Closed loop Reaction Curve method for Identification of TITO systems

Abstract

A closed loop reaction curve method is presented to identify FOPTD (First Order plus Time Delay) model parameters of a Two Input Two Output (TITO) multivariable stable system which is controlled by decentralized PI/PID (Proportional Integral/ Proportional Integral Derivative) controllers. First, the responses and the interactions that are obtained for a step change in the set points separately are modeled by a SOPTD (Second Order plus Time Delay) models and integrated plus SOPTD models respectively. The parameters of these models are obtained in time domain by the extension of Yuwana and Seborg method originally proposed for SISO (Single Input Single Output) systems. From the identified closed loop transfer function matrix and the given controller transfer function matrix, the open loop transfer function matrix is obtained from the relation between the open loop and the closed loop transfer functions model. From the derived expressions for the open loop transfer functions, simplified FOPTD models are fitted in the s domain. The closed loop responses and interactions using the decentralized PI /PID controllers and the identified model are found to be matching satisfactorily with that of the original system. Further improved values of model parameters are obtained by using these identified model parameters as initial guess in the standard least square optimization method. For arbitrary values of the initial guess, the optimization method does not convergence.