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Semi-active control methods were developed as an attempt to reduce vibration in structures exposed to earthquake motion and overcome the difficulties encountered due to the ignorance of the real seismic responses as well as its real proper time history. Furthermore, the availability of excellent devices such as the Magneto Rheological damper for developing an adequate control force based on control law estimation in real time has been urging researchers in the last few years to design a robust controller. In this case the big challenge is to find an appropriate controller design correlated with a performant algorithm for current or tension fitting. In this paper, an adaptive sliding mode controller is proposed for controlling the vibrations of a scaled three-story structure equipped with a MR damper installed on its ground floor. The scaled structure is exposed to the Boumerdès and theEl Centro's earthquake excitations. The numerical simulation results for the proposed adaptive controlled structure compared with the results obtained for the uncontrolled structure have shown the effectiveness, stability and robustness of the semi-active feedback adaptive control design.

The sliding mode controller is one of the interesting classical nonlinear controllers in structural vibration control. From its apparition, in the middle of the twentieth century, this controller was a subject of several studies and investigations. This controller was widely used in the control of various semi-active or active devices in the civil engineering area. Nevertheless, the sliding mode controller offered a low sensitivity to the uncertainties or the system condition variations despite the presence of the Chattering defect. However, the adaptation law is one of the frequently used solutions to overcome this phenomenon offering the possibility to adapt the controller parameters according to the system variations and keeping the stability of the whole system assured. The chapter provides a sliding mode controller design reinforced by an adaptive law to control the desired state of an excited system. The performance of the adaptive controller is proved by numerical simulation results of a three-story excited structure.

Recently, the semi-active control of structural vibration has demonstrated its ability to preserve human life and keep structures safe during earthquakes. In the civil engineering area, the literature is full of investigation in both numerical and experimental research in which the Magneto-Rheological damper is the most used device. This paper investigates the semi-active control of three scaled excited structures. The proposed control is assured by a Magneto-Rheological damper controlled using a hybrid Fuzzy Sliding Mode controller. Although, a Clipped optimal algorithm is proposed to calculate the required current for the damper operating. Otherwise, the robustness of the suggested controller is proved by the obtained numerical results of the seismic excited scaled structure. Therefore, the tested structure is subjected to four time-scaled earthquake records. Finally, the effectiveness of the proposed semi-active control strategy in mitigating earthquake structural vibration is shown clearly in the compared controlled and uncontrolled responses. The simulation results show that the peak reduction reaches 65% under the 2011 Tōhoku earthquake. In addition, the performance indices prove the robustness of the proposed strategy.