DocumentCode :
867168
Title :
The elliptic describing function
Author :
Jopling, A.D. ; Johnson, R.A.
Author_Institution :
Canadian Armament Res. and Development Establishment, Valcartier, Quebec, Canada
Volume :
9
Issue :
4
fYear :
1964
fDate :
10/1/1964 12:00:00 AM
Firstpage :
458
Lastpage :
468
Abstract :
A new describing function called the Elliptic Describing Function (EDF) is defined which allows the waveshape of a limit cycle to be determined after the amplitude and frequency have been found. The application of the EDF is nonrigorous mathematically but is justified by examples. The technique is based on the fitting of the nonlinear characteristic-whatever its shape so long as it is single-valued, odd-symmetrical, and frequency-independent-by an odd cubic polynomial. Considerable evidence exists which justifies this seemingly drastic approximation. Three examples are given illustrating the errors involved. Comparisons are made with the ordinary DF and new RMS DF for two examples and with a total of six DF´s for a third. The results are encouraging.
Keywords :
Describing functions; Limit cycles; Frequency; Helium; Limit-cycles; Mathematical analysis; Nonlinear systems; Shape;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1964.1105765
Filename :
1105765
Link To Document :
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