Semi-active Control of Magneto-Rheological Dampers with Negative Stiffness

Effective damping of large and flexible structures by semi-active dampers relies greatly on the control strategy applied, which should combine the robustness of passive devices and the increased damping performance often available from active control. For structural control the Magneto-rheological (MR) damper is among the most popular and promising devices due to its low power requirement, high dynamic range, high force capacity and robustness. The objective of this paper is to formulate semi -active feedback control methods based on simple linear damper models, which lead to increased damping performance by introduction of apparent negative damper stiffness. The design of the control strategy aims at maximizing the damping ratio of the critical mode of the structure. Explicit solutions for the complex valued natural frequency of the damped structure and the associated damping ratio are obtained by the two-component system reduction technique, which shows that a potential increase in damping is associated with a similar reduction of stiffness, or even with the introduction of negative stiffness. For linear control strategies negative stiffness can only be realized by active control, which is limited by stability. In the present paper it is realized by having the MR damper force track the simple pure viscous damper model with vanishing stiffness and the Kelvin model with negative stiffness. The applied voltage of the MR damper should be controlled in such a way that the desired control force is followed sufficiently accurate. This is done by letting the desired force be the input to an inverse Bingham model, which provides the corresponding desired voltage level of the MR damper. Numerical simulations are conducted to demonstrate the performance of the proposed semi-active control strategy with apparent negative stiffness.