Modelling of Cascade-Connected Systems using Quasi-Orthogonal Functions

Abstract

Abstract-This paper presents a new method for modelling dynamic systems based on quasi-orthogonal functions. First, we defined a new class of Legendre type quasi-orthogonal functions that can be used for signal approximation as well as for modelling, analysis, synthesis, and simulation of dynamic systems, especially systems that suffer from some imperfections. In this paper, functions have been applied in modelling of cascade-connected dynamic system, typical for tire industry. Considered rubber cooling system is a represent of complex, nonlinear, and stochastic systems with imperfections. Developed quasi-orthogonal adjustable models can be used for modelling of arbitrary dynamic systems. Optimal model parameters in the sense of the mean-squared error were obtained using genetic algorithm. For experimental purposes, simplified cascade-connected system with four transporters has been practically realized. The experimental results proved the accuracy, simplicity, and quality of realized quasi-orthogonal model.

Design of generalised orthogonal filters: application to the modelling of dynamical systems

“…The authors of this article have developed specific methods for obtaining orthogonal functions and found their wide application in engineering [11,[15][16][17][19][20][21][22].…”

“…Papers [15,[19][20][21] have introduced almost and quasi-orthogonal polynomials, based on a generalization of the classical definition of orthogonality, suitable for applications in various fields of engineering. Using these polynomials when designing almost and quasi orthogonal filters, we use much smaller number of components in implementation in relation to the already existing filters.…”

“…Using these polynomials when designing almost and quasi orthogonal filters, we use much smaller number of components in implementation in relation to the already existing filters. All the necessary definitions and relations related to new types of orthogonality are presented in [19,21]. One class of almost orthogonal rational functions of Legendre type on interval (0, ∞) is described in [11], while Laguerre type is considered in [23].…”

“…Quasi-orthogonal functions can also be used for modelling of dynamical systems [16,19,[24][25][26]. Generalized quasi-orthogonal Legendre type polynomials are considered in [4,19], quasi-orthogonal polynomials of other classical polynomials i.e.,…”

“…Generalized quasi-orthogonal Legendre type polynomials are considered in [4,19], quasi-orthogonal polynomials of other classical polynomials i.e.,…”