Modelling of dynamical systems based on almost orthogonal polynomials

A new class of the almost orthogonal filters is described in this article. 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 over the interval (0, infinity). It is well known that all real systems suffer from some imperfections, so the models of these systems should reflect this fact. A new method for obtaining an imperfect system model is proposed. This method uses an almost orthogonal filter, which is based on almost orthogonal functions. Experiments with modular servo drive were performed to validate theoretical results and demonstrate that the method described in the article is suitable for modelling of imperfect systems.