Fractional Describing Function Analysis of Systems with Backlash and Impact Phenomena

This paper analyses the dynamical properties of systems with backlash and impact phenomena based on the describing function method. It is shown that this type of nonlinearity can be analyzed in the perspective of the fractional calculus theory. The fractional-order dynamics is illustrated using the Nyquist plot and the results are compared with those of standard models. I. INTRODUCTION The area of Fractional Calculus (FC) deals with the operators of integration and differentiation to an arbitrary (including noninteger) order and is as old as the theory of classical differential calculus. The theory of FC is a well- adapted tool to the modelling of many physical phenomena, allowing the description to take into account some peculiarities that classical integer-order models simply neglect. For this reason, the first studies and applications involving FC had been developed in the domain of fundamental sciences, namely in physics (5) and chemistry (20). Besides the in tensive research carried out

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