Design of an Estimator Based on Duality Principle for Unknown and Time-varying Delay Estimation in LTI Systems

In this article, a novel observer has been designed for the online estimation of time delay in SISO-LTI continuous time systems with uncertain and time variant delay in the control input. It is obvious that Laplace transfer function of a delayed system includes a time delay factor. In this paper, it is assumed that the only uncertain and time variant parameter in the system is the very system’s time delay parameter. The main idea used in designing the proposed observer is based on the establishment of duality principle between controller and observer, such that a direct adaptive controller structure (MRAS) is indirectly used for designing an estimator. For this, the main sections in an MRAS control system are organized the way that designing the controller will lead to designing the delay estimator in dual problem. In fact, adaptation rule in designing the controller will express the same estimator mechanism in the dual problem. Also, in computing the estimation mechanism, the two methods, one based on Lyapunov Theory and the other based on MIT rule, are used. Eventually, simulation results are indicative of the rather desirable performance of the proposed estimator in dealing with uncertain and time varying delays.