A method for the independent design of proportional-integral/proportional-integral derivative (PI/PID) controllers is proposed based on the equivalent transfer function (ETF) model of the individual loops and the simplified decoupler matrix. It is shown that the conventional effective open-loop transfer function (EOTF, derived from the dynamic relative gain array (DRGA)) is equivalent to the ETF (derived from the relative normalized gain array (RNGA) and relative average residence time array (RARTA)). This relation is used to approximate the decoupled process models as ETF models. The simplified decoupler is shown to decompose the multiloop systems into independent loops (multi-single loop systems) with the ETFs as the resulting decoupled process model. The concept of the ETF (perfect control approximation) is validated by introducing the decoupler. Based on the corresponding ETFs, the decentralized PI controllers are designed using the simplified internal model control (SIMC) method. Three simulation examples of multi-input multi-output (MIMO) process models are considered to demonstrate the simplicity and effectiveness of the proposed method. The performance of the proposed control system is compared with the ideal, normalized, inverted decoupling, and centralized control systems.
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).
An optimization method is presented for the closed-loop identification of first-order-plus-time-delay (FOPTD) transfer function models of multivariable systems using step responses. A standard least-squares optimization method is used to obtain the parameters of the FOPTD models by matching the closed-loop step responses of the model with those of the actual process. A simple method is proposed to obtain the initial guess values for the transfer function model parameters from the process main and interaction responses. The effects of measurement noise and controller settings on the identified model parameters were also studied. This method was applied to stable FOPTD and higher-order transfer function models of multivariable systems. The proposed method considerably reduces the computational time (by about a factor of 15) for the optimization when compared with the genetic algorithm method reported by Viswanathan et al. (Ind. Eng. Chem. Res.20014028182826).
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