Adaptive Observer for Systems with Unknown Pure Time Delay

Abstract

This paper is concerned with the application of adaptive techniques for simultaneous parameter identification and state estimation to the design of an adaptive observer for systems having unknown pure time delay and parameters.
First, by using the Padé approximation method, we derive a lumped parameter composite system for the time delay system of which time delay element is expressed by a transportlag type distributed parameter subsystem. Then, Luders-Narendra type adaptive observer is constructed for the composite system which approximates the original time delay system. Stability of thus obtained observer is guaranteed by the Popov's hyperstability theorem and the parameter, adjusting laws in this case are given by integral plus proportional terms. Simulation results of a second-order time delay system are presented to demonstrate the effectiveness of the design method proposed here.