Degree Type

Dissertation

Date of Award

1984

Degree Name

Doctor of Philosophy

Department

Mathematics

Abstract

This dissertation is the analysis of the existence, local uniqueness and stability properties of almost sinusoidal oscillations in a class of nonlinear control systems. These systems are modeled by nonlinear ordinary differential equations of the form q(D)x + n(p(D)x) = r(t), where p and q are real polynomials, the degree of p is strictly less than the degree of q, n((.)) is an odd continuous function with some additional piecewise differentiability properties, D = d/dt and r(t) is either identically zero or periodic with a nontrivial period.;The analysis uses the classical single-input sinusoidal describing function, averaging and standard perturbation arguments. If a system parameter is sufficiently small, the existence and local uniqueness of an almost sinusoidal oscillation is guaranteed. Furthermore, the stability of the oscillation is easily checked by a modified Routh-Hurwitz test.;Numerical examples illustrating the results are included.

DOI

https://doi.org/10.31274/rtd-180813-6842

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Gary Steven Krenz

Language

en

Proquest ID

AAI8505835

File Format

application/pdf

File Size

179 pages

Included in

Mathematics Commons

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