Finite Dimensional Linear Systems

Brockett, Roger W.

doi:10.1137/1.9781611973884

Cited by 502 publications

(223 citation statements)

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“…Theorem 2.1: [10]. The linear time-periodic system (1) is asymptotically stable if and only if the eigenvalues of the state transition Φ(T, 0) lie within the unit circle.…”

Section: Periodic Systemsmentioning

confidence: 99%

Analysis and design of a tower motion estimator for wind turbines

Lio

Jones

Rossiter

2016

2016 IEEE International Conference on Renewable Energy Research and Applications (ICRERA)

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Abstract-The use of blade individual pitch control (IPC) provides a means of alleviating the harmful turbine loads that arise from the uneven and unsteady forcing from the oncoming wind. Such IPC algorithms, which mainly target the blade loads at specific frequencies, are designed to avoid excitations of other turbine dynamics such as the tower. Nonetheless, these blade and tower interactions can be exploited to estimate the tower movement from the blade load sensors. As a consequence, the aim of this paper is to analyse the observability properties of the blade and tower model and based on these insights, an estimator design is proposed to reconstruct the tower motion from the measurements of the flap-wise blade loads, that are typically available to the IPC. The proposed estimation strategy offers many immediate benefits, for example, the estimator obviates the need for hardware sensor redundancy, and the estimated signals can be used for control or fault monitoring purposes. We further show results obtained from high-fidelity turbine simulations to demonstrate the performance of the proposed estimator.

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“…Theorem 2.1: [10]. The linear time-periodic system (1) is asymptotically stable if and only if the eigenvalues of the state transition Φ(T, 0) lie within the unit circle.…”

Section: Periodic Systemsmentioning

confidence: 99%

Analysis and design of a tower motion estimator for wind turbines

Lio

Jones

Rossiter

2016

2016 IEEE International Conference on Renewable Energy Research and Applications (ICRERA)

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“…In some publications, the conditions in statement (2) are used as defining properties for positive realness of scalar-valued rational functions, see [9,40]. For matrix-valued rational functions, the implication (1) ⇒ (2) appears in [32, Theorem 5.10], albeit with slightly different terminology.…”

Section: Lemma 62 Letmentioning

confidence: 99%

Transfer functions of infinite-dimensional systems: positive realness and stabilization

Guiver

Logemann

Opmeer

2017

Math. Control Signals Syst.

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We consider a general class of operator-valued irrational positive-real functions with an emphasis on their frequency-domain properties and the relation with stabilization by output feedback. Such functions arise naturally as the transfer functions of numerous infinite-dimensional control systems, including examples specified by PDEs. Our results include characterizations of positive realness in terms of imaginary axis conditions, as well as characterizations in terms of stabilizing output feedback, where both static and dynamic output feedback are considered. In particular, it is shown that stabilizability by all static output feedback operators belonging to a sector can be characterized in terms of a natural positive-real condition and, furthermore, we derive a characterization of positive realness in terms of a mixture of imaginary axis and stabilization conditions. Finally, we introduce concepts of strict and strong positive realness, prove results which relate these notions and analyse the relationship between the strong positive realness property and stabilization by feedback. The theory is illustrated by examples, some arising from controlled and observed partial differential equations.

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“…In this section we will give a brief introduction to Floquet theory [20]. We define the Monodromy matrix and give stability conditions for the Hill's equation in terms of the Monodromy matrix.…”

Section: Preliminariesmentioning

confidence: 99%

Arnold Tongues for Discrete Hill’s Equation

Servin¹,

Collado²

2017

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In this work we study two types of Discrete Hill's equation. The first comes from the discretization process of a Continuous-time Hill's equation, we called Discretized Hill's equation. The Second is a naturally obtained in Discrete-Time and will be called Discrete-time Hill's equation. The objective of discretization is preserving the continuous-time behavior and we show this property. On the contrary a completely different dynamic property was found for the Discrete-Time Hill's equation. At the end of the paper is shown that both types share the nonoscillatory behavior of solutions in the 0-th Arnold Tongue.

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Finite Dimensional Linear Systems

Cited by 502 publications

References 0 publications

Analysis and design of a tower motion estimator for wind turbines

Analysis and design of a tower motion estimator for wind turbines

Transfer functions of infinite-dimensional systems: positive realness and stabilization

Arnold Tongues for Discrete Hill’s Equation

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