Semi-active vibration control of structural systems based on linear approximation of switched linear system

Abstract

For vibration control of structural system, semi-active control is expected to show better performance than other control methods in terms of energy efficiency. However, because of the energy dissipation characteristics of the semi-active control devices, the mathematical model of the semi-active control system becomes a hybrid model. Optimal control of hybrid models can be solved by mixed integer quadratic programming. However, this method is computationally expensive because the optimization problem must be solved for every sampling instant. One such computationally inexpensive method is clipped-optimal control, but its performance is not guaranteed because it does not consider the constraints of energy dissipation of the semi-active device. The clipped-optimal control can be expressed as a switching system of three systems under the influence of energy dissipation constraints. In a 1-DOF (degree of freedom) system, the switching conditions of the three systems can be expressed as angles on a phase plane. The 1-DOF vibration system draws an ellipse in the forced vibration and a spiral in an initial response on the phase plane. In the case of a vibration system that draws a circle-like trajectory on the phase plane, unlike other switching systems, the selection of these three systems is performed at a substantially constant rate. In this study, we propose a semi-active control method using a single linear system composed of the above three systems. The linear systems are referred to as the averaged systems in the study. We propose a method to systematically design the clipped-optimal control, which has been conventionally designed by trial and error, with the averaged system. Simulation studies show the effectiveness of the proposed semi-active control approach.