Describing function

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The Describing function method of Krylov and Bogolyubov is an approximate procedure for analyzing nonlinear control problems. It is based on quasi-linearization, that is the replacement of the non-linear system under investigation by a system that is linear except for a dependence on the amplitude of the input waveform. This quasi-linearization must be carried out for a specific family of input waveforms.

An example might be the family of sine wave inputs; in this case the system would be characterized by an SIDF or sine input describing function $H (A,ω)$ giving the system response to an input consisting of a sine wave of amplitude A and frequency $ω$ . (This SIDF is a generalization of the transfer function $H (ω)$ used to characterize linear systems).

Other types of describing functions that have been used are DFs for level inputs and for Gaussian noise inputs. While not a complete description of the system, the DFs often suffice to answer specific questions about control and stability.

[edit] References

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[edit] Further reading

Krylov N., and N. Bogolyubov: Introduction to Nonlinear Mechanics, Princeton University Press, 1947
Gelb, A., and W. E. Vander Velde: Multiple-Input Describing Functions and Nonlinear System Design, McGraw Hill, 1968.
http://ocw.mit.edu/OcwWeb/Aeronautics-and-Astronautics/16-30Spring2004/Readings/index.htm#Downloadable (downloadable version of above book).