A novel ARX-based discretization method for linear non-rational systems

Abstract

This paper presents a novel, simple, flexible and effective discretization method for linear non-rational systems including arbitrary linear fractional order systems (LFOS). The discretization algorithm relies on the direct integration in the complex domain and application of ARX (AutoRegressive eXogenous) model. Parameters of ARX-model are obtained by numerical inversion of Laplace transform from the set of input/output data from recorded step response to model of non-rational system. Numerical simulations of several representatives of LFOS (e.g. fractional order PID controller, fractional logarithmic filter, fractional oscillator etc.) are used to demonstrate the effectiveness of the proposed discretization method, both in the time and frequency domains. The obtained results indicate that the proposed ARX-based discretization method is adequate technique for obtaining digital approximation of LFOS.