Identification of a Non-Linear System Using Volterra Series Model with Calculated Kernels by Legendre Orthogonal Function

Abstract

Modeling and identification of non-linear systems have gained lots of attentions especially in industrial processes. Most of the actual systems have non-linear behavior and the first and simplest solution in modeling such systems is to linearize them which in most cases the result of linearization is not satisfactory. In this paper, modeling of non-linear systems is investigated using Volterra series model based on Legendre orthogonal function. Expansion of Volterra series kernels by Legendre orthogonal functions causes a reduction in the number of model parameters; hence, complexity of calculations would be decreased. Besides, if the free parameter is selected properly in these orthogonal functions, error is reduced and convergence speed of parameters is increased which leads to an increase in identification accuracy. In this paper, identification of non-linear system is presented with Volterra series expanded by Legendre function and PSO algorithm is used to calculate the optimum free parameters of Legendre function. Finally, in order to validate the efficacy and accuracy, the proposed algorithm is implemented on a non-linear system i.e. heat exchanger with actual data