The single shooting method is applied to the optimal control of very flexible aeroelastic wings and the combined structural and control design (co-design) of geometrically nonlinear beam models in vacuum. As large deflections occur, the dynamical properties of these systems can undergo substantial changes. Efficient actuation strategies require characterising, and possibly exploiting, these phenomena. With this purpose, geometrically-nonlinear models are built using composite beams and an unsteady vortex-lattice aerodynamics description. Optimal control is employed to identify actuations time-histories. Numerical solutions are obtained via single-shooting and sequential quadratic programming upon parametrisation of the control input. The approach is also extended to assess the feasibility of an integrated design strategy for active geometrically-nonlinear structures.


Numerical studies are first presented for a very flexible actuated pendulum with large rigid-body motion. The impact of local (B-splines) and global (discrete sines) basis functions is investigated for increasing levels of actuation authority, underlining the importance of the time-frequency resolution of the parametrisation on the convergence properties and outcome quality of the process. Locking between control and structural vibrations around specific design points is found, thus highlighting the limitations of a sequential design approach. Simultaneous designing of control law and structure is seen, instead, to explore more efficiently larger portions of the design space.


The lateral manoeuvring of very flexible partially-supported wings is then considered. A flight-dynamics model based on elastified stability derivatives is shown to capture the relevant dynamics either under slow actuation or for stiff wings, and it is hence used as a reference. Embedding the full aeroelastic description into the optimisation framework expands the space of achievable manoeuvres, allowing for quick wing response with low structural vibrations or large lateral forces with minimal lift losses.