Robust intelligent backstepping control system using RCMAC for tracking periodic trajectories

Since the backstepping control technique is a systematic and recursive design methodology for nonlinear systems, a robust intelligent backstepping control (RIBC) system is proposed in this study to control a linear ultrasonic motor (LUSM) for the tracking of periodic reference trajectories. In the proposed control system, an adaptive recurrent cerebellar model articulation controller (RCMAC) is used to mimic an ideal backstepping control and a robust controller is designed to attenuate the effects caused by unmodeled dynamics, disturbances and approximate errors. The proposed adaptive RCMAC has superior capability to the conventional cerebellar model articulation controller (CMAC) in efficient learning mechanism and dynamic response. Moreover, the Taylor linearization technique is employed to derive the linearized model of the RCMAC. The online adaptation laws of the RIBC system are derived in the sense of the Lyapunov function, the Taylor linearization technique and the H∞H∞ control approach, so that the stability of the system and robust tracking performance can be guaranteed. Finally, the effectiveness of the proposed control system is indicated in comparison with an integral–proportional (IP) position control system. Experimental results show that high-precision tracking performance can be achieved by using the proposed RIBC system.