Adaptive wavelet neural network control with hysteresis estimation for piezo-positioning mechanism

An adaptive wavelet neural network (AWNN) control with hysteresis estimation is proposed in this study to improve the control performance of a piezo-positioning mechanism, which is always severely deteriorated due to hysteresis effect. First, the control system configuration of the piezo-positioning mechanism is introduced. Then, a new hysteretic model by integrating a modified hysteresis friction force function is proposed to represent the dynamics of the overall piezo-positioning mechanism. According to this developed dynamics, an AWNN controller with hysteresis estimation is proposed. In the proposed AWNN controller, a wavelet neural network (WNN) with accurate approximation capability is employed to approximate the part of the unknown function in the proposed dynamics of the piezo-positioning mechanism, and a robust compensator is proposed to confront the lumped uncertainty that comprises the inevitable approximation errors due to finite number of wavelet basis functions and disturbances, optimal parameter vectors, and higher order terms in Taylor series. Moreover, adaptive learning algorithms for the online learning of the parameters of the WNN are derived based on the Lyapunov stability theorem. Finally, the command tracking performance and the robustness to external load disturbance of the proposed AWNN control system are illustrated by some experimental results.