Constrained Optimal Control of Vibration Dampers

Optimal control of dampers has been proposed to mitigate vibration effects in mechanical systems. In many cases, systems are subject to periodic forcing and the goal is to maximize the energy dissipated by the damper. In contrast to prior work utilizing instantaneous or infinite-time−horizon optimization, this paper employs periodic optimal control to maximize the energy dissipated per cycle. For single-degree-of-freedom systems in which the maximum allowable control effort is of the same order as the forcing magnitude, a state-dependent singular control law is shown to deliver maximum energy dissipation. Alternate control laws are proposed for situations when rattle space requirements dictate damper displacements other than that of the singular solution. Saturation of the damping force is also considered. 7 1998 Academic Press