FBFN-based adaptive repetitive control of nonlinearly parameterized systems

Abstract

An adaptive repetitive control scheme is presented for a class of nonlinearly parameterized systems based on the fuzzy basis function network (FBFN). 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. Based on the Lyapunov stability theory, an adaptive repetitive control law is proposed to guarantee the closed-loop stability and the tracking performance. By means of FBFNs, which avoid the nonlinear parameterization from entering into the adaptive repetitive control, the controller singularity problem is solved. The proposed approach does not require an exact structure of the system dynamics, and the proposed controller is utilized to control a model of permanent-magnet linear synchronous motor subject to significant disturbances and parameter uncertainties. The simulation results demonstrate the effectiveness of the proposed method.

State of the Art of Repetitive Control in Power Electronics and Drive Applications

“…In order to deal with the case of a nonlinear system with nonlinear parameters, adaptive RCs have been proposed in [97], [98]. Authors in [98] applies a collection of fuzzy ifthen rules to approximate the input of RC.…”

“…In order to deal with the case of a nonlinear system with nonlinear parameters, adaptive RCs have been proposed in [97], [98]. Authors in [98] applies a collection of fuzzy ifthen rules to approximate the input of RC. In such way, the approximated input of RC is model-free, and the nonlinear parameterization will not affect the RC.…”

Iterative Learning Control for a Class of Time-Delay Systems with Time-Varying Uncertainties

“…Recently, several Learning Control (LC) approaches have been proposed to tackle tracking control problems of nonlinear systems with time-varying uncertainties [1][2][3]. A repetitive learning control is proposed in [1] for high-order nonlinearly parameterized uncertain systems with timevarying and time-invariant parameters, this method can be applied to uncertain systems with timevarying parameters which are varying rapidly and periodically in an unknown compact set. Paper [2] introduces a new ILC method, which overcomes the limitation of traditional ILC in that it can enable learning from different tracking control tasks.…”