Non-linear dynamics of a flexible airship

Abstract : The autonomous flying machines interest more and more the community of the mechanics and the control engineers. The researches on this subject is intensified in these last decades. In one hand the development of technologies makes it possible to consider innovating concepts, and on the other hand it is a question of extending operational capabilities of these machines to be able to carry out more complex missions. Nevertheless, certain technical difficulties must be mastered, in particular the study of the effect of structural flexibility, consideration of the aerodynamic phenomena, and the design of adequate control laws. The autonomous airships are part of this class of machines promised a bright future in particular in the field of sustainable development or the monitoring. The design of airships is often characterized by its classicism. The researchers often avoided the inherent mathematical complexities of the non-ellipsoidal shapes. But in order to optimize the performances of these machines, various original forms were proposed these last years, in particular by the network DIRISOFT-FRANCE whose airship MC500 represents the support of my work. In this context, this manuscript focuses on the modelling and control of a flexible airship characterized by its flying wing shape. We will study initially the kinematic and dynamic modelling of the airship in its “rigid” form, and in a second step, we will include the study of its flexibility taking into account, in both cases, the aerodynamic efforts. We admit that these flying machines undergo large displacements and small elastic deformation. The phenomenon of the added masses is also taken into account. An analytical study of this phenomenon was developed for the case of the rigid configuration and similarly for the case of the flexible configuration in large displacements. The study is based on the concept of the velocity potential of the fluid, and the development of the kinetic energy of the fluid under the effect of an overall motion of the airship. This method made it possible to seek solutions with the problem of Dirichlet through the search for functions satisfying the Laplace equation for fluids interacting with a structure. We assume that the complex shape of the airship is able to be initially approximate by a truncated cone of elliptic section. Consequently, the study of the velocity potential of the fluid around the airship led to the famous equations of Lamé that have to be solved by taking account of certain assumptions. A complete non-linear dynamic model of the airship could therefore be established. A study on the control law is carried out on the “rigid” model of the airship by two approaches: The first is linear. It is based on the linearized tangent model. The second is multi-model and based on the quasi-LPV (linear parameter varying) representation. This approach enables us to put the airship in a polytope well defined by its summits. We thus obtained, by this approach, a space of convergence of the airship towards a desired point. This q-LPV approach also enables us to express the non-linear dynamic model of the airship by means of linear subsystems, and we solve these subsystems by the LMI formulation (linear matrix inequality).The study of the robustness of the control laws chosen by the approach q-LPV was drawn up and proven for this system in the presence of uncertainties on the parameters of the airship as well as noise of measurements of the states of this flying machine. Numerical simulations are presented justifying the theoretical results obtained, and a critical analysis of these two approaches are presented.
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  • HAL Id : tel-01147195, version 1

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Saïd Chaabani. Non-linear dynamics of a flexible airship. Automatic. Université d'Evry Val d'Essonne; Ecole Polytechnique de Tunisie, 2014. English. ⟨tel-01147195⟩

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