Structural Vibration Mitigation Using Dissipative Smart Damping Devices

Abstract

An important problem in semiactive control of structures using “smart” damping devices for vibration mitigation is the development of an efficient control algorithm which accounts for the dissipative characteristics of the device. For smart dampers, the dissipative nature can be represented by a nonlinear inequality constraint that cannot be directly imposed on optimal control strategies using standard techniques. In previous research, the authors introduced a method using linear matrix inequality (LMI) methods to include a dissipativity constraint in a linear quadratic regulator (LQR) problem for semiactive control of structures. In this method, the LQR problem is defined as an eigenvalue problem (EVP) in terms of LMIs. Then, the dissipativity constraint is appended to the EVP in its weak expected value form. In this paper, this method is applied to realistic building and damper models. The structure is chosen to be a 9-story benchmark building and a recently-developed 20-ton magnetorheological (MR) fluid damper model as the control devices. It is found that the proposed method provides a more efficient controller, with reduced force levels and almost the same performance compared to a conventional LQR approach.