Received: 13 March 2017 Revised: 17 April 2018 Accepted: 18 April 2018 DOI: 10.1002/stc.2206 RESEARCH ARTICLE Hysteretic active control of base-isolated buildings Francesc Pozo Yolanda Vidal Guillem Garcia Leonardo Acho José Rodellar Control, Modeling, Identification and Applications (CoDAlab), Departament de Matemàtiques, Escola d'Enginyeria de Barcelona Est, Universitat Politècnica de Catalunya, Campus Diagonal-Besòs, Eduard Maristany, 16, Barcelona 08019, Spain Correspondence Francesc Pozo, Control, Modeling, Identification and Applications, Departament de Matemàtiques, Escola d'Enginyeria de Barcelona Est, Universitat Politècnica de Catalunya, Campus Diagonal-Besòs, Eduard Maristany, 16, Barcelona 08019, Spain. Email: francesc.pozo@upc.edu Funding information Spanish Ministry of Economy and Competitiveness, Grant/Award Number: DPI2017-82930-C2-1-R, DPI2014-58427-C2-1-R and DPI2015-64170-R ; Catalonia Government (Generalitat de Catalunya), Grant/Award Number: 2017 SGR 388 Summary In this work, an active control law for base-isolated buildings is proposed. The crucial idea comes from the observation that passive base-isolation systems are hysteretic. Thus, an hysteretic active control strategy is designed in a way that the control force is smooth and limited by a prescribed bound. Furthermore, given a specific actuator with a physically limited maximum force and maximum rate of change, it is proven that the design parameters in the contributed control law can be chosen such that the control signal inherently satisfies the actua- tor constraints. Eight different ground-acceleration time-history records and a model of a 5-story building are used to study and compare the performance of a passive pure friction damper alone, with the addition of the proposed active control. Numerical analysis demonstrates that our control strategy effectively mitigates base displacement and shear without an increase in superstructure drift or acceleration. KEYWORDS active control, base-isolated building, bounded control, hysteresis, rate of change 1 INTRODUCTION Civil structures are affected by several kinds of dynamic excitations such as earthquakes; winds; or, in the case of bridges, traffic loading. In this regard, base isolation has been extensively considered as an adequate technology to protect flex- ible building structures producing a dynamic decoupling of the structure from its foundation. 1-3 However, the resulting base displacement may be excessive. Consequently, the combination of active or semiactive systems installed along with passive base-isolation bearings may alleviate the negative effects of such loads. An excellent state-of-the-art review of structural control systems is given in Saaed et al, 4 where these systems are classified into four main groups: passive; semiactive; active; and hybrid systems, based on their operational mechanisms. Two more reviews are also proposed in Casciati et al 5 and Basu et al, 6 the last one being focused on recent approaches in civil structural control across Europe. The traditional passive base-isolation approaches can suppress the seismic responses of the upper structure, but, at the same time, they can induce substantial deformation of the base-isolation device. 7 An excessive base drift may cause the degradation and even the damage of the base-isolation system. Therefore, supplemental control devices can be implemented in the common base-isolation system to construct hybrid control systems and reduce the base drifts of structures. Semiactive control of base-isolated structures has received in the last few years an enormous attention, as they consume less power than active devices but allow controllability over passive systems. 8 In fact, the combination of base-isolated Struct Control Health Monit. 2018;e2206. wileyonlinelibrary.com/journal/stc Copyright © 2018 John Wiley & Sons, Ltd. 1 of 18 https://doi.org/10.1002/stc.2206