Does the higher order mean the better internal delay rational approximation?

Abstract

The aim of this contribution is to test by simulations whether the higher order rational approximation for exponential elements in linear time-invariant time-delay systems (LTI-TDS) automatically means the better (i.e. more accurate) finite dimensional approximating model. The presented approximations are utilized to the Laplace transfer function model in the form of fractions of socalled quasipolynomials and the methods are chosen so that they are easy to handle with. Namely, Padé approximation, shift operator approximations-Laguerre and Kautz shift-and Fourier analysis based method are introduced and benchmarked. The work is motivated i.a. by the fact that direct controller design for LTI-TDS based on such models is mostly rather intricate and there are no theoretical results for internal delays. Moreover, the authors intend to use the results for rationalization of so-called anisochronic controllers when their discretization. The quality of approximation is measured by the well known H2 and H∞ norms instead of exact analytic calculations since it is sufficient for practical engineering problems. Some simulation examples for anisochronic controllers by means of a developed program testing interface in Matlab-Simulink environment are presented as well.