This thesis examines the fundamental relationship between a continuous-time system and its discrete-time models. This involves a study of the conditions that the state space realization of a model must satisfy in order to be valid. While such a study has been performed for models whose order equals that of the continuous-time system, this thesis also includes "higher order discrete-time models", that is, models whose order is higher than the continuous-time system. A strict mathematical definition for models is presented based upon the convergence in a certain sense of the time responses of the continuous-time system and its model. Theorems are also presented which can be used to prove the validity of models, and shown are that many common discretization techniques, such as mapping models and hold equivalent models, are valid. Using these theorems some of these discretization techniques can be generalized. However, the aim of this thesis is not to prove the validity of common discretization techniques, but to understand the conditions which a model must satisfy in order to be valid. Common discretization techniques simply provide convenient examples for this understanding. / The definition of models is later expanded to consider discrete-time time-varying and multi-rate system. It is with multi-rate systems that the importance of higher order models becomes particularly apparent. Depending on the particular ratio of sampling rates between the plant input and output, some multi-rate systems must include inherently discrete-time operations, resulting in a higher order, for these systems to be considered valid. Also shown is that it is possible for a discrete-time periodically-time-varying system to model a time-invariant continuous-time system. / Finally, using the developed model concept, the practical problem of the multi-rate implementation of an analogue control system is considered. The method presented is an extension of the plant input mapping method which is the only method capable of guaranteeing the stability of the digital closed-loop system provided the sampling period is nonpathological. Simulation examples illustrate the effectiveness of the proposed methods, even for very slow sampling periods.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.34709 |
| Date | January 1997 |
| Creators | Comeau, A. Raymond (André Raymond) |
| Contributors | Hori, Noriyuki (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Mechanical Engineering.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001619712, proquestno: NQ44389, Theses scanned by UMI/ProQuest. |
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