Abstract
This paper proposes an adaptive backstepping optimal control (ABOC) with recurrent radial basis function network (RRBFN) uncertainty observer so as to achieve high dynamic performance for permanent-magnet synchronous motor (PMSM)-driven linear motion stage with a ball-screw. The objective of this paper is to design an ABOC scheme, which not only guarantees the stability of the linear stage, but also achieves the optimal control performance as well. The ABOC scheme combines a backstepping controller (BC), a RRBFN uncertainty observer with a robust controller and an optimal controller. Moreover, the BC is designed in the sense of Lyapunov stability theorem. However, the uncertainty terms in the BC laws due to friction and backlash nonlinearities of the ball-screw as well as the parameter variations and nonlinearities of the PMSM servo drive can destroy the performance of the linear stage seriously. Therefore, a RRBFN uncertainty observer with robust controller for the approximation of online nonlinear uncertainties is developed. Further, the robust controller is designed to recover the residual of the RRBFN approximation errors. As well, to optimize the design of the BC, an optimal controller is developed and combined to the BC law. Furthermore, the online adaptive control laws are derived based on the sense of optimal control technique and Lyapunov stability analysis; so that the stability of the ABOC scheme can be guaranteed. The experimental results confirm that the proposed ABOC can achieve favorable tracking performance.