DocumentCode :
796954
Title :
Application of the describing function technique in a single-loop feedback system with two nonlinearities
Author :
Davison, E.J.
Author_Institution :
University of Toronto, Toronto, Ontario, Canada
Volume :
13
Issue :
2
fYear :
1968
fDate :
4/1/1968 12:00:00 AM
Firstpage :
168
Lastpage :
170
Abstract :
A graphic procedure is presented which allows the describing function technique to be extended to a single-loop feedback system with two nonlinearities. The graphic technique is very simple and immediately allows qualitative answers, or quantitative answers subject to the usual errors and restrictions of the describing function technique, to be obtained regarding the presence of limit cycles, regions of stability, instability, etc. The method essentially is as follows. A plot of G_{1}(j\\omega ) G_{2}(j_\\omega ) in Fig. 1 vs. ω is made, and the point of intersection of G_{1}(j\\omega ) G_{2}(j\\omega ) with the negative real axis is noted, for example, at G_{1}(j\\omega ^{\\ast }) G_{2}(j\\omega ^{\\ast }) =-1/\\Gamma , \\Gamma > 0 . By plotting |G_{d_{1}}(A1)| vs. A1in the second quadrant, and |G_{d_{2}}(A_{2})| vs. A2in the fourth quadrant, it is possible to plot a curve (relating |G_{d_{1}}| vs. |G_{d_{1}}|) in the first quadrant. If this curve intersects |G_{d_{1}}| |G_{d_{2}}| = \\Gamma , a limit cycle exists in the system. If no intersection takes place, then no limit cycle exists in the system.
Keywords :
Describing functions; Nonlinear systems; Artificial intelligence; Feedback; Frequency; Gain; Graphics; Limit-cycles; Linearity; Low pass filters; Polynomials; Stability;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1968.1098854
Filename :
1098854
Link To Document :
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