STABILIZATION AND ROBUST CONTROL OF METAL ROLLING MODELED AS A 2D LINEAR SYSTEM K. Galkowski W. Paszke E. Rogers D. H. Owens Institute of Control and Computation Engineering, University of Zielona Gora, Poland. Department of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, UK. {etar}@ecs.soton.ac.uk Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield S1 3JD, UK. Copyright @ 2002 IFAC Abstract: Repetitive processes are a distinct class of 2D linear systems with applications in areas ranging from long-wall coal cutting and metal rolling operations through to iterative learning control schemes. The main feature which makes them distinct from other classes of 2D linear systems is that information propagation in one of the two independent directions only occurs over a finite duration. This, in turn, means that a distinct systems theory must be developed for them, which can then be translated (if appropriate) into efficient routinely applicable controller design algorithms for applications domains. In this paper, we give some new results on LMI based stabilization and robust control of so-called discrete linear repetitive processes and illustrate them by application to a metal rolling process. Keywords: 2D linear systems, metal rolling, robust control. 1. INTRODUCTION The essential unique characteristic of a repetitive, or multipass, process 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 forcing function on, and hence contributes to, the dynamics of the next pass profile. This, in turn, leads to the unique control problem for these processes in that the output sequence of pass profiles generated can contain oscillations that increase in amplitude in the pass to pass direction. To introduce a formal definition, let α ∞ denote the pass length (assumed constant). Then in a repeti- tive process the pass profile y k 0 t α , generated on pass k acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile y k 1 t 0 t α k 0 Physical examples of repetitive processes include long-wall coal cutting and metal rolling operations (Edwards, 1974; Smyth, 1992). Also in recent years applications have arisen where adopting a repetitive process setting for analysis has distinct advantages over alternatives. Examples of these so-called algori- thmic applications of repetitive process theory include classes of iterative learning control schemes (Amann et al., 1998) and iterative algorithms for solving non- linear dynamic optimal control problems based on the maximum principle (Roberts, 2000). Attempts to control these processes using standard (or 1D) systems theory/algorithms fail (except in a few very restrictive special cases) precisely because such an approach ignores their inherent 2D systems struc- ture, i.e. information propagation occurs from pass to pass and along a given pass, and the pass initial conditions are reset before the start of each new pass. In seeking a rigorous foundation on which to develop Copyright © 2002 IFAC 15th Triennial World Congress, Barcelona, Spain