Oscillations of nonlinear feedback systems which contain tightly coupled subsystems in cascade
D. A. Hoeflin,Richard K. Miller +1 more
TLDR
In this article, the authors formulate and prove a theorem which gives a rigorous theoretical justification for the use of describing functions to predict the existence of limit cycles in a multiple nonlinear feedback system.Abstract:
We formulate and prove a theorem which gives a rigorous theoretical justification for the use of describing functions to predict the existence of limit cycles in a multiple nonlinear feedback system and to predict the stability properties of these limit cycles. Our approach uses the classical sinusoidal-input describing function and the theory of integral manifolds. We demonstrate the applicability of our result by means of two specific examples.read more
Citations
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Journal ArticleDOI
A general approach for constructing the limit cycle loci of multiple-nonlinearity systems
TL;DR: In this paper, a widely convergent algorithm for finding a limit cycle of systems with multiple nonlinearities is presented, and a systematic approach is proposed for constructing the limit cycle loci on the parameter planes.
Proceedings ArticleDOI
On the stability of limit cycles in nonlinear feedback systems: Analysis using describing functions
TL;DR: In this article, the authors established computable conditions for the stability and instability of limit cycles in nonlinear feedback systems, which in part justify the popular quasistatic stability analysis (Loeb's criterion).
Journal ArticleDOI
On limit cycles in feedback polynomial systems
Roberto Genesio,Alberto Tesi +1 more
TL;DR: In this paper, the existence and uncertainty of limit cycles in nonlinear feedback systems is examined and sufficient conditions are derived to ensure in the neighborhood the existence of a true periodic solution and to evaluate its corresponding bounds.
References
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Book
Theory of Ordinary Differential Equations
TL;DR: The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable as discussed by the authors, which is a useful text in the application of differential equations as well as for the pure mathematician.
Book
Foundations of Optimal Control Theory
Ernest Bruce Lee,Lawrence Markus +1 more
TL;DR: This complete and authoritative presentation of the current status of control theory offers a useful foundation for both study and research.
Book
Multiple-Input Describing Functions and Nonlinear System Design
TL;DR: The theory of automatic control has been advanced in important ways during recent years, particularly with respect to stability and optimal control, but these theories do not, however, lay to rest all questions of importance to the control engineer.