City Research Online

Abstract

The implementation of digital control schemes, involves issues such as fixed-point arithmetic, computer quantization, round off error effects and the selection of sampling scheme. The selection of sampling is crucial in the design of digital controllers and may affect drastically the quality of the discretized model on which design is based. The selection of sampling is so far dominated by the rules of signal processing theory and practical heuristics. The development of a theory and methodology for selection of sampling based on the overall quality of the discretized model, which is complementary to that provided by signal processing theory, is a long term objective of this research area and this thesis aspires to contribute to its development.

The thesis is mainly concerned with the study of the effect of sampling on the fundamental structural properties of the resulting discretized model. As such, this study is part of the more general area of investigating the transformation-preservation of qualitative and quantitative properties of continuous time models to discrete time models under sampling. Throughout the thesis we assume linear systems and constant sampling rate. The emphasis is studying the effect of sampling on fundamental model characteristics such as Jordan forms, eigenspaces, controllability, observability properties and finite-infinite zeros. Central to the approach developed here is the study of implications of a phenomenon referred to as “eigenvalue collapsing” that corresponds to the case where distinct eigenvalues of the continuous model become repeated eigenvalues of the discretized model. This phenomenon provides a classification of sampling rates into regular and irregular. A thorough investigation of the “eigenvalue collapsing” phenomena is given and their implication on the structural properties of the discretized model is given. In particular we examine the effect of such phenomena on the Segré characteristics, structure of eigenspaces, Jordan forms, controllability, observability, dimensions of controllability, observability properties, degrees of decoupling zeros and finite-infinite zeros of the discretized model.

The developments in the above directions have required some additional work in the study of certain structural properties of continuous time models, such as a detailed study of spectral properties of controllability, observability, which lead to a new characterization of decoupling zeros and their computation.

The result presented here provide a basis for the development of a model based theory of sampling, which is significant for the development of a general implementation methodology of digital systems.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics T Technology > T Technology (General)
Departments:	School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses School of Science & Technology > Engineering

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