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UBC Theses and Dissertations

Adaptive control based on orthonormal series representation Zervos, Christos Constantine


This thesis describes a novel approach to adaptive control systems design using orthonormal series representation. The class of adaptive algorithms considered is that commonly referred to as self-tuning controllers developed for discrete-time systems. A common characteristic of the self-tuning schemes so far studied for industrial applications is that they are usually based on ARMAX models. These existing adaptive control algorithms have been shown to be globally asymptotically stable under certain theoretical assumptions and they have performed well in various applications. These theoretical assumptions are somehow too restrictive from an engineering and practical point of view. Real industrial plants always contain considerable time delays, have unmodeled dynamics, exhibit time varying dynamics and are subject to various disturbances. The purpose of this thesis is to explore a new way of representing and controlling dynamic systems in an effort to find another way, probably better and more robust, to handle a certain class of industrial applications. The behaviour of adaptive controllers in the presence of unmodelled dynamics and in the presence of time-varying plant delays along with the need for reduced a-priori information as dictated by the conditions encountered usually in practice have led us to abandon the usual ARMA transfer function representation for a new representation by orthonormal series. Our new approach is advantageous because it eliminates the need for assumptions about the plant order and the time-delay, i.e. accurate assumptions about their true values are not necessary. A physical dynamical plant, including its time delay, is modelled by an orthonormal set of functions. The sets considered here are mainly the Laguerre set, a modified version of it, and a set based on complex poles. Other orthonormal functions may also be used. A simple predictive control law is proposed from which an adaptive controller is then designed. The schemes developed are explicit and implicit, deterministic and stochastic. Some multivariable schemes are also presented. Simulations of these new controllers show they are easy to use, able to handle non-minimum phase plants, and more robust than the conventional model-based approaches. Results from industrial trials confirm the applicability of these new schemes.

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