Sliding Mode Control for Differential Linear Repetitive Processes Based on a Novel Reaching Law

In this paper, the sliding mode control problem of differential linear repetitive processes is addressed via the reaching law approach. A linear sliding function is first constructed based on the current process state. Reaching conditions of differential LRPs are defined, which combines the characteristics of continuous and discrete systems. Accordingly, a novel reaching law is proposed and the corresponding sliding mode controller is provided, which not only reflect the influence of signals in both directions (along the pass as well as pass-to-pass directions) but also guarantee the reachability of sliding domain. Through the introduction of a model transformation matrix, the sliding mode dynamics are obtained and the corresponding stability along the pass is achieved. Finally, a numerical example is presented to illustrate the effectiveness of the proposed control scheme.