Control and optimization of structures with fluid interaction

by Borglund, Dan

Various problems on the optimal design of elastic structures subject to nonconservative uid-dynamic forces are considered. The optimal design problem is typically posed as minimizing structural weight subject to constraints on structural stability. Traditionally, structural dimensions and orientations of ber composite materials are common design variables. It is demonstrated that the structural weight can be reduced further by including the design of a stabilizing control 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 mayresultinadesignwith signi cantly 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 notbeachieved in practice. The importance of this fundamental di culty is emphasized throughout the thesis by comparing numerically obtained results to experiments. The rst part of the thesis is concerned with the stability and optimal design of a beam subject to forces induced by uidow through attached pipes. A nozzle control system de ecting the uid 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 modi ed optimization problem. The stability ofa exible wing structure with acontrollable trailing edge ap is investigated. Due to uncertainties in the numerical stability analysis, the wing is predicted to become unstable at a signi cantly higher speed than what is observed in wind tunnel tests. Two di erent approaches to stabilize the wing in utter is demonstrated. First, numerical optimization is used to design a controller which at each ow speed maximizes the damping of the utter 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 atwo-step procedure may berequired to obtain a design with minimum weight andacontrol law thatiswell-de ned for all operating conditions. Control and optimization of structures with uid interaction 5 Dissertation This doctoral thesis is based on a brief introduction to the area of research and the following appended papers: Paper A D. Borglund. On the optimal design of pipes conveying uid. Journal of Fluids and Structures, 12:353-365, 1998. Paper B D. Borglund. Active nozzle control and integrated design optimization of a beam subject to uid-dynamic forces. Journal of Fluids and Structures,13:269- 287, 1999. Paper C