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Modeling and control of a wing at low Reynolds number with high amplitude aeroelastic oscillations

Fabien Niel 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : At high angles of attack or low Reynolds number, aircraft wings or blades of helicopters or even wind turbines may encounter separation of the ow which can eventually lead to aeroelastic couplings such as utter. These instabilities can be particularly destructive and are limiting for numerous applications. This thesis aims at considering the aeroelastic modeling and control of a pitching wing in utter conditions and at providing a general approach to tackle this problem. First, an aeroelastic model is developed based on previous works. This model provides an extension of the model proposed by Goman-Khrabrov, and modi ed by Williams, using the ONERA BH model. If the rst component of the model captures the hysteresis of the aerodynamic load of a pitching wing, the second one allows us to capture the vortex shedding and dynamic stall model which can be observed. This second component is particularly challenging to predict, while it plays an important role in the dynamics of the wing. The aerodynamic model is then trained and successfully compared to experimental data for a NACA 0018 rigid wing undergoing pitch oscillations at low Reynolds number. This model, like many aeroelastic or aerodynamic models, su ers from its inherent complexity and nonlinearities which make its analysis and control highly complicated with respect to the automatic control point of view. For this reason, the set of equations is conveniently manipulated to encapsulate the nonlinearities in a polytopic formulation with unknown parameters. Then, control strategies dedicated to linear time invariant systems are derived to account for this polytopic formulation. In addition, rate and magnitudes saturations are a major and recurrent issue in ight control and are also considered as an additional constraint in the control loop. Based on linear quadratic regulation theory, several theorems are developed using framework of linear matrix inequalities and allow not only to synthesize a stabilizing controller but also to de ne the region of attraction. The theorems are then applied to solve the problem of stall utter and successfully stabilize the closed-loop system in presence of rate and magnitude saturations, which demonstrate the potential of the contributions developed within this PhD approach.
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Fabien Niel. Modeling and control of a wing at low Reynolds number with high amplitude aeroelastic oscillations. Automatic Control Engineering. INSTITUT SUPERIEUR DE L'AERONAUTIQUE ET DE L'ESPACE (ISAE), 2018. English. ⟨tel-01763500⟩

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