An approach for relay-based identification of anisochronic models

Abstract

Models of dynamic systems containing both input and state delays were labeled as anisochronic. These models have some practical and attractive features, e.g. they enable to capture the dynamics of systems with very high order and mathematical models of many processes results in anisochronic form. In this paper an engineering utilizable idea of the identification principle for anisochronic models based on limit cycles is investigated. Unlike traditionally approaches connected with the frequency analysis of a transfer function, the proposed methodology is based on computation with functional differential equation only. Identified parameters are obtained analytically. Parameter estimation is also improved using ATV+ technique which required two relay tests. Some numerical aspects of the proposed method are discussed. The method is verified by an illustrative example in which parameters of a tenth order system are approximated by a first order anisochronic model. The developed approach can be easily utilized also for autotuning principles.