Ali Mohammed Hussein Kadhim Al-Judi

This paper proposes an automated pairing approach for configuration selection of decentralized controllers which considers system uncertainties. Following the relative interaction array (RIA) pairing rules, the optimal control configuration, that is, the configuration that fits best the pairing rules, is obtained automatically by formulating the control configuration selection problem as an assignment problem (AP). In this AP, the associated costs related to each input–output pairing are given by the RIA coefficients. The push–pull algorithm is used to solve the AP for the nominal system and to obtain the set of costs for which the resulting configuration remains optimal, also called the perturbation set. The introduction of uncertainty bounds on the RIA-based costs enables the testing of the possible violation of the optimality conditions.

This article presents a procedure that utilizes the local polynomial approximation approach in the estimation of the Dynamic Relative Gain Array (DRGA) matrix and its uncertainty bounds for weakly nonlinear systems. This procedure offers enhanced frequency resolution and noise reduction when random excitation is used. It also allows separation of nonlinear distortions with shorter measuring time when multisine excitation is imposed. The procedure is illustrated using the well-known quadruple tank process as a case study in simulation and in real life. Besides, a comparison with the pairing results of the static RGA, nonlinear RGA and DRGA based on linearized quadruple tank model for different simulation cases is performed.

This article presents a procedure to estimate the relative gain array (RGA) matrix for weakly nonlinear systems by means of nonparametric identification of the frequency response matrix (FRM). Specifically, the best linear approximation of nonlinear systems and the covariance of the nonlinear distortions are used in the relative gain array estimation. For the estimation neither process model nor model structure need to be known which is an advantage over methods that require accurate knowledge of a parametric process model. The proposed approach is compared with the original RGA and a nonlinear RGA calculation using the well-known quadruple tank process as a case.

This article proposes computationally tractable, easy to expand and tight relative gain variation bound for uncertain systems. The proposed bound is a further development of previous work, which is summarized and discussed. Using several examples, the new method is compared with previous results and the advantages are highlighted. The prediction of sign changes in relative gain array elements due to uncertainties is important for pairing decisions. Based on the proposed bound, a method for the prediction of the uncertainty levels which render sign changes is suggested. The prediction method is currently limited to certain classes of systems. In this prediction method neither prior knowledge of the uncertainty nor numerous calculations are needed.