Indian Journal of Science and Technology

Abstract

Objective: To obtain mathematical model and parameters of poorly understood and imprecisely known plant/process. Methods: One solution to this problem is to obtain these using identification techniques. Process identification is a technique where a mathematical model of the process under study is build from process input-output data. Several autoregressive models are used to estimate the present value of the model using its past values of the process. Initially, the data set is generated for the given system and the auto regressive model is fitted to it, for the estimation of the model parameters. Residual error for a system is calculated using auto regression model parameters. Findings: A mathematical model for plant under study can be formulated with different system identification using Linear Regression methods like Auto Regressive eXogenous variable (ARX), Auto Regressive Moving Average with an eXogenous variable (ARMAX), Output Error (OE) and Box-Jenkins (BJ). For high model order ARX model is preferred and takes low computations but only suitable for white noise. The ARMAX model considers disturbance affecting process and provides higher performance index i.e. fitness which reveals percentage variation in output estimated by respective model. The Output-Error (OE) model estimates process model but cannot model disturbance features. The residual analysis of Box-Jenkins model shows that the prediction error is not auto-correlated, correlated and is uncorrelated with the input applied to process, thus showing Box-Jenkins model ability to capture noise dynamics of process. Applications/Improvements: The process model can be identified for the unknown, poorly known or partially known system and formulated model can be used in model Predictive controller design and Adaptive control techniques.
Keywords: ARX, ARMAX, BJ, Parametric, Plant Modelling, System Identification OE