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Closed-Loop Identification of Second-Order Plus Time Delay (SOPTD) Model of Multivariable Systems by Optimization Method

Rajapandiyan, C., Chidambaram, M.
Industrial & Engineering Chemistry Research 2012 v.51 no.28 pp. 9620-9633
algorithms, chemistry, engineering, least squares, models, system optimization
The closed-loop identification of second-order plus time delay (SOPTD) transfer function models of multivariable systems is presented based on optimization method using the combined step-up and step-down responses. The need for combined step up and step down changes in the set point is brought out for the convergence of the model parameters. A standard nonlinear least-squares optimization method is used to obtain the parameters of the SOPTD model transfer function matrix by minimizing the sum of squared errors between the closed-loop responses of the model and the actual process responses. A simple method is proposed to obtain the initial guess values of SOPTD transfer function model parameters from the main and interaction responses of the actual process. This method was applied to two-input two-output (TITO) second-order plus time delay (SOPTD), higher order and 3 × 3 SOPTD transfer function models of multivariable systems. The proposed method considerably reduces the computational time for the optimization for 2 × 2 SOPTD model systems (11 min and 11 s) when compared with the genetic algorithm (GA) method reported by Viswanathan et al. (Ind. Eng. Chem. Res.2001, 40, 2818–2826).