Adaptive repetitive control design of nonlinearly parameterized systems

In this paper, an adaptive repetitive control scheme is presented for a class of nonlinearly parameterized systems based on fuzzy basis function networks (FBFNs). The parameters of the fuzzy rules are tuned with adaptive schemes. To attenuate chattering effectively, the discontinuous control term is approximated by an adaptive PI control structure. The bound of the discontinuous control term is assumed to be unknown and estimated by an adaptive mechanism. The adaptive repetitive control law is derived by using Lyapunov synthesis method to guarantee the closed-loop stability and the tracking performance. By means of FBFNs, the controller singularity problem is solved as it avoids the nonlinear parameterization from entering into the adaptive control and repetitive control. The proposed approach has the added advantage that it does not require an exact structure of the system dynamics. The proposed controller is applied to control a model of permanent-magnet linear synchronous motor (PMLSM) subject to significant disturbances and parameter uncertainties. The simulation results demonstrate the effectiveness of the proposed method in terms of significant reduction in chattering while maintaining asymptotic convergence.