This thesis examines the propagation of small relative errors in poles in discrete-time domains $z, varepsilon={{z-1} over {T}}, z sp prime=z-1, w sp prime={2 over {T}}{{z-1} over{z+1}}$ and z = ${{z-1} over{Tz}},$ where T is the sampling period, to the continuous-time domain. By prescribing pole locations in the discrete-time domains or usable sampling periods in a continuous-time context, sensitivity specifications in time constant of a real pole, natural frequency, damping ratio and uncertain relative region of a complex pole can be achieved. It is shown in this thesis that the alternative discrete-time operators, $ varepsilon, z sp prime, w sp prime$ and z, provide superior performance in the propagation of errors coming from coefficient quantization of first order control laws than the z operator at fast sampling rates, and possess sensitivity properties converging to those of an equivalent continuous-time system as the sampling interval approaches zero. A two-stage least squares identification process of a high order plant is studied with emphasis placed on sensitivity effects as well as on the effect of the accuracy of the digital-to-analog and analog-to-digital converters. The Euler form identification process is shown to yield the most accurate continuous-time pole estimates among the operator forms examined in this work and the accuracy of the converters is shown to bring an upper limit on the sampling rate, at which the data are captured for identification, so that relatively accurate pole estimates are obtained.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.23267 |
| Date | January 1995 |
| Creators | Rabbath, Camille Alain |
| Contributors | Hori, N. (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 | 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: 001476847, proquestno: MM07983, Theses scanned by UMI/ProQuest. |
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