Control and optimization of structures with fluid interaction

Abstract: Various problems on the optimal design of elastic structures subject to nonconservative fluid-dynamic forces are considered. The optimal design problem istypically posed as minimizing structural weight subject to constraints on structural stability. Traditionally, structural dimensions and orientations of fibercomposite materials are common design variables. It is demonstrated that the structural weight can be reduced further by including the design of a stabilizingcontrol system in the structural design optimization, giving an integrated optimization problem where both structural and control system parameters are used as design variables. The integrated approach may result in a design with significantly improved performance compared to traditional methods, both in terms of reduced structural weight and control system performance. Using optimization for design of mechanical systems with nonconservative external load tends to increase the likelihood of obtaining a design which is very sensitive to imperfections. As a result, the predicted performance of the optimal design may not be achieved in practice. The importance of this fundamental difficulty is emphasized throughout the thesis by comparing numerically obtained results to experiments.The first part of the thesis is concerned with the stability and optimal design of a beam subject to forces induced by fluid flow through attached pipes. A nozzle control system deflecting the fluid jet at the beam tip is used to improve the stability of the system. The simultaneous design of the control system and the beam shape minimizing structural mass is performed using numerical optimization. The inclusion of the control system in the optimization gives a considerable reduction of the beam weight but results in an optimal design which is very sensitive to imperfections. An optimal design with improved robustness is obtained by solving a modified optimization problem. The stability of a flexible wing structure with a controllable trailing edge flap is investigated. Due to uncertainties in the numerical stability analysis, the wing is predicted to become unstable at a significantly higher speed than what is observed in wind tunnel tests. Two different approaches to stabilize the wing in flutter is demonstrated. First, numerical optimization is used to design a controller which at each flow speed maximizes the damping of the flutter mode observed in the wind tunnel experiment. Second, an integrated approach is adopted, where a simultaneous mass balancing and control law design is performed. It is argued that a two-step procedure may be required to obtain a design with minimum weight and a control law that is well-defined for all operating conditions.