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Relative Gain Array Variation for Norm Bounded Uncertain Systems
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: 0000-0002-5888-8626
Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.ORCID iD: 0000-0002-0079-9049
Number of Authors: 32015 (English)In: IEEE 54th Annual Conference on Decision and Control (CDC): Osaka, Japan, 15-18 Dec. 2015, Piscataway, NJ: IEEE Communications Society, 2015, p. 5959-5965, article id 7403156Conference paper, Published paper (Refereed)
Abstract [en]

This article proposes computationally tractable, easyto expand and tight relative gain variation bound for uncertain systems. The proposed bound is a further development of previous work, which is summarized anddiscussed. 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.

Place, publisher, year, edition, pages
Piscataway, NJ: IEEE Communications Society, 2015. p. 5959-5965, article id 7403156
Series
I E E E Conference on Decision and Control. Proceedings, ISSN 0743-1546
National Category
Control Engineering
Research subject
Control Engineering
Identifiers
URN: urn:nbn:se:ltu:diva-27878DOI: 10.1109/CDC.2015.7403156ISI: 000381554506025Scopus ID: 84962026626Local ID: 173b8281-2160-4cfe-afc7-8655ccaa121eISBN: 978-1-4799-7884-7 (electronic)OAI: oai:DiVA.org:ltu-27878DiVA, id: diva2:1001069
Conference
IEEE Conference of Decision and Control : 16/12/2015 - 18/12/2015
Note

Godkänd; 2015; 20150726 (alikad)

Available from: 2016-09-30 Created: 2016-09-30 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, AliBirk, WolfgangGustafsson, Thomas

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