Optimal vibration control and co-design of very flexible actuated structures

The single shooting method is applied to the optimal control and combined structural and control design (co-design) of very flexible beams. The objective is to assess feasibility, advantages and limitations of an integrated design approach when dealing with actuated structures exhibiting large oscillations and, more generally, strongly nonlinear couplings. A gradient based approach is proposed for the large design space defined by both the optimal control and co-design problems. Numerical studies are presented for the case of a very flexible actuated pendulum with large rigid-body motion. The impact of local (B-splines) and global (discrete sines) set of basis functions is investigated for increasing levels of actuation authority, showing 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 disciplines around specific design points is found, thus highlighting the disadvantage of a sequential design approach. Simultaneous designing of control law and structure is seen, instead, to explore efficiently larger regions of the design space.