Semi-active control of flexible structures using closed-loop input shaping techniques Tarek Edrees Alqado 1,2, * ,† , George Nikolakopoulos 3 and Leonidas Dritsas 4 1 Department of Civil, Environmental and Natural Resources Engineering, Division of Structural and Construction Engineering, Luleå University of Technology, Luleå, Sweden 2 College of Engineering, Department of Civil Engineering, University of Mosul, Mosul, Iraq 3 Department of Computer Science, Electrical and Space Engineering, Division of Signals and Systems, Luleå University of Technology, Luleå, Sweden 4 Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education, ASPETE, Athens, Greece SUMMARY In this research effort, a novel approach on the control of structures with magnetorheological (MR) dampers is pre- sented, based on an appropriately adapted closed-loop version of the generic input shaping control theory. The MR damper is a very promising kind of semi-active control system (actuator), mixing the advantages of the active and passive structural control systems, hence their increasing use as attenuators that reject the effects of dynamic loads on civil engineering structures. The main contribution of this article is the application and performance evaluation of the novel ‘Linear Matrix Inequality-based’ feedback version of the input shaping control theory for the first time in the area of structural control. The need for the use of a feedback version of input shaping control stems from the design trade-off between robustness and speed of response requirements. A simulation of a benchmark three-story building with one MR damper is employed to verify the efficiency of the proposed control approach. The nonlinear behaviour of the MR damper, rigidly connected between the first floor of the structure and the ground, is captured by the well-known Bouc–Wen model. The superiority and effectiveness of the proposed scheme in reducing the responses of the structure were proved using seven quantifiable evaluation criteria and by comparing these results with those achieved by classical and well-established alternative control schemes. Copyright © 2016 John Wiley & Sons, Ltd. Received 9 November 2015; Revised 26 April 2016; Accepted 20 June 2016 KEY WORDS: semi-active control; input shaping; time-delay control; flexible structures; magnetorheological (MR) damper; vibration control; structural control; multiple time delays; system stability 1. INTRODUCTION Civil engineering structures are subject to different kinds of dynamic loading because of winds, earth- quakes and traffic loading. In the past, these structures had to rely on their own stiffness and strength to counteract such loadings [1]. Nowadays, the utilisation of different structural control systems for the reduction of the effects of these loads on structures is widespread and at the same time an area of active research [2]. The semi-active control systems are considered to be particularly effective for structural control of this sort because they combine the best advantages of passive and active control systems [3]. Many different control theories have been used to the control of buildings and structures in general, each one being effective for specific type of structures and inadequate for others. The reason for this variety of control strategies is the different type of premises and assumptions made at the design stage *Correspondence to: Tarek Edrees Alqado, Department of Civil, Environmental and Natural Resources Engineering, Division of Structural and Construction Engineering, Luleå University of Technology, Luleå, Sweden. † E-mail: tarek.edrees@ltu.se STRUCTURAL CONTROL AND HEALTH MONITORING Struct. Control Health Monit. (2016) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/stc.1913 Copyright © 2016 John Wiley & Sons, Ltd.