Intelligent complementary sliding-mode control for lusms-based X-Y-θ motion control stage

An intelligent complementary sliding-mode control (ICSMC) system using a recurrent wavelet-based Elman neural network (RWENN) estimator is proposed in this study to control the mover position of a linear ultrasonic motors (LUSMs)-based X-Y-Θ motion control stage for the tracking of various contours. By the addition of a complementary generalized error transformation, the complementary sliding-mode control (CSMC) can efficiently reduce the guaranteed ultimate bound of the tracking error by half compared with the sliding-mode control (SMC) while using the saturation function. To estimate a lumped uncertainty on-line and replace the hitting control of the CSMC directly, the RWENN estimator is adopted in the proposed ICSMC system. In the RWENN, each hidden neuron employs a different wavelet function as an activation function to improve both the convergent precision and the convergent time compared with the conventional Elman neural network (ENN). The estimation laws of the RWENN are derived using the Lyapunov stability theorem to train the network parameters on-line. A robust compensator is also proposed to confront the uncertainties including approximation error, optimal parameter vectors, and higher-order terms in Taylor series. Finally, some experimental results of various contours tracking show that the tracking performance of the ICSMC system is significantly improved compared with the SMC and CSMC systems.