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PERIODIC SOLUTIONS OF FLEXIBLE SYSTEMS
UNDER DISCONTINUOUS CONTROL
by
Michael K. Borre
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MECHANICAL ENGINEERING)
May 2011
Copyright 2011 Michael K. Borre
Object Description
| Title | Periodic solutions of flexible systems under discontinuous control |
| Author | Borre, Michael K. |
| Author email | borre@usc.edu; mborre@mbengineering.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Mechanical Engineering |
| School | Viterbi School of Engineering |
| Date defended/completed | 2011-03-29 |
| Date submitted | 2011 |
| Restricted until | Unrestricted |
| Date published | 2011-04-28 |
| Advisor (committee chair) | Flashner, Henryk |
| Advisor (committee member) |
Yang, Bingen Ioannou, Petros A. |
| Abstract | A method for calculating all periodic solutions and their domains of attraction for flexible systems under nonlinear feedback control is presented. The systems considered consist of mechanical systems with multiple flexible modes and a relay type controller coupled with a linear or nonlinear control law operating in a feedback configuration. The proposed approach includes three steps. First, limit cycle frequencies and periodic fixed points are computed exactly, using a block-diagonal state-space modal representation of the plant dynamics. Then the relay switching surface is chosen as the Poincaré mapping surface and is discretized using the cell mapping method. Finally, the region of attraction for each limit cycle is computed using the cell mapping algorithm and employing an error based convergence criterion. The method is demonstrated on four application examples, each with a different type of relay and/or control law to demonstrate the versatility and accuracy of the method. |
| Keyword | limit cycles; flexible structures; relay feedback control; region of attraction; numerical-analytical methods |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m3803 |
| Contributing entity | University of Southern California |
| Rights | Borre, Michael K. |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | cisadmin@lib.usc.edu |
| Filename | etd-Borre-4560 |
| Archival file | uscthesesreloadpub_Volume14/etd-Borre-4560.pdf |
Description
| Title | Page 1 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | PERIODIC SOLUTIONS OF FLEXIBLE SYSTEMS UNDER DISCONTINUOUS CONTROL by Michael K. Borre A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MECHANICAL ENGINEERING) May 2011 Copyright 2011 Michael K. Borre |
