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.

Abstract. Seismic vibration control using a magneto-rheological damper is a technique that interests several researchers around the world. This technique offers suitable structural building protection, ensuring human safety against earthquake excitation damages. The robustness of these devices depended in many cases on the designed law of control. Over the years, research focused on the development and modelling of various controllers to enhance the structural vibration elimination of buildings. The emphasis of this paper is on the evaluation of semi-active control robustness to reduce the displacements of a three-storey tested structure. The semi-active control device is a magneto-rheological fluid damper installed on the ground floor of the earthquake's excited structure and is controlled by an adaptive non-linear controller coupled to a clipped optimal algorithm to drive the current. The proposed controller is a sliding-mode controller reinforced by an adaptive technique to perform the control gain choice and overcome the chattering problem. The present law of adaptation is a switching conditional law between two laws offering the required gain depending on the system state. The numerical simulation results prove the effectiveness of the proposed semi-active control strategy in attenuating the displacements of the tested structure.