Control of Underactuated Dynamics in Active Tuned Mass Damper Systems*

Active tuned mass dampers (ATMDs) are very effective in suppressing vibrations in structures due to specific external excitations. Since the number of degrees of freedom of an ATMD is larger than the number of its actuators, it is an underactuated system. It is also proved in this paper that the controllability matrix of the simplest ATMD system is ill-conditioned. An intuitive controller is suggested to stabilize the primal system by using the feedback linearization design, but it will result in unbounded auxiliary dynamics. A strategy to preserve passivity in the auxiliary system is proposed to modify the feedback linearization controller. The design problem can then be regarded as the solution of the Lyapunov equation, and may be solved numerically.