Rational Approximations for Time-Delay Systems: Case Studies

Linear time-invariant time-delay systems (LTI-TDS) constitute a widespread family of plants and systems, not only limited to industrial ones. They can be represented by Laplace transfer functions in the form of fractions of so-called quasipolynomials. Direct controller design for LTI-TDS based on such models is mostly rather intricate. Many approaches require a rational approximation of the transfer function. In this contribution, description and comparison of some selected easy-handling rational approximations of exponential elements in LTI-TDS transfer functions is presented. Namely, Padé approximation, shift operator approximations and Fourier analysis based method are introduced. Unlike traditional concept which is well examined, internal (state) delays are considered as well here. A program testing interface in Matlab-Simulink environment is developed and some study cases are presented by applying the application. Key-Words: Time-delay systems, rational approximation, Padé approximation, Laguerre shift, Kautz shift, Fourier analysis