Control law design for discrete linear repetitive processes with non-local updating structures

Abstract

Repetitive processes are a class of 2D systems where information propagation in one direction is of finite duration. These processes make a series of sweeps, termed passes, through a set of dynamics and on completion of each pass resetting to the starting position occurs ready for the start of the next pass. The control problem is that the previous pass output, termed the pass profile, acts as a forcing function on the current pass and can result in oscillations that increase in amplitude from pass-to-pass. In the case of discrete dynamics, these processes have structural links with 2D systems described by the well known Roesser and Fornasini–Marchesini state-space models but some applications require updating structures that cannot be represented by these models. This requirement arises either in adequately modeling the dynamics or as a result of the control law structure and requires the development of a systems theory for eventual use in applications. In this paper such a theory is advanced through the development of new control law design algorithms.