Limit cycle based identification of time delay SISO processes

Abstract

The paper presents a relay feedback experiment for the generation of sustained oscillations or limit cycle in a class of time delay single-input single-output (SISO) processes. Based on limit cycle information, a generalized set of explicit expressions is deduced for modelling and identification of unknown processes in terms of first order plus time delay (FOPTD), second order plus time delay (SOPTD) models with or without zero. As compared to recent relay based identification methods, the proposed scheme does not require any prior guess for the initial conditions for a set of simultaneous nonlinear equations. Thereafter, the robustness of the proposed explicit expressions is dependent on the limit cycle parameters shown through the addition of random signals at the process output. Validation of the proposed identification scheme is performed through simulations for well-known examples in literature and experimental tests on a level control system. Finally, the efficacy of the proposed scheme is compared with potential results available in literature through appropriate performance metric and step response plots.