A general method for deriving the describing functions for a certain class of nonlinearities
ABSTRACT Since Goldfarb's original work on describing functions, a considerable number of papers have been published in which the describing functions of particular nonlinearities have been derived. It appears however that little effort has been made to classify the nonlinearities. Since the describing function method is one of the more powerful methods available at present to analyze nonlinear feedback systems, it appears desirable to collect the expressions for the describing functions of a few different types of nonlinearities in one paper. It is the purpose of this paper to derive the describing functions of two general types of nonlinearities and show how the describing functions of many other practical types of nonlinearities for which the describing function analysis is valid naturally follow.
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ABSTRACT: A graphical technique is presented for determining the closed loop response of nonlinear control systems driven by sinusoidal inputs. The nonlinear portion of the system is represented by its conventional describing function, which may be frequency dependent as well as amplitude dependent. The linear portion of the system is represented by its complex frequency response function G(jomega) . A transparent overlay is used to mechanize a functional transformation similar to that performed by a Nichols chart, allowing rapid determination of the system output for sinusoidal inputs. The accuracy of the method is limited by the accuracy of the describing function approximation. In addition to offering a rapid solution to what has been regarded as a time consuming problem, the method gives the designer sufficient insight into the behavior of the system to allow the intelligent choice of compensating networks to improve system performance. A numerical example is used as a vehicle for discussion of compensation, and experimental results are presented to verify the analysis.IRE Transactions on Automatic Control 08/1962;
- European Journal of Control 01/2004; 10(2). · 0.79 Impact Factor
- IRE Transactions on Automatic Control 02/1962; 7(1):79- 81.