Réduction de modèle et contrôle en couche limite décollée, au moyen de modes globaux.

Nous utilisons les modes globaux bi-dimensionnels comme base de projection pour étudier la dynamique et en tant que modèle réduit pour contrôler un prototype de couche limite décollée. Une zone de recirculation est induite dans une couche limite par la présence d'une cavité. Une étude de croissance transitoire optimale montre que la famille de modes globaux fortement non-normaux est capable de représenter la croissance convective d'une perturbation initiale localisée. De plus, un modèle réduit de l'écoulement construit en projetant les équations de Navier-Stokes sur ces modes globaux permet de décrire correctement la dynamique. Nous utilisons ce modèle linéaire dans une procédure de contrôle optimal en boucle fermée, avec une sonde et un actionneur, et montrons que l'écoulement peut être stabilisé

Reduced order models for control of fluids using the Eigensystem Realization Algorithm

In feedback flow control, one of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A number of techniques are presently used to develop such reduced-order models, such as proper orthogonal decomposition (POD), and approximate snapshot-based balanced truncation, also known as balanced POD. Each method has its strengths and weaknesses: for instance, POD models can behave unpredictably and perform poorly, but they can be computed directly from experimental data; approximate balanced truncation often produces vastly superior models to POD, but requires data from adjoint simulations, and thus cannot be applied to experimental data. In this paper, we show that using the Eigensystem Realization Algorithm (ERA) \citep{JuPa-85}, one can theoretically obtain exactly the same reduced order models as by balanced POD. Moreover, the models can be obtained directly from experimental data, without the use of adjoint information. The algorithm can also substantially improve computational efficiency when forming reduced-order models from simulation data. If adjoint information is available, then balanced POD has some advantages over ERA: for instance, it produces modes that are useful for multiple purposes, and the method has been generalized to unstable systems. We also present a modified ERA procedure that produces modes without adjoint information, but for this procedure, the resulting models are not balanced, and do not perform as well in examples. We present a detailed comparison of the methods, and illustrate them on an example of the flow past an inclined flat plate at a low Reynolds number.Comment: 22 pages, 7 figure

SISO model-based control of separated flows: Sliding mode and optimal control approaches

International audienceThe challenging problem of active control of separated flows is tackled in the present paper using model-based design principles, and applied to data issued from a two-dimensional separated flow experiment. First, a bilinear state and input delay model of the system has been obtained from experimental data by means of a modified identification procedure. Adequacy and precision of the obtained model are demonstrated and compared with existing results. Next, two control problems (setpoint tracking and optimal control) have been formulated and studied using sliding mode control methodology and averaging analysis. The theoretical control results are supported with numerical simulations

Analysis of current and sea level observations from Trondheimsleia

Sea level and current measurements from Trondheimsleia have been analysed and the parameters of the tidal ellipses for the major tidal components M2, S2, N SUB>2, and K1 have been calculated. Harmonic constants for sea level and tidal ellipse parameters have been compared with the corresponding data from a high resolution tidal model in order to validate the performance of the model. Short periodic oscillations with period about 40 minutes are observed at the time of peak tidal current at one station located in a channel with relatively strong tidal currents

Global stability and feedback control of boundary layer flows

In this thesis the stability of generic boundary layer flows is studied from a global viewpoint using optimization methods. Global eigenmodes of the incompressible linearized Navier-Stokes equations are computed using the Krylov subspace Arnoldi method. These modes serve as a tool both to study asymptotic stability and as a reduced basis to study transient growth. Transient growth is also studied using adjoint iterations. The knowledge obtained from the stability analysis is used to device systematic feedback control in the Linear Quadratic Gaussian framework. The dynamics is assumed to be described by the linearized Navier-Stokes equations. Actuators and sensors are designed and a Kalman filtering technique is used to reconstruct the unknown flow state from noisy measurements. This reconstructed flow state is used to determine the control feedback which is applied to the Navier-Stokes equations through properly designed actuators. Since the control and estimation gains are obtained through an optimization process, and the Navier-Stokes equations typically forms a very high-dimensional system when discretized there is an interest in reducing the complexity of the equations. A standard method to construct a reduced order model is to perform a Galerkin projection of the full equations onto the subspace spanned by a suitable set of vectors, such as global eigenmodes and balanced truncation modes.QC 2010092

Global stability and feedback control of boundary layer flows

In this thesis the stability of generic boundary layer flows is studied from a global viewpoint using optimization methods. Global eigenmodes of the incompressible linearized Navier-Stokes equations are computed using the Krylov subspace Arnoldi method. These modes serve as a tool both to study asymptotic stability and as a reduced basis to study transient growth. Transient growth is also studied using adjoint iterations. The knowledge obtained from the stability analysis is used to device systematic feedback control in the Linear Quadratic Gaussian framework. The dynamics is assumed to be described by the linearized Navier-Stokes equations. Actuators and sensors are designed and a Kalman filtering technique is used to reconstruct the unknown flow state from noisy measurements. This reconstructed flow state is used to determine the control feedback which is applied to the Navier-Stokes equations through properly designed actuators. Since the control and estimation gains are obtained through an optimization process, and the Navier-Stokes equations typically forms a very high-dimensional system when discretized there is an interest in reducing the complexity of the equations. A standard method to construct a reduced order model is to perform a Galerkin projection of the full equations onto the subspace spanned by a suitable set of vectors, such as global eigenmodes and balanced truncation modes.QC 2010092

Network Gaming : Performance and Traffic Modeling

There are several different types of games that are played in multiplayer mode over networks. The type of network games that, from a network’s perspective, are the most demanding is real-time based multiplayer games. Users of such games both assume and require that game play interaction happens in near real-time and these games often support a large number of simultaneous players. Most networks are specialized to either voice traffic (such as the first and second generation of mobile networks) or data traffic (such as wired data networks). It is not clear that the requirements for such real time games can always be met on either type of network. The core of this thesis investigates the performance requirements real-time multiplayer games place on packet switched data networks and the connection between network impairments and game quality degradation. Traffic generated by network games distinguishes itself from other traffic both regarding its general characteristics and the requirements it places on the network. Understanding these traffic characteristics, requirements, and what consequences failures to support such requirements entail are of great importance when designing new networks in order to guarantee suitable quality of service for such real-time games.Det finns idag en stor mängd datorspel som spelas i flerspelarläge över nätverk. De spel som från ett hårdvaru- och nätverksperspektiv ställer högst krav är realtidsbaserade flerspelarspel. Slutanvändare av dessa realtidsspel både förutsätter och tar för givet att interaktionen sker i så nära realtid som möjligt samtidigt som dessa spel ofta stödjer ett stort antal samtidiga användare. De flesta nätverk är i första hand anpassade för rösttrafik (som första och andra generationens mobilnät) eller datatrafik (som trådade datanätverk). Det står inte klart huruvida någon av dessa nätverk kan garantera tillräcklig prestanda för att en acceptabel spelkvalité skall uppnås för slutanvändaren. Kärnan i denna rapport utreder vilka krav som dagens mest krävande realtidsbaserade flerspelarspel ställer på nätverken de spelas över samt kopplingen mellan brister i dessa nätverk och den upplevda spelkvalitén för användarna. Trafik genererad av realtidsbaserade flerspelarspel särskiljer sig från annan trafik både när det gäller generell karaktäristik och när det gäller de krav som de ställer på nätverken. Det är viktigt att ha en förståelse kring den trafik som dessa spel skapar, kraven de ställer, samt de konsekvenser ett misslyckande av upprätthållande av sådana krav medför. Denna förståelse är av yttersta vikt när man designar nya nätverk för att kunna erbjuda en passande Quality of Service för denna typ av interaktiva multimediatjänster

Feedback Control of Spatially Evolving Flows

In this thesis we apply linear feedback control to spatially evolving flows in order to minimize disturbance growth. The dynamics is assumed to be described by the linearized Navier--Stokes equations. Actuators and sensor are designed and a Kalman filtering technique is used to reconstruct the unknown flow state from noisy measurements. This reconstructed flow state is used to determine the control feedback which is applied to the Navier--Stokes equations through properly designed actuators. Since the control and estimation gains are obtained through an optimization process, and the Navier--Stokes equations typically forms a very high-dimensional system when discretized there is an interest in reducing the complexity of the equations. One possible approach is to perform Fourier decomposition along (almost) homogeneous spatial directions and another is by constructing a reduced order model by Galerkin projection on a suitable set of vectors. The first strategy is used to control the evolution of a range of instabilities in the classical family of Falkner--Skan--Cooke flows whereas the second is applied to a more complex cavity type of geometry.QC 2010112