Online Identification of Multivariable Discrete Time Delay Systems Using a Recursive Least Square Algorithm

Saïda Bedoui,Majda Ltaïef,Kamel Abderrahim

doi:10.1155/2013/658194

Abstract

This paper addresses the problem of simultaneous identification of linear discrete time delay multivariable systems. This problem involves both the estimation of the time delays and the dynamic parameters matrices. In fact, we suggest a new formulation of this problem allowing defining the time delay and the dynamic parameters in the same estimated vector and building the corresponding observation vector. Then, we use this formulation to propose a new method to identify the time delays and the parameters of these systems using the least square approach. Convergence conditions and statistics properties of the proposed method are also developed. Simulation results are presented to illustrate the performance of the proposed method. An application of the developed approach to compact disc player arm is also suggested in order to validate simulation results.

Highlights

Time delay system identification has received great attention in the last years since time delay is a physical phenomenon which arises in most control loops industrial systems [1, 2]
This paper addresses the problem of simultaneous identification of linear discrete time delay multivariable systems
We present a simulation example and an experimental validation to illustrate the performance of the proposed approach for the simultaneous identification of time delays and parameter matrices of square multivariable systems

Summary

Introduction

Time delay system identification has received great attention in the last years since time delay is a physical phenomenon which arises in most control loops industrial systems [1, 2]. The method developed in [3] consists, It consists, firstly, in using the recursive least square approach to identify the parameters assuming that the time delay is known, and secondly, in estimating the time delay, taking into account the results of the first step. We develop a new formulation of the problem allowing to define the time delay and the dynamic parameters in the same estimated vector and to build the corresponding observation vector We use this formulation to propose a new method to identify the time delays and the parameters of these systems using the least square approach. Simulation results and experimental test are provided in the last section

Problem Statement

The Proposed Approach

Convergence Properties

Results

Conclusions