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Relative Gain Array of Weakly Nonlinear Systems using a Nonparametric Identification Approach
Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.ORCID iD: 0000-0001-7598-4815
Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.ORCID iD: 0000-0002-9992-7791
Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.ORCID iD: 0000-0002-5888-8626
Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.ORCID iD: 0000-0002-0079-9049
2015 (English)In: 2015 IEEE International Conference on Control Applications (CCA 2015): Sydney, Australia, September 21-23, Piscataway, NJ: IEEE Communications Society, 2015, p. 1612-1617, article id 7320840Conference paper, Published paper (Refereed)
Abstract [en]

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

Place, publisher, year, edition, pages
Piscataway, NJ: IEEE Communications Society, 2015. p. 1612-1617, article id 7320840
Series
I E E E International Conference on Control Applications. Proceedings, ISSN 1085-1992
National Category
Control Engineering Signal Processing
Research subject
Control Engineering; Signal Processing
Identifiers
URN: urn:nbn:se:ltu:diva-40297DOI: 10.1109/CCA.2015.7320840Scopus ID: 84964355520Local ID: f5fd5d67-cccf-4910-9d34-0fbcbe476a16ISBN: 978-1-4799-7787-1 (electronic)OAI: oai:DiVA.org:ltu-40297DiVA, id: diva2:1013819
Conference
IEEE International Conference on Control Applications : 21/09/2015 - 23/09/2015
Note
Validerad; 2016; Nivå 1; 20150717 (wolfgang)Available from: 2016-10-03 Created: 2016-10-03 Last updated: 2018-03-19Bibliographically approved
In thesis
1. Selection of Decentralized Control Configuration for Uncertain Systems
Open this publication in new window or tab >>Selection of Decentralized Control Configuration for Uncertain Systems
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Industrial processes nowadays involve hundreds or more of variables to be maintained within predefined ranges to achieve the production demands. However, the lack of accurate models and practical tools to design controllers for such large processes motivate the engineers/practitioners to break the processes down into smaller subsystems and applying decentralized controllers.

In contrast to the centralized controller, the decentralized controller is favourable in large-scale systems due to its robustness against loop failures and model uncertainties as well as being easier to tune and update. Yet, two steps are required prior to synthesizing these single-input single-output (SISO) controllers that comprise the decentralized controller. In the first step, a set of manipulated and the controlled variables need to be selected while the second step deals with pairing these variables to close the SISO control loops in a manner that limits the interaction between the loops. The latter step, called "input-output pairing", is usually performed by means of interaction measures (IM) tools using a nominal system model. Taking model uncertainties into consideration when deciding the pairing selection of the decentralized controller is necessary since adopting the pairing based on the nominal system model might be misleading and resulting in poor system performance or instability. It is therefore essential to have tools indicating the extent to which the pairing based on the nominal model persists against gain variations due to uncertainties.

The work in this thesis presents a methodology that determines whether the effect of gain uncertainty would invalidate the selected pairing. This has been done following the definition of the most established IM tool used in the industry, the relative gain array (RGA), and some of its variants. Further, a procedure has been developed to automatically obtain the optimal input-output pairing by formulating the pairing rules of relative interaction array (RIA) method as an \textit{assignment problem} (AP), and thus, simplifying the pairing selection for large-scale systems. Thereafter, uncertainty bounds of the RIA elements are employed to validate the pairing selection under the effect of given variations of the system gain. Moreover, following the RIA pairing rules, a method is proposed to calculate a minimum amount of uncertainty that renders a perturbed system for which the pairing, obtained from the nominal system model, becomes invalid.

In the aforementioned methodologies, a parametric system model is assumed to be known. To relax this constraint, an approach is therefore proposed and evaluated which identifies the pairing of the decentralized controller directly from the input-output data. This approach has the advantage of exempting the user from deriving a complete parametric model of the plant to decide the input-output pairing, and hence saves the efforts by finding the parameters of the most significant subsystems in a multivariable system. The frequency response of the system and its covariance, and subsequently the dynamic RGA (DRGA) and corresponding uncertainty bounds, are estimated from the input-output data by employing a nonparametric system identification approach. 

In short, the work presented in this thesis provides beneficial methodologies for researchers in academia as well as engineers in industry to predict the influence of the system gain uncertainty on the pairing selection of decentralized controllers.

Place, publisher, year, edition, pages
Luleå: Luleå University of Technology, 2018
Series
Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544
National Category
Engineering and Technology Control Engineering
Research subject
Control Engineering
Identifiers
urn:nbn:se:ltu:diva-67649 (URN)978-91-7790-053-5 (ISBN)978-91-7790-054-2 (ISBN)
Public defence
2018-04-10, A109, Luleå University of Technology, Luleå, 10:00 (English)
Opponent
Supervisors
Available from: 2018-02-14 Created: 2018-02-14 Last updated: 2018-03-23Bibliographically approved

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Kadhim, AliCastano, MiguelBirk, WolfgangGustafsson, Thomas

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