Quasi sliding mode control of differential linear repetitive processes with unknown input disturbance

Linear repetitive processes are a distinct class of 2-D systems, which have extensive applications in the practical industry, such as long-wall coal cutting and metal rolling operations. In this paper, the observer-based sliding mode control (SMC) problem is investigated for differential linear repetitive processes with unknown input disturbance. The main advantage of the proposed scheme is that it eliminates the need for the state variables and pass profile variables to be fully accessible for its control. This is possible through the use of a sliding mode controller, which performs its control by employing state estimates obtained from the sliding mode observer. A sufficient condition for the existence of desired observer is established in terms of a linear matrix inequality, and an SMC law is synthesized to guarantee the stability along the pass of the overall closed-loop process. It is shown that the proposed control scheme ensures the reachability of the sliding surfaces in both the state estimate space and the estimation error space. An illustrative example is given to demonstrate the effectiveness of the proposed designed scheme.