Preview repetitive control for linear discrete‐time periodic systems

Abstract

A discrete-time preview repetitive control (PRC) scheme was proposed for linear discrete-time periodic systems that were subjected to previewable reference signals. First, the state augmentation technique was used to derive an augmented system that included future information on previewable signals. Second, a two-dimensional (2D) model was developed for the augmented system so that the control and leaning actions can be adjusted preferentially by using control gains. Sufficient conditions that guarantee the closed-loop stability of the augmented 2D systems were derived, and the design of a periodic controller with preview action and repetitive control was proposed using the linear matrix inequality approach. Finally, the effectiveness of the proposed PRC was established by using two numerical simulation examples.

Estimation and rejection of periodic disturbance in a preview repetitive control system

“…Using the Matlab LMI toolbox to solve the inequality (38) in Theorem 1 and combining (52), we obtain…”

“…Solving the feasible problem (38) in Theorem 1 and the numerical solution (52) in Theorem 2, it gives that The adjustment parameter H is taken as 6.8, and prelength is s. results are shown in Figures 10 and 11. Apparently, as can be seen in Figure 10, our method has a significantly better disturbance compensation effect than the PRC with EID.…”

“…Recently, in the field of discrete-time systems, an observer-based PRC design method for uncertain discrete-time systems was presented [37]. The problem of PRC of linear discrete-time periodic systems was investigated [38]. Based on the optimal control theory, the optimal PRC design method was first obtained for continuous-time linear systems [39].…”