Describing functions revisited

1 August 1975

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control

Vol. 20 (4) , 473-478
https://doi.org/10.1109/tac.1975.1101025

Abstract

The well-known graphical describing function procedure can be simply modified to provide a completely reliable method for predicting whether or not certain kinds of nonlinear feedback system can oscillate. The modified method is easy to use and quantifies, in a natural way, the usual intuitive ideas about describing function reliability. In addition to the usual graphs, the user has to draw a band which measures the amount of uncertainty introduced by the approximations inherent in the method; in return for this extra work, the method gives error bounds for oscillation predictions, as well as ranges of frequency and amplitude over which oscillation is impossible. The main restriction is that the nonlinear element must be single valued and have bounded slope.

Keywords

This publication has 3 references indexed in Scilit:

Describing functions, circle criteria and multiple-loop feedback systems
Proceedings of the Institution of Electrical Engineers, 1973
The Describing Function Matrix
IMA Journal of Applied Mathematics, 1972
Justification of the Describing Function Method
SIAM Journal on Control, 1971