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The Describing Function

Module overview.

This module defines the describing function (DF) of a nonlinearity and shows how it may be used to study the behavior of a feedback loop with a single nonlinearity. DFs are derived for single and double valued nonlinearities and examples are given to show how DFs can be used for examining the stability of a nonlinear system. Since the method is approximate comments are made on its accuracy.



Module objectives. When you have completed this module you should be able to:

  1. Define a describing function of a nonlinearity
  2. Evaluate the describing function of a given nonlinearity
  3. Use the describing function approach to understand the dynamic behavior of a feedback loop with a single nonlinearity
  4. The approximations and limitations of the describing function method.


Module prerequisites. First year mathematics, Fourier series,transfer functions,frequency response, stability



Subsections

D. P. Atherton 2005-01-27