Time optimal semiactive vibration damping of a mechanical oscillator with variable damping coefficient

In this paper the semiactive vibration control of a single degree of freedom oscillator is considered. The oscillator comprises a magnetic viscous damper, providing a damping force which can be easily changed in real time. A semiactive control law acting on this parameter is developed, with the aim of damping as fast as possible the free oscillations of the structure. The application of the Pontryagin minimum principle formally proves that, if the goal is to reach in minimum time a small invariant set around the origin (that is, the rest position), the optimal control law for the considered bilinear system consists of a switching (bang-bang) feedback, operating at either the lowest or the highest available level of the damping force. Simulation results are presented, showing that the proposed vibration control scheme always outperforms a benchmark case of a mechanical oscillator with constant damping coefficient equal to the critical value.