Describing function

In control systems theory, the describing function (DF) method, developed by Nikolay Mitrofanovich Krylov and Nikolay Bogoliubov in the 1930s,[1][2] and extended by Ralph Kochenburger[3] is an approximate procedure for analyzing certain nonlinear control problems. It is based on quasi-linearization, which is the approximation of the non-linear system under investigation by a linear time-invariant (LTI) transfer function that depends on the amplitude of the input waveform. By definition, a transfer function of a true LTI system cannot depend on the amplitude of the input function because an LTI system is linear. Thus, this dependence on amplitude generates a family of linear systems that are combined in an attempt to capture salient features of the non-linear system behavior. The describing function is one of the few widely applicable methods for designing nonlinear systems, and is very widely used as a standard mathematical tool for analyzing limit cycles in closed-loop controllers, such as industrial process controls, servomechanisms, and electronic oscillators.

  1. ^ Krylov, N. M.; N. Bogoliubov (1943). Introduction to Nonlinear Mechanics. Princeton, US: Princeton Univ. Press. ISBN 0691079854. Archived from the original on 2013-06-20.
  2. ^ Blaquiere, Austin (2012-12-02). Nonlinear System Analysis. Elsevier Science. p. 177. ISBN 978-0323151665.
  3. ^ Kochenburger, Ralph J. (January 1950). "A Frequency Response Method for Analyzing and Synthesizing Contactor Servomechanisms". Trans. AIEE. 69 (1). American Institute of Electrical Engineers: 270–284. doi:10.1109/t-aiee.1950.5060149. S2CID 51646567.