Design and application of reduced-order adaptive observer with exponential rate of convergence for single-input single-output linear systems

Abstract

This paper is concerned with the design of an adaptive observer to estimate state variables and identify parameters of an unknown linear single-input single-output system with desired rate of exponential convergence. The observer structure is based on the Kreisselmeier types representation of parametrized form, but the adaptive law is obtained by a new scheme. The adaptive law is determined by equations forcing the errors into decreasing exponentially and it is designed to guarantee the asymptotic stability of the identification and estimation processes globally. A method of reducing the order of the adaptive law is also proposed. The reduction of the order is executed by using a priori information regarding relations between the unknown parameters. An experimental application using a heated tank with water jacket is included to show the practical effectiveness of the reduced-order adaptive scheme.