Modeling of imperfect system based on almost orthogonal polynomials

Abstract

A new class of the almost orthogonal filters is defined in this paper. These filters are a generalization of the classical orthogonal filters commonly used in the circuit theory, control system theory, signal processing, and process identification. Almost orthogonal filters generate the series of almost orthogonal Legendre functions on the interval (0, ∞). It's a well known fact that every real system is imperfect, so the models of these systems should be imperfect, also. A new method for obtaining an imperfect system model by using almost orthogonal filters based on almost orthogonal functions is proposed. Simulations are performed to approve theoretical results and demonstrate that the method described in the paper is suitable for modelling of imperfect systems.