Poles residues descent algorithm for optimal frequency-limited &amp;#x210B;&lt;inf&gt;2&lt;/inf&gt; model approximation

Vuillemin, Pierre; Poussot-Vassal, Charles; Alazard, Daniel

doi:10.1109/ecc.2014.6862152

Cited by 13 publications

(20 citation statements)

References 15 publications

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“…12 Obviously, from the original model H, other approximation methods might be applied to obtainĤ. For instance, the IRKA [22], DARPO [23], etc.. However, this is another issue not covered in the present paper (see e.g.…”

Section: A First Approach: Frequency-domain Matrix Function Interpolmentioning

confidence: 97%

Gust Load Alleviation: Identification, Control, and Wind Tunnel Testing of a 2-D Aeroelastic Airfoil

Poussot-Vassal

Demourant

Lepage

et al. 2017

IEEE Trans. Contr. Syst. Technol.

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One important element in the progression of aircraft environmental impact reduction is to reduce their overall weight (without impacting other consumption-oriented performance index, such as drag). In addition to the numerous work conducted in material and structural engineering, from a control viewpoint, this challenge is strongly connected to the need of the development and assessment of dedicated load control strategies in response to gust disturbances. Indeed, the load factors due to gust are considered as a sizing criteria during the aircraft conception steps and require specific verification according to the certification process. To this end, a dedicated experimental research program based on Wind Tunnel (WT) campaigns has been carried out. More specifically, the paper contributions are twofold: (i) to identify the gust load effect using two different versatile frequency-domain techniques, namely the Loewner interpolation and a modified subspace approach, and (ii) to design and implement an active closed-loop control to alleviate the gust main effect. The entire procedure is validated in a wind tunnel setup , involving a gust generator device and a 2D aeroelastic airfoil, for varying configuration travelling from sub to transonic airflow and varying angles of attack, emphasizing the effectiveness and robustness of the overall approach.

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Section: A First Approach: Frequency-domain Matrix Function Interpolmentioning

confidence: 97%

Gust Load Alleviation: Identification, Control, and Wind Tunnel Testing of a 2-D Aeroelastic Airfoil

Poussot-Vassal

Demourant

Lepage

et al. 2017

IEEE Trans. Contr. Syst. Technol.

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“…For the finite-dimensional case, many algorithms have been derived, e.g., H 2 model reduction [4,6] and frequency-limited H 2 model reduction [23]. The approaches mentioned in these references are based on the fact that a realization of the model to be reduced is available.…”

Section: Problem 1 (H 2 Approximation Problem)mentioning

confidence: 99%

Model Reduction for Norm Approximation: An Application to Large-Scale Time-Delay Systems

Duff

Vuillemin

Poussot-Vassal

et al. 2016

Delays and Networked Control Systems

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The computation of H 2 and H 2,Ω norms for LTI Time-Delay Systems (TDS) are important challenging problems for which several solutions have been provided in the literature. Several of these approaches, however, cannot be applied to systems of large dimension because of the inherent poor scalability of the methods, e.g., LMIs or Lyapunov-based approaches. When it comes to the computation of frequency-limited norms, the problem tends to be even more difficult. In this chapter, a computationally feasible solution using H 2 model reduction for TDS, based on the ideas provided in [3], is proposed. It is notably demonstrates on several examples that the proposed method is suitable for performing both accurate model reduction and norm estimation for large-scale TDS. IntroductionForewords: Modeling is an essential step to well understand and interact with a physical dynamical phenomena. It, among other, permits to analyze, simulate, optimize, and control dynamical processes. The values of a model lies on its ability to describe the reality as accurately as possible. In general, dynamical models are described by equations and their complexity is somehow linked to its number of equations and variables. Although complex models have a high degree of likeness with reality, in practice, due to numerical limitations, they are problematic to manipulate. Actually, complex models are difficult to analyze and to control, due to limited computational capabilities, storage constraints, and finite machine precision. Therefore, a good model has to reach a trade-off between its accuracy and complexity.In addition to high state-space complexity, we will be interested in how any delay may affect the system. This kind of models fall then in the class of infinitedimensional systems. As a matter of consequence, classical analysis and control methods are not applicable as it. Even if many dedicated approaches have been derived to handle TDS problems (see [18]), most of them are limited to delay systems with low-order state-space vector and associated methods are not scalable when the number of state variables is increasing. Many examples can be found in the context of network systems, where delays appear naturally as the amount of time necessary to transmit some information between different systems (communication lag). In other systems, they are intrinsic part of the natural phenomena as it can be seen in chemical reactions, traffic jam, and heating systems.This context justifies the search of simpler models in order to avoid numerical issues and to apply the classical methods of analysis and control. This is the philosophy of model approximation methods and they will be the main tool of this chapter. These methods permit to obtain a simpler model which well approximates the original one, even of infinite dimension.Contribution: In this chapter, we will work in the framework of linear timeinvariant dynamical systems and the complexity will be associated with the dimension of the state space of the systems. The aim of this chapter is ...

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“…() In terms of vibration control, some frequencies are of particular interest because the excitations in real world usually have limited frequency bands and mainly affect narrow bands around dominant modal frequencies of the systems with little or no damping. Therefore, we utilize the frequency‐limited versions of

H_{\infty}

‐ and

H_{2}

‐norms () in the optimization of TMD parameters, that is, computing the

H_{\infty}

‐ and

H_{2}

‐norms over bounded frequency intervals around dominant modal frequencies of the SCOLE model, which is numerically cheaper. Note that the modal frequencies of the SCOLE model are absolute values of the imaginary parts of the eigenvalues of A in Σ d (2.35)–(2.36) excluding TMDs.…”

Section: Optimization Of Tmds For Vibration Suppression Of the Nonunimentioning

confidence: 99%

“…We use

{(‖‖, H)}_{\infty, ([], ω_{l}^{i}, ω_{r}^{i})}

and

{(‖‖, H)}_{2, ([], ω_{l}^{i}, ω_{r}^{i})}

to denote the frequency‐limited

H_{\infty}

‐ and

H_{2}

‐norms of the transfer function matrix H of Σ d (2.35)–(2.36) over the frequency range

([], ω_{l}^{i}, ω_{r}^{i})

(in rad/s,

{normalω}_{l}^{i}, {normalω}_{r}^{i} \in R^{+}

{normalω}_{l}^{i} < {normalω}_{r}^{i}

) around the i th dominant modal frequency ω i , respectively. The numerical computation of

{(‖‖, H)}_{2, ([], ω_{l}^{i}, ω_{r}^{i})}

was based on the Gramian‐based formulation …”

Section: Optimization Of Tmds For Vibration Suppression Of the Nonunimentioning

confidence: 99%

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Passive vibration control of the SCOLE beam system

Tong

Zhao

2018

Struct Control Health Monit

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Summary We investigate the optimization of multiple tuned mass dampers (TMDs) to reduce vibrations of flexible structures described by partial differential equations, using the nonuniform Spacecraft Control Laboratory Experiment (NASA SCOLE) beam system with multiple dominant modes as an illustrative application. We use multiple groups of TMDs with each group being placed at the antinode of the mode shape of a dominant mode of the SCOLE beam. We consider both the harmonic and random excitations, for which we employ frequency‐limited H∞ and H2 optimizations respectively to determine the parameters of the TMDs. Our optimization scheme takes into account the trade‐off between effectiveness and robustness of the multiple TMDs to suppress the multiple dominant modes of the SCOLE beam. Simulation studies show that our scheme achieves substantial improvements over the traditional methods in terms of both effectiveness and robustness and that with equal total mass, TMD systems with each group having multiple TMDs are more effective and more robust than the ones with each group having a single TMD.

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Poles residues descent algorithm for optimal frequency-limited ℋ<inf>2</inf> model approximation

Cited by 13 publications

References 15 publications

Gust Load Alleviation: Identification, Control, and Wind Tunnel Testing of a 2-D Aeroelastic Airfoil

Gust Load Alleviation: Identification, Control, and Wind Tunnel Testing of a 2-D Aeroelastic Airfoil

Model Reduction for Norm Approximation: An Application to Large-Scale Time-Delay Systems

Passive vibration control of the SCOLE beam system

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