Low‐order sliding mode repetitive control for discrete‐time systems under complex disturbance environment

Abstract

A novel sliding mode repetitive control scheme is proposed for discrete‐time systems. It aims to address aperiodic disturbances, and simultaneously address a set of disturbances of known frequencies that can be unrelated. The sliding mode handles the former, and a repetitive control algorithm deals with the latter, creating a low‐order sliding model repetitive control law. The approach addresses each disturbance frequency individually. In contrast to the usual repetitive control approach, this allows one to address multiple unrelated frequencies without difficultly. Even when the addressed frequencies are harmonically related, but a relatively small number have significant error, this approach offers both substantial computation benefit, and benefit facilitating improved control of aperiodic disturbances. When both multiperiodic and aperiodic disturbances are present, the system trajectories can converge to a smaller switching band and keep moving within it. When there is only multiperiodic disturbance, the system trajectories will cross the switching surface within every specific steps when in the switching zone, and will converge to zero eventually. Simulation results demonstrate obvious advantages compared with the traditional method.

Low-order sliding mode repetitive control for uncertain linear systems perturbed by band-limited periodic disturbances

“…In this section, we presents three examples to demonstrate the efficacy of the LO-SMRC synthesized using the controller design method described in ''Proposed method'' section. Moreover, to highlight the merits of the proposed LO-SMRC, we also compare its performance with those of other relevant controllers, which have been presented in Jia et al 28 and Kurniawan et al 30,36 Example 1: a servomotor We now present an example of a Quanser servomotor 37 perturbed by periodic disturbances and controlled using the LO-SMRC. The servomotor dynamics is modeled as a discrete-time linear system as follows…”

“…We notice that a systematic method for synthesizing the LO-SMRC was first described in Kurniawan et al 27 However, this article presents more comprehensive results than those of Kurniawan et al 27 by providing stability and robustness analyses and a discussion on the LO-SMRC performance (via numerical examples) in contrast to other relevant controllers. In particular, the LO-SMRC we propose is compared with that presented in Jia et al 28 We found that the structure of our LO-SMRC is relatively simpler than that of the LO-SMRC constructed using the method of Jia et al 28 This consequently renders our LO-SMRC outperform the LO-SMRC of Jia et al 28 in terms of the rate of transient responses with predictable convergence periods. Moreover, the LO-SMRC of Jia et al 28 involves a noncausal switching function and yields two control regimes, yet it needs to be made clear how to determine their transition to suit particular applications.…”

“…In particular, the LO-SMRC we propose is compared with that presented in Jia et al 28 We found that the structure of our LO-SMRC is relatively simpler than that of the LO-SMRC constructed using the method of Jia et al 28 This consequently renders our LO-SMRC outperform the LO-SMRC of Jia et al 28 in terms of the rate of transient responses with predictable convergence periods. Moreover, the LO-SMRC of Jia et al 28 involves a noncausal switching function and yields two control regimes, yet it needs to be made clear how to determine their transition to suit particular applications. In contrast, these issues do not appear when applying our method to synthesize the LO-SMRC.…”

“…., g l , Hjs k j, F(q À1 ), G(q À1 ), and I(q À1 ) are defined. As discussed in Jia et al, 28 the second order system of Sun et al 21 given as…”

Integral sliding mode predictive control with disturbance attenuation for discrete‐time systems

“…In [7], for discrete‐time nonlinear systems with input and state constraints and constrained disturbances, a sliding‐mode control method was designed by means of control inputs obtained in advance. Via combining sliding mode control and repetitive control, a novel sliding mode repetitive control strategy was presented in [8] for discrete‐time systems subject to aperiodic disturbances and periodic disturbances. Integral sliding mode control (ISMC) method has attracted a great deal of interest of scholars in recent decades as it can offer better control performance than conventional one [9].…”