A novel recurrent wavelet-based Elman neural network (RWENN) control system is proposed in this study to control the mover position of a multi-axis motion control stage using linear ultrasonic motors (LUSMs) for the tracking of various contours. First, the structure and operating principles of the LUSMs are introduced briefly. Since the dynamic characteristics and motor parameters of the LUSMs are non-linear and time varying, the RWENN is proposed to control the mover of the X-Y-θ motion control stage to track various contours precisely using a direct decentralised control strategy. In the proposed RWENN, each hidden neuron employs a different wavelet function as an activation function. Moreover, the recurrent connective weights are added in the RWENN. Therefore compared with the conventional Elman neural network (ENN), both the precision and time of convergence are improved. Furthermore, the on-line learning algorithm based on the supervised gradient descent method and the convergence analysis of the tracking error using a discrete-type Lyapunov function of the RWENN are developed. Finally, some experimental results of various contours tracking show that the tracking performance of the RWENN is significantly improved compared with the ENN.
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