Disturbance Suppression for Fuzzy Repetitive-Control Systems Using an Enhanced Equivalent-Input-Disturbance Method

This article presents a two-degree-of-freedom structure of a fuzzy repetitive-control system that accurately tracks periodic signals and effectively suppresses aperiodic disturbances based on an enhanced equivalent-input-disturbance (EEID) method. To make full use of the learning characteristic, a 2-D model of the fuzzy repetitive-control system is established to independently regulate the control and learning behaviors. The EEID approach decouples the design of the observer and the estimator by adding a flexible controller to the estimator. This makes it possible to simultaneously reduce the estimated and filtered errors, which is a contradictory problem in the conventional EID method. The two errors cannot be eliminated due to the lack of an internal model of the external disturbance. To actively cancel the negative influence of the two errors, a new observation-error compensator is added to the observer input to improve the disturbance-suppression performance. Two low-conservative linear-matrix-inequality stability conditions are derived using the Lyapunov–Krasovskii functionals and zero equations with free-weighting matrices. The nondominated sorting genetic algorithm II and the particle swarm optimization algorithm are used to optimize the parameters of the controllers for the tracking and disturbance-suppression systems based on the stability conditions and performance indexes. The effectiveness and superiority of the design are verified by numerical simulation and comparison results.