Intelligent Control Using the Wavelet Fuzzy CMAC Backstepping Control System for Two-Axis Linear Piezoelectric Ceramic Motor Drive Systems

This study aims to propose a more efficient control algorithm to achieve precision trajectory tracking control for a two-axis linear piezoelectric ceramic motor (LPCM). Since the inherent nonlinear nature and cross-coupling effect of a two-axis LPCM, its accurate model is difficult to obtain; thus, an intelligent adaptive wavelet fuzzy cerebellar model articulation controller backstepping (AWFCB) control system is designed to achieve high precision trajectory tracking control for a two-axis LPCM drive system. A novel wavelet fuzzy cerebellar model articulation controller (CMAC) is proposed in this paper; in some special cases, it can be reduced to a fuzzy system, a fuzzy neural network, a wavelet fuzzy neural network, or a conventional CMAC. The developed wavelet fuzzy CMAC incorporates the wavelet decomposition property and a fuzzy CMAC fast learning ability; thus, it is used for the LPCM control. In the AWFCB control system, a wavelet fuzzy CMAC is used to imitate an ideal backstepping controller, and a smooth compensator is designed to eliminate the residual of the approximation error between the wavelet fuzzy CMAC and the ideal backstepping controller. In order to guarantee the convergence of the tracking error, analytical methods using the Lyapunov function are utilized to derive the adaptation laws to tune the parameters of the control system online. Thus, the stability of the two-axis LPCM control system can be guaranteed. Finally, the experimental results show the precision of the trajectory tracking using AWFCB control. Compared with PID control and adaptive fuzzy sliding-mode control, the AWFCB control can achieve tracking error reduction of about 80%similar to 99% and 48%similar to 97%, respectively.