Premium
Classical control theory applied to potentially chaotic systems
Author(s) -
Brogan William L.
Publication year - 1995
Publication title -
computer applications in engineering education
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.478
H-Index - 29
eISSN - 1099-0542
pISSN - 1061-3773
DOI - 10.1002/cae.6180030206
Subject(s) - chaotic , computer science , simple (philosophy) , nonlinear system , stability (learning theory) , nyquist stability criterion , nyquist–shannon sampling theorem , chaos (operating system) , control theory (sociology) , synchronization of chaos , mathematics , chaotic systems , chaos theory , control (management) , calculus (dental) , artificial intelligence , physics , machine learning , medicine , parametric statistics , philosophy , statistics , computer security , epistemology , dentistry , quantum mechanics , computer vision
Some nonlinear systems of order three or higher become chaotic for certain parameter values and initial conditions. Interesting examples have been discussed in recent years, using sophisticated mathematical analysis and/or simulation. This article presents a simple method of predicting if chaos is possible and under what conditions, using classical control theory tools such as Nyquist's stability theorem and describing functions. The method is demonstrated using several examples.