Using Pade approximation in system modelling and simulation with state-space representation

Abstract

Today, in a variety of application the statistical characteristics of a system response is important in order for analysis and model the systems. In this study, we mainly made an investigation to the system analyzing and modelling methods. Especially, we considered Autoregressive Moving Average (ARMA) and Pade' approximation methods to find the modelled system transfer function coefficients. Theie are several algorithms to calculate these coefficients. In our study we used Modified yule Walker Algorithm (MYWE) and AKAIKE algorithms for ARMA and a new Pade' algorithm developed by Biyiksiz for Pade' approximation. When these three methods were simulated, it was seen that Pade' is mainly less sensitive to the coefficient quantization error and arithmetic round-off error accumulation introduced by finite word length. On the other hand it is not a good approximation for higher orders.It was seen that if the lower orders were used, Pade' approximation gave really good results compared to the MYWE and AKAIKE. But these ARMA models also are not guaranteed to give stable solutions for higher orders. In some cases for higher or lower order ARMA models produced good results especially for higher orders. But these orders should be choosen with one of the methodologies described for model order selection. An extension of research was done to the state-space error sensitivity. When the mentioned errors were investigated for different representation types of the state-space approach, it was shown that Pade' algorithm was less sensitive to such errors especially for some of the representation types.