A Novel Iterative Linear Matrix Inequality Design Procedure for Passive Inter-Substructure Vibration Control

• Main Authors: Josep Rubió-Massegú, Francisco Palacios-Quiñonero, Josep M. Rossell, Hamid Reza Karimi
• Format: Article
• Language: English
• Published: MDPI AG 2020-08-01
• Series: Applied Sciences
• Subjects: passive vibration control; fluid viscous dampers; static output-feedback control; decentralized control; iterative linear matrix inequalities; interstory damping systems
• Online Access: https://www.mdpi.com/2076-3417/10/17/5859

In vibration control of compound structures, inter-substructure damper (ISSD) systems<br />exploit the out-of-phase response of different substructures to dissipate the kinetic vibrational<br />energy by means of inter-substructure damping links. For seismic protection of multistory buildings,<br />distributed sets of interstory fluid viscous dampers (FVDs) are ISSD systems of particular interest.<br />The connections between distributed FVD systems and decentralized static output-feedback<br />control allow using advanced controller-design methodologies to obtain passive ISSD systems<br />with high-performance characteristics. A major issue of that approach is the computational<br />difficulties associated to the numerical solution of optimization problems with structured bilinear<br />matrix inequality constraints. In this work, we present a novel iterative linear matrix inequality<br />procedure that can be applied to obtain enhanced suboptimal solutions for that kind of optimization<br />problems. To demonstrate the effectiveness of the proposed methodology, we design a system of<br />supplementary interstory FVDs for the seismic protection of a five-story building by synthesizing a<br />decentralized static velocity-feedback H¥ controller. In the performance assessment, we compare the<br />frequency-domain and time-domain responses of the designed FVD system with the behavior of the<br />optimal static state-feedback H¥ controller. The obtained results indicate that the proposed approach<br />allows designing passive ISSD systems that are capable to match the level of performance attained by<br />optimal state-feedback active controllers.