Gani A., Langley R.

The active suppression of structural vibration is normally achieved by either feedforward or feedback control. In the absence of a suitable reference signal feedforward control cannot be employed and feedback control is the only viable approach. Conventional feedback control algorithms (e.g. LQR and LQG) are designed on the basis of a mathematical model of the system and ideally the performance of the system should be robust against uncertainties in this model. The aim of this paper is to numerically investigate the robustness of various algorithms by designing the controller for a nominal system, and then assessing (via Monte Carlo simulation) the effects of uncertainties in the system. The ultimate concern is with the control of high frequency vibrations, where the short wavelength of the structural deformation induces a high sensitivity to imperfection. It is shown that standard algorithms such as LQR and LQG are unfeasible for this case unless there is near collocation of sensor and actuator pairs. This leads to a consideration of design strategies for the robust active control of high frequency vibrations. The system chosen for the numerical simulation concerns two coupled plates, which are randomised by the addition of point masses at random locations. By adjusting the modal density and the modal overlap of the plates, and changing the strength of coupling, a wide range of generic dynamic behaviour can be captured, and a wide range of control objectives (e.g. global control or local control) can be investigated.