Flutter Control of Bridge Deck Using Experimental Aeroderivatives and LQR-Driven Winglets

Control of wind-induced flutter of a bridge deck section by using winglets is considered in this paper. The Scanlan-Tomko model was considered for self-excited wind forces acting on a deck and winglets. For this, the required flutter derivatives (FDs) of the deck were fitted using the Rogers rational function approximation. Vertical, lateral, and torsional degrees of freedom of the bluff body deck and their 18 corresponding experimental FDs were considered. Winglets were modeled as flat plates, for which FDs were obtained using Theodorsen's function. The time domain formulation involving aerodynamic states yields a divergence speed much lower than the correct divergence speed obtained by quasi-steady theory. Hence, a trial-and-error method involving sweeping through both speed and frequency was considered for the control study. Control inputs, that is, winglet rotations relative to the deck, were obtained using linear quadratic regulator (LQR) control with full state feedback. The state to be fed back was estimated by a full-order observer designed using pole placement. In order to prevent winglet stall, their absolute rotations were restricted within bounds. The flutter condition was verified using controlled responses and the results compared with those from closed-loop eigenvalue analysis. The control strategy appears to be quite effective in attenuating response and enhancing flutter speed.