The motion of friction dampers, either passive or semi-active, involves sticking and slipping phases. The idea for increasing the performance of semi-active friction damper is to maintain its motion in the slipping phase as much as possible, since energy is dissipated during the slipping phase rather than the sticking phase. The effectiveness of semi-active friction damper depends on the control strategy used. Because of nonlinear characteristic of the friction damper, the establishment of an effective control strategy is a challenging effort. In optimal control theory, the bang-bang is a class of classical control laws. However, when applied to real structure control, it will produce some problems. One of disadvantages is that differential equation has to be solved on-line during the control process, which will lead to time delay and instability to the control system. The other is that the undesirable spikes will emerge near the origin of the state space due to high speed switching of the control force. In this paper, a new strategy based on the T-S fuzzy model and modified bang-bang algorithm is proposed. First, the theory of the T-S fuzzy model is briefly introduced. Next, the modified bang-bang control law is reviewed. Then, the implementation procedure of the proposed control method is detailed for description, and the optimal control force in the consequent part of the T-S model is achieved by the genetic algorithm. Finally, on the establishment of the semi-active control law, the approach here is applied to the vibration control of a three story building with a semi-active friction damper. Numerical simulation results indicate that the proposed control strategy not only effectively reduce the chattering effect as the responses of the structure cross through the zero points in the state space but also is adaptive to varying excitations from weak and strong earthquakes.

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