Improved elman networks and applications for controlling ultrasonic motors

Two improved Elman network models, output-input feedback (OIF) and output-hidden feedback (OHF), are proposed based on the modified Elman network. A recurrent back-propagation control (RBPC) network model is developed by using the OIF Elman network as a passageway of the error back-Propagation. The stability of the improved Elman and RBPC networks is analyzed. Adaptive learning rates are given in the form of discrete-type Lyapunov stability theory, which could guarantee the convergence of the improved Elman and RBPC networks. The speed of the ultrasonic motor is identified using the modified Elman network, OIF and OHF Elman networks, respectively, and some useful comparable results are presented. Numerical results show that the RBPC controller is effective for various kinds of reference speeds of the USM and the proposed scheme is fairly robust against random disturbance to the control variable.