This thesis compares the numerical performance of digital control laws implemented in the Z operator, z, and the Euler operator, $ epsilon$ = ${z-1 over T}$ where T is the sampling period, and provides some useful guidelines for estimating the conservative wordlength for relatively low order controllers which are implemented using floating point arithmetic. The relative merits of these two discrete-time operators are studied analytically with regard to coefficient representation and roundoff errors, which are two major sources of numerical error. It is shown in this thesis that the $ epsilon$ operator form has superior performance in the coefficient representation to the z operator form for the sampling rates often used in practice. It is also shown that control laws implemented in the $ epsilon$ operator provide superior performance in the introduction of roundoff errors and in the propagation of these errors through subsequent sampling instants than the z operator, at least for high sampling rates. Extensive numerical simulations are also performed to compare the $ epsilon$ and z forms to obtain useful rules of thumb for estimating the wordlength required by a controller based on the sampling rate and the dynamic characteristics of the controller.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.60666 |
| Date | January 1991 |
| Creators | Comeau, Raymond |
| 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 | Master of Engineering (Department of Mechanical Engineering.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001274380, proquestno: AAIMM74504, Theses scanned by UMI/ProQuest. |
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