Relative gain array estimation based on non-parametric frequency domain system identification

Abstract

Since the introduction of the Relative Gain Array (RGA) by Bristol in 1966, it has received a high level of attention as a practical tool for solving the input-output pairing problem in decentralized control. Moreover, many extensions have been proposed like e.g. for the dynamic case and non-square system matrices. Recently, extensions that provide tools for uncertain parametric process models were suggested. In order to remove the dependency of these tools on a parametric description and accurate knowledge of a nominal model this paper proposes a method to calculate the RGA directly from a non-parametric frequency response matrix (FRM), derived from frequency domain system identification approach. The proposed method reduces the influence of model uncertainties on the calculation of the RGA and derives the RGA at frequencies of interest. Using Monte-Carlo principles, the variance of the estimated RGA is derived and compared with recently proposed methods. The results are exemplified on 2×2, 2×3 and 3×3 systems. It concluded that the proposed methods performs well and robust, while simplifying the estimation of the RGA.

Dynamic Relative Gain Array Estimation using Local Polynomial Approximation Approach

“…In previous work, (Kadhim et al, 2014) and (Kadhim et al, 2015b), the authors have investigated an approach that seems obvious yet was not thoroughly discussed before which requires less user interaction and efforts in estimating RGA and DRGA. The approach employs a nonparametric system identification method to estimate the system Frequency Response Matrix (FRM) from input-output data and then calculates RGA and DRGA.…”

“…This work aims to overcome the shortcomings represented by the low frequency resolution in Kadhim et al (2014) and the long experiment running time in Kadhim et al (2015b) while preserving the advantages of using the nonparametric identification approach in DRGA calculation. To achieve this for weakly nonlinear systems, the Local Polynomial Approximation Method (LPA) and the Local Polynomial Approximation-Fast Method (LPA-FM) introduced in Pintelon and Schoukens (2012) are employed with both random and multisine excitation signals, respectively.…”

“…Such an approach reduces the uncertainties arising from incorrect user decisions by avoiding the parametric model identification. In Kadhim et al (2014), both RGA and DRGA of linear systems are first determined using random excitation signal. Following the approach defined in Pintelon and Schoukens (2012), data is divided into sub-records and the frequency response is averaged over these sub-records to reduce the effect of the leakage that result from the nonperiodic nature of the random signal.…”

Modeling and Control of Membrane Filtration Systems for Offshore Produced Water Treatment

“…Cross couplings between the control loops can be accounted for by deploying advanced multiple-input-multiple-output (MIMO) control strategies, such as MPC. However, MPC is rarely deployed for membrane filtration, conceivably because of its reliance on an accurate model and complex tuning, compared to the PID structure [56,163]. Alternatively, the RGA method can be used to design a SISO control system where the control pairings can be selected to minimize interaction between the individual control loops [164].…”