement of piezoelectric actuators with external and stochastic disturbances. This method establishes a stochastic nonlinear closed-loop control system with computational adaptive gain adjustment by introducing Lyapunov function and adaptive update law. The proposed adaptive structure is innovative in terms of the probability boundedness of the output of the piezoelectric actuator and the mean square convergence of the tracking error between the output and the reference model output. In addition, the proposed method only requires an understanding of the boundedness of uncertain disturbances and stochastic noise intensity. The simulation results demonstrate the effectiveness and superiority of the designed adaptive gain regulator.