Analysis and control of linear repetitive processes

Abstract

Repetitive processes are a distinct class of 2D systems of both practical and algorithmic interest, with a growing list of application areas. Their main identifying characteristics is a series of sweeps, termed passes here, through a set of known dynamics with explicit interaction between successive outputs, or pass profiles, as the process evolves. As a result of the explicit dependence of the process dynamics on two independent variables (in the along the pass and pass to pass directions) existing theory cannot be applied. This fact, together with the growing list of application areas has prompted an ongoing research programme into the development of a 'mature' systems theory for these processes.

As part of this programme, this thesis gives new results on the analysis and control of the subclasses known as differential and discrete linear repetitive processes. Novel results are presented in three separate research areas. Firstly new stability results are presented, including the further development of a two-dimensional Lyapunov equation based approach. These results provide computable information of performance which is not available from alternative stability characterisations. An initial study of robustness analysis is provided, including a discussion of a potentially promising new approach to stability margin analysis. Preliminary results on the design of controller structures are given, including the use of simple structure control schemes and fast sampling considerations. Finally some areas for short to medium term future research are discussed.

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