Variable-structure repetitive control for discrete-time linear systems with multiple-period exogenous signals

Abstract

A new method to construct a discrete-time variable-structure repetitive controller for a class of linear systems perturbed by multiple-period exogenous signals is presented. The proposed control scheme combines the features of the discrete-time multiple-period repetitive control (MP-RC) and variable-structure control (VSC) techniques. The MP-RC part is assigned to simultaneously track and reject periodic signals consisting of multiple uncorrelated fundamental frequencies. The VSC part is then integrated to provide a fast transient response and robustness against plant parameter variations. Stability and robustness analyses are also elaborated to ensure that the resulting closed-loop system satisfies the desired control objectives. Moreover, it is shown through an example that the repetitive control system constructed using the proposed control method can effectively track a sinusoidal reference signal despite the presence of a multiple-period disturbance.

A Performance Evaluation of Repetitive and Iterative Learning Algorithms for Periodic Tracking Control of Functional Electrical Stimulation System

“…The above-mentioned nonpredictive control systems such as sliding mode control (SMC) and adaptive control can be classified as robust control approaches aiming to handle model uncertainties and to compensate for some disturbances. Based on the studies in [25]- [29], the performances of such as SMC and adaptive control-based schemes are inferior for tracking/rejection periodic signal compared to predictive-based control methods. This is due to the above controlled systems do not have capability to learn from the previous error and use it to refine the current control signal.…”