Modelling of Cascade-Connected Systems using Quasi-Orthogonal Functions

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.