Nonlinear systems - describing functions analysis and using

Department of Automation and Control, Tomas Bata University in Zlin, Jižní Svahy, Nad Stránêmi 4511, 760 05, Zlin, Czech Republic

^* Corresponding author: urednicek@utb.,cz

Abstract

The paper presents a basic description and examples of the use of so called descriptive functions, allowing analysing the influence of inherent and indispensable components of all mechatronic systems mechanical subsystems - so called hard nonlinearities. These parts “causing” - in addition to the centrifugal and Coriolis generalized forces- the nonlinearity of the system, can be analysed by the abovementioned method from the point of view of their origin and the estimation of the basic parameters of their frequent consequences - so-called limit cycles. After a short introduction, which introduces and explains describing functions using the example of a nonlinear system taken from the literature, some of the socalled hard nonlinear subsystems (such as the mechanical chain of robots) are shown to be used. The paper is the first part of a more extensive description analysis of nonlinear systems concept using these functions in order to enable analysis and prediction of limit cycles.