Robust control and model and controller reduction of linear parameter varying systems

El-Zobaidi, H.; Jaimoukha, Imad M.

doi:10.1109/cdc.1998.757952

Cited by 17 publications

(16 citation statements)

References 9 publications

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“…We now state the convex condition to search for contractive factorizations (similar conditions appear in Wood, Goddard, & Glover 1996;El-Zobaidi & Jaimoukha 1998 in the context of LPV systems).…”

Section: Lmi-based Algorithm For Structured Coprime Factor Model Redumentioning

confidence: 99%

“…To avoid this problem, in this paper we seek structured model reduction methods in the coprime factor description of a system. In the absence of structure, such methods have been developed by Anderson & Liu (1989); Liu & Anderson (1986); McFarlane & Glover (1990); Meyer (1990);El-Zobaidi & Jaimoukha (1998), and can be applied even to unstable systems; they are briefly reviewed in Section 2. Particularly attractive are reductions based on normalized coprime factorizations, since robustness results on closed-loop stability are available.…”

Section: Introductionmentioning

confidence: 99%

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Structured coprime factor model reduction based on LMIs☆

LI¹,

Paganini²

2005

Automatica

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In this paper we discuss dynamic model reduction methods which preserve a certain structure in the underlying system. Specifically, we consider the situation where the reduction must be consistent with a partition of the system states. This is motivated, for instance, in situations where state variables are associated with the topology of a networked system, and the reduction should preserve this. We build on the observation that imposing block structure to generalized controllability and observability gramians automatically yields such state-partitioned model reduction. The difficulty lies in ensuring feasibility of the resulting Lyapunov inequalities, which is in general very restrictive. To overcome this, we consider coprime factor model reduction. We derive an LMI characterization of expansive and contractive coprime factorizations that preserve structure, and use this to build a more flexible method for structured model reduction. An example is given to illustrate the method.

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Section: Lmi-based Algorithm For Structured Coprime Factor Model Redumentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Structured coprime factor model reduction based on LMIs☆

LI¹,

Paganini²

2005

Automatica

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show abstract

“…Using the energy propagation concept in-troduced by [14], and applied to the closed-loop model reduction algorithm of [6], it can be shown that the eigenvalues of the Gramians used in our controller balancing and truncation have a controller input/output energy interpretation.…”

Section: Remark Iv2mentioning

confidence: 99%

Normalized H/sub ∞/ controller reduction with a priori error bounds

El-Zobaidi¹,

Jaimoukha²,

Limebeer³

2001

IEEE Trans. Automat. Contr.

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Abstract-This note describes an approach to the reduction of controllers for the normalized coprime factor robustness problem as well as the normalized problem. It is shown that a relative error approximation of a coprime factor representation of any suboptimal controller leads to a stability guarantee and an upper bound on the performance degradation when the reduced order controller is implemented. When the approximation is performed on the controller generator, guaranteed a priori stability and performance bounds are obtained in terms of the synthesis Riccati equation solutions of the normalized control problems.

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“…In comparison with Zobaidi et.al [6] method, it is different in the controller design technique. Zobaidi [6] et.al use solutions of the control and filtering riccati inequalities to construct a full-order parameter dependent controller, whereas in this paper it is constructed from the solutions of the linear matrix inequalities developed by Apkarian [2]. We also investigate the degradation of the parameter dependent closed-loop performance in norm due to the reduced-controller.…”

Section: Introductionmentioning

confidence: 99%

“…The LTI model approximation techniques of BT method have been extended to reduce a Linear Time Varying (LTV) systems [10,11]. Wood et.al [12] and Zobaidi et.al [6] generalized this method to reduce parameter dependent systems with unbounded rate parameter model and controller. They [10,11,12] extend the twice the sum of the tail formula well known in the LTI case.…”

Section: Introductionmentioning

confidence: 99%

Controller Reduction of Parameter Dependent Systems

Widowati¹,

Riyanto²,

Saragih³

2004

itbj.eng.sci.

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Abstract. This paper proposes a controller reduction of linear parameter dependent systems. A measure of the degradation is derived for the parameter dependent closed-loop performance caused by applying the reduced-order parameter dependent controller. This measure can be obtained by extending the degradation of the closed-loop performance of the balanced truncation of the corresponding time invariant systems. To verify the performance of the reducedorder controller, an application of the proposed controller reduction method to vertical acceleration of a missile is presented. Keywords: balanced truncation; closed-loop performance; parameter dependent controller; reduced-order controller. IntroductionAlmost all physical systems have parameter dependent representations, but many the current modelling and control of physical systems use Linear Time Invariant (LTI) systems. As operating conditions change, the behavior of the physical systems and the linear time invariant model vary so that the closed loop performance designed by LTI controller may degrade. To cope with this problem, it is required that the parameter dependent is designed using parameter dependent controller. Moreover, modern controller design theories such as and synthesis usually produce controllers that have the same order as that of the model. Thus, the application of these design techniques to high order models will produce high order controllers. The design and analysis of highorder controllers demand high computational cost and may results in numerical difficulties while its implementation is very complex. Hence, it is important to find the low (reduced)-order controllers for parameter dependent systems.

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Robust control and model and controller reduction of linear parameter varying systems

Cited by 17 publications

References 9 publications

Structured coprime factor model reduction based on LMIs☆

Structured coprime factor model reduction based on LMIs☆

Normalized H/sub ∞/ controller reduction with a priori error bounds

Controller Reduction of Parameter Dependent Systems

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