Analyse en stabilité par une nouvelle approche algorithmique basée sur les IQC : application à un avion d'arme

International audienceTo analyze a non-linear, uncertain and time-varying closed loop representing a fighter aircraft model interconnected with a control law, an Integral Quadratic Constraint (IQC) approach has been used. This approach is particularly interesting for two reasons. The first one is that it is possible with the same stability criterion to analyze a large class of stability problems. The second reason is that the stability criterion is based on frequency dependent inequalities (FDI). Usually, the Kalman-Yakubovich-Popov (KYP) lemma is used, in order to transform this infinite set of inequalities into one linear matrix inequality (LMI). However, this kind of approach leads to a steep increase in the number of optimization variables. Consequently, a new FDIbased algorithmic approach has been developed. Usually, the number of FDI that must be satisfied is infinite or, thanks to a frequency domain gridding, it is possible to avoid this problem but with the drawback of not being able to guarantee the validity of the solution throughout the frequency domain continuum. To tackle this problem, a specific technique has been developed. It consists in computing a frequency domain where the solution is valid. By an iterative approach, this domain is extended to cover [0,+∞[. Thus, the solution obtained from the FDI is necessarily valid throughout the frequency domain continuum and the number of optimization variables remains limited, which makes the IQC approach tractable for high-order models.Une approche basée sur les IQC a été mise en œuvre pour analyser la stabilité d'un avion d'arme en boucle fermée en présence de non-linéarités, de paramètres variant dans le temps et d'incertitudes. L'approche IQC est particulièrement intéressante pour deux raisons. La première est qu'il est possible, avec le même critère mathématique, d'analyser une large classe de problèmes en stabilité. La seconde raison est que ce critère mathématique est basé sur des inégalités dépendant de la fréquence (IDF). Habituellement cet ensemble infini d'inégalités fréquentielles est remplacé par une unique inégalité matricielle affine (IMA) grâce au lemme de Kalman-Yakubovich-Popov (KYP) . Mais cette transformation n'est pas gratuite puisqu'elle engendre une forte augmentation du nombre de variables de décision. Pour éviter cela, une nouvelle approche algorithmique basée sur les IDF a été développée. Initialement le nombre de contraintes fréquentielles à satisfaire est infini, mais devient fini si l'on se restreint à un maillage du domaine fréquentiel considéré. La difficulté vient du fait qu'on ne dispose alors d'aucune garantie de stabilité et de performance entre les points du maillage. Pour traiter ce problème une technique spécifique a été développée. Elle consiste à déterminer la validité de la solution sur un continuum fréquentiel. Ainsi, par une approche itérative, il est possible de couvrir tout le domaine [0;+∞[. De cette façon, la solution obtenue à partir des IDF est nécessairement valide sur tout le domaine fréquentiel, tout en conservant un nombre limité de variables de décision rendant ainsi possible la mise en œuvre des techniques IQC sur des modèles d'ordre élevé

Dynamical medium (large) -scale model reduction and interpolation with application to aircraft Systems

International audienceAlthough the need for even more accurate system, phenomena and process modeling is required in order to reduce development time and costs, the number of variables linear and non-linear optimization tools can handle is still a practical and theoretical limiting factor. This is especially true in aircraft dynamical performance analysis, monitoring and control design, where dynamical models are accurately designed at varying local flight configurations, in order to handle flexible modes, aerodynamic delays, etc., leading to high-dimensional problems [5]. Although Onera has a well established tradition of proposing complete and efficient tools for optimizing controllers and analyzing dynamic system performances through the use of Linear Fractional Representation (LFR) mathematical objects [2, 15, 22], recent growth in the dimensions of models has led to strong time and computational limitations when using these tools. The aim of this paper is to give an overview of the solutions developed within Onera to approximate a set of large-scale dynamical models with a parameterized LFR lower order model, which can be used in place of the original ones to effectively synthesize control laws and achieve performance analysis

A linear parameter-varying multiobjective control law design based on youla parametrization for a flexible blended wing body aircraft

This article presents a methodology for a linear parameter-varying (LPV) multiobjective flight control law design for a blended wing body (BWB) aircraft and results. So, the method is a direct design of a parametrized control law (with respect to some measured flight parameters) through a multimodel convex design to optimize a set of specifications on the full-flight domain and different mass cases. The methodology is based on the Youla parameterization which is very useful since closed loop specifications are affine with respect to Youla parameter. The LPV multiobjective design method is detailed and applied to the BWB flexible aircraft example

Structured Control for a Satellites Platoon Formation in Low Earth Orbit Using Youla-Parametrization.

The paper presents the design and analysis of a control strategy appropriate in the case of two or more spacecrafts in low Earth orbit and in close along-track configuration. The well known dynamics of the relative motion are briefly recalled and their decoupling properties allow to restrict the multivariable control design to an in-plane problem. An H1 synthesis is used to obtain a control law for a formation of two satellites. The control of a formation of four satellites, in the case of local measurements between each satellite and the preceding one, falls in the framework of structured control. A Youla-parameter based technique (convex synthesis) allows to use convex optimization to improve the initial blockdiagonal structure derived from the two-satellites controllers, with a great flexibility to take into account frequency and time constraints

A new frequency-domain subspace algorithm with restricted poles location through LMI regions and its application to a wind tunnel test

<p>In this paper, an innovative method is presented to identify models with a modified frequency-domain subspace method. This new approach allows to introduce in the subspace resolution constraints on the identified model poles location. Here, a very general formulation is proposed to take into account regions in continuous/discrete map. This formulation is based on an LMI (linear matrix inequalities) description where the stability domain represents a particular case. These LMI constraints are combined with the frequency-domain subspace resolution to obtain identified models whose poles are situated in the specified LMI regions. This approach is benchmarked with the Loewner one, which belongs to the class of frequency-domain input–output model identification and approximation methods. Besides the fact that they both belong to the data-driven model approximation class, they result to have slightly different objectives and show complementary performances. This discussion is illustrated in practice with experimentations that have been performed for the identification and control of the gust disturbance over a 2D wing span, from sub to transonic, in a wind tunnel facility.</p

Analyse de stabilité d'un ensemble de modèle dynamiques incertains de grande dimension en présence de saturations et application à un modèle d'avion d'affaires

International audienceFrom a sparse set of large-scale Linear Time Invariant (LTI) dynamical models, a methodology to generate a low-order parameter-dependent and uncertain model, with guaranteed bounds on the approximation error is firstly obtained using advanced approximation and interpolation techniques. Secondly, the stability of the aforementioned model, represented as a Linear Fractional Representation (LFR) and subject to actuator saturation and dynamical uncertainties, is addressed through the use of an irrational multiplier-based Integral Quadratic Constraint (IQC) approach. The effectiveness of the approach is assessed on a complex set of aeroservoelastic aircraft models used in an industrial framework for control design and validation purposes.Partant d'un ensemble de modèles dynamiques linéaires et invariants dans le temps de grande dimension, une procédure permettant de générer un modèle paramétrique de faible dimension avec des garanties sur les erreurs d'approximation et d'interpolation est présentée. Puis, sur la base de la représentation linéaire fractionnaire de ce modèle paramétrique, une analyse de stabilité en présence de saturations sur les actionneurs et prenant en compte des incertitudes dynamiques est conduite. Cette analyse repose notamment sur l'utilisation de multiplieurs irrationnels dans des contraintes intégrales quadratiques. Enfin, l'efficacité de la procédure est illustrée sur un ensemble de modèles d'avions aéroélastiques utilisés dans l'industrie pour la synthèse de lois de contrôle et leur validation

Frequency-domain data-driven control design in the Loewner framework

In this article, a direct data-driven design method, based on frequency-domain data, is proposed. The identification of the plant is skipped and the controller is designed directly from the measurements. The identification task is reported on a fixed-order controller using for the first time the Loewner approach, known for model approximation and reduction. The method is validated on two numerical examples including the control of an industrial hydroelectric generation plant, modelled by irrational equations