International Journal of Dynamics and Control https://doi.org/10.1007/s40435-019-00559-0 Adaptive sliding mode vibrations control for civil engineering earthquake excited structures Leyla Fali 1 · Mohamed Djermane 1 · Khaled Zizouni 2 · Younes Sadek 1 Received: 22 February 2019 / Revised: 14 June 2019 / Accepted: 17 June 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract In recent years, the semi-active control of structural vibrations has interested several researchers. It has been demonstrated that semi-active control strategies are economical solutions for the safety of structure against earthquake or wind excitations. In this study, a semi active device which utilizes the Magneto-Rheological fluid characteristics to dissipate the earthquake excitation energy is proposed. The Magneto-Rheological damper is adopted to control the undesired vibrations of an earthquake-excited structure. Furthermore, a sliding mode controller coupled to the Clipped optimal algorithm is proposed to control this semi- active device. Otherwise, the sliding mode controller is reinforced by an adaptive gain law and the effectiveness of the new proposed adaptive controller to control the structural earthquake vibrations is proved by the compared numerical simulation results of the controlled and uncontrolled structure. Thus, the improvement of the sliding mode controller through the adaptive gain law is proved by the evaluation indices of an excited three-story scaled structure. Hence, a comparison between the results of the proposed adaptive sliding mode controller and the uncontrolled structure under the El Centro 1940 and the Boumerdès 2003 earthquakes excitations are discussed. Keywords MR damper · Semi-active control · Earthquake vibration · Adaptive control · Sliding mode control 1 Introduction Earthquakes around the world are the most tragedies natural phenomena which leaved behind serious structural damage, collapsed buildings and bridges and therefore a consider- able number of human life losses. However, the most deadly earthquake ever recorded was the Huaxian 1556 earthquake in China causing about 830,000 casualties [1]. On March 11, 2011 an earthquake devastated the pacific coast of Tohoku, Japan with a magnitude ever recorded of 9.1 followed by a Tsunami killed more than 20,000 peoples [2]. Algeria was subjected to two strong earthquakes. The first one was El Asnam earthquake of October 10, 1980 with a magni- tude of 7.2 caused 2500 casualties, 25,000 housing units destroyed and 300,000 homeless [3]. The second one was the Boumerdès earthquake of May 21, 2003 with a magni- B Leyla Fali falileyla@gmail.com 1 FIMAS Lab, TAHRI Mohamed University, PB 417, Béchar, Algeria 2 ArchiPEL Lab, TAHRI Mohamed University, PB 417, Béchar, Algeria tude of 6.8 caused death to more than 2200 persons and more than 15,000 homeless [4]. During the last decades, remarkable efforts have been devoted to the development of structural control strategies in wide variety of numerical and experimental studies on structures subjected to dynamical loads [5]. However, the structural control offered a considerable additional protec- tion to the structures against earthquake and wind excitations using an external device to reduce the dynamic motion of the structure caused by these natural hazards. According to the dissipation of dynamic energy mode of the external device the structural control is ranged in three ranges: passive, active and semi active control [6]. A combination of two ranges between the three cited ranges is considered as a forth range called hybrid control. One of the oldest forms of vibration control is the pas- sive control where several historical structures were built based on the concept of the seismic base isolation [7]. Until now, tremendous progress has been made in this area and divers researchers focused on the studies of the passive con- trol development. Due to its simplicity the passive control systems still attracted several researches. Thus, these systems can control the structure vibrations using the structure motion 123