Vibration suppression control for a structural system using an AMD with restricted stroke

The problem of suppressing the vibrations of a one-degree-of-freedom structural system using an AMD (active mass damper) with restricted stroke is considered; it can be formulated as the problem of stabilizing a linear system with a state constraint. First this problem is reduced to the one with an input constraint by compensating the driving system for the weight (the auxiliary mass) of the AMD to have a second-order lag transfer function. Then a saturating control is designed by a partial state feedback technique. The control law has the following properties: 1) a good control performance is obtained controlling the weight of the AMD within the stroke constraint; 2) the control law is simple and easily implemented; and 3) in the case where the controller is used in the linear range a good frequency response property is obtained that the peak gains of the frequency responses of the weight and the structure for disturbances are lowered. The effectiveness of the control law is demonstrated by experiments and simulations.