An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation

Ahmad Jazlan, Pantazis Houlis, Victor Sreeram, Roberto Togneri

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    In this paper, an improved parameterized controller reduction technique via a new frequency weighted model reduction formulation is developed for the feedback control of MIMO discrete time systems particularly for non-unity feedback control system configurations which have the controller located in the feedback path. New frequency weights which are a function of a free parameter matrix are derived based on a set of equivalent block diagrams and this leads to a generalized double sided frequency weighted model reduction formulation. Solving this generalized double sided frequency weighted model reduction problem for various values of the free parameter results in obtaining controllers which correspond to each value of the free parameter. It is shown that the proposed formulation has a useful characteristic such that selecting a controller which corresponds to a large value of the free parameter results in obtaining an optimal reduced order controller and using this optimal reduced order controller in a closed loop system results in significant reduction in the infinity norm of the approximation error between the original closed loop system and the closed loop system which uses an optimal reduced order controller (when compared to existing frequency weighted model reduction methods).

    Original languageEnglish
    Pages (from-to)1920-1930
    Number of pages11
    JournalAsian Journal of Control
    Volume19
    Issue number6
    DOIs
    Publication statusPublished - 1 Nov 2017

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    Controllers
    Closed loop systems
    Feedback control
    MIMO systems
    Feedback
    Control systems

    Cite this

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    title = "An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation",
    abstract = "In this paper, an improved parameterized controller reduction technique via a new frequency weighted model reduction formulation is developed for the feedback control of MIMO discrete time systems particularly for non-unity feedback control system configurations which have the controller located in the feedback path. New frequency weights which are a function of a free parameter matrix are derived based on a set of equivalent block diagrams and this leads to a generalized double sided frequency weighted model reduction formulation. Solving this generalized double sided frequency weighted model reduction problem for various values of the free parameter results in obtaining controllers which correspond to each value of the free parameter. It is shown that the proposed formulation has a useful characteristic such that selecting a controller which corresponds to a large value of the free parameter results in obtaining an optimal reduced order controller and using this optimal reduced order controller in a closed loop system results in significant reduction in the infinity norm of the approximation error between the original closed loop system and the closed loop system which uses an optimal reduced order controller (when compared to existing frequency weighted model reduction methods).",
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    An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation. / Jazlan, Ahmad; Houlis, Pantazis; Sreeram, Victor; Togneri, Roberto.

    In: Asian Journal of Control, Vol. 19, No. 6, 01.11.2017, p. 1920-1930.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation

    AU - Jazlan, Ahmad

    AU - Houlis, Pantazis

    AU - Sreeram, Victor

    AU - Togneri, Roberto

    PY - 2017/11/1

    Y1 - 2017/11/1

    N2 - In this paper, an improved parameterized controller reduction technique via a new frequency weighted model reduction formulation is developed for the feedback control of MIMO discrete time systems particularly for non-unity feedback control system configurations which have the controller located in the feedback path. New frequency weights which are a function of a free parameter matrix are derived based on a set of equivalent block diagrams and this leads to a generalized double sided frequency weighted model reduction formulation. Solving this generalized double sided frequency weighted model reduction problem for various values of the free parameter results in obtaining controllers which correspond to each value of the free parameter. It is shown that the proposed formulation has a useful characteristic such that selecting a controller which corresponds to a large value of the free parameter results in obtaining an optimal reduced order controller and using this optimal reduced order controller in a closed loop system results in significant reduction in the infinity norm of the approximation error between the original closed loop system and the closed loop system which uses an optimal reduced order controller (when compared to existing frequency weighted model reduction methods).

    AB - In this paper, an improved parameterized controller reduction technique via a new frequency weighted model reduction formulation is developed for the feedback control of MIMO discrete time systems particularly for non-unity feedback control system configurations which have the controller located in the feedback path. New frequency weights which are a function of a free parameter matrix are derived based on a set of equivalent block diagrams and this leads to a generalized double sided frequency weighted model reduction formulation. Solving this generalized double sided frequency weighted model reduction problem for various values of the free parameter results in obtaining controllers which correspond to each value of the free parameter. It is shown that the proposed formulation has a useful characteristic such that selecting a controller which corresponds to a large value of the free parameter results in obtaining an optimal reduced order controller and using this optimal reduced order controller in a closed loop system results in significant reduction in the infinity norm of the approximation error between the original closed loop system and the closed loop system which uses an optimal reduced order controller (when compared to existing frequency weighted model reduction methods).

    KW - balanced truncation

    KW - Controller reduction

    KW - finite frequency model reduction

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