Simplified inverse dynamics models for MR fluid dampers

The magnetorheological (MR) damper is considered to be one of the most promising semi-active control devices for reduction of structural vibration. Due to the damper's nonlinear characteristics, its inverse dynamics model is difficult to obtain. In this paper, a simplified approach, namely the simplified inverse dynamics (SID) model, has been developed for both the Bingham plasticity model and the Bouc-Wen hysteresis model. SID models have then been used to calculate the optimal fluid yield stress or input current, in order to realize the desirable control forces obtained from various optimal control algorithms. For each model, a piston velocity feedback (PVF) algorithm and a damper force feedback (DFF) algorithm have been formulated. The proposed model has been shown to be applicable to both small-scale and large-scale MR dampers. Also, different configurations of MR dampers, such as ones with different dimensions, coil resistances, types of MR fluid, have been employed to show the generic nature of the SID model. The effectiveness of force tracking using the SID model has been demonstrated through a series of numerical simulations. A multi-storey frame structure with MR damper-brace systems, using a large-scale 20-ton MR damper, has been adopted. Numerical results show that the MR damper with the proposed SID model can produce forces very close to the optimal control forces, and that the response reduction is very close to that for the case of fully active control. Also, equally high accuracy of force tracking for different shaking levels and frequency contents of ground motions can be observed. The results demonstrate that the SID model can be a simple, yet effective, tool for both research and application purposes.