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
Copyright Date
1984
Language
en
Proquest ID
AAI8505835
File Format
application/pdf
File Size
179 pages
Recommended Citation
Krenz, Gary Steven, "On the stability in oscillations in a class of nonlinear feedback systems containing numerator dynamics " (1984). Retrospective Theses and Dissertations. 8181.
https://lib.dr.iastate.edu/rtd/8181
