Simultaneous Optimal Design of the Lyapunov-Based Semi-Active Control and the Semi-Active Vibration Control Device: Inverse Lyapunov Approach

Abstract

We address a simultaneous optimal design problem of a semi-active (SA) control law and design parameters in a semi-active control device for civil structures. The vibration control device (VCD) that is being developed by authors is used as the semi-active control device. The VCD is composed of a ball screw with a flywheel for the inertial resistance force and an electric motor with an electric circuit for the damping resistance force. A new bang–bang type semi-active control law referred to as inverse Lyapunov approach is proposed. In the inverse Lyapunov approach, the Lyapunov matrix in the bang–bang type semi-active control based on the Lyapunov function is searched so that the control performance of the semi-active control system is optimized. Design parameters to determine the Lyapunov function and those of the VCD are optimized with the genetic algorithm (GA). The effectiveness of the proposed approach is presented with simulation studies.