Describing functions and prediction of limit cycles

Abstract

This paper deals with the so called describing functions method description as a simplified method of describing certain types of nonlinear systems, using the complex function of frequency response. The first part showed its using as an example of some so-called hard nonlinear systems (e.g. the mechanical chain of robots). In the actual last part, the formalization of the limit cycle prediction process is performed based on the representation of the non-linear element by describing function. The basic approach for this prediction is based on the application of an extended version of the well-known Nyquist criterion from linear control theory to a description of the systems with describing function utilization. © 2018, World Scientific and Engineering Academy and Society. All rights reserved.