Robust Control of Discrete Linear Repetitive Processes with Parameter Varying Uncertainty

Abstract

Repetitive processes propagate information in two independent directions where the duration of one of these is infinite.They pose control problems that cannot be solved by application of results for other classes of 2D systems. This paper develops robust controller design algorithms for discrete linear processes based on the poly-quadratic stability that produce less conservative results than currently available alternatives. IntroductionRepetitive processes are a distinct class of 2D systems of both system theoretic and applications interest whose unique characteristic is a series of sweeps, termed passes, through a set of dynamics defined over a fixed finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a

New results on strong practical stability and stabilization of discrete linear repetitive processes

“…Also it can be verified that (15) holds if and only if (14) holds and therefore it remains to establish the feasibility of the LMI (14), which can be written as…”

“…Consider the linearized model of the metal rolling process given in [14], obtained by applying the backward Euler discretization method with sampling time T = 0.002 (s) to the governing differential equation. and hence (24) with K 1 = 6.9666 · 10 3 , K 2 = −3.9766 · 10 3 results in a controlled process that is strongly practically stable.…”