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