Truly optimal semi-active damping to control free vibration of a single degree of freedom system

Abstract

This paper studies a single degree of freedom system under free vibration and controlled by a general semi-active damping. A general integral of squared error is considered as the performance index. A one-time switching damping controller is proposed and optimized. The Pontryagin Maximum Principle is used to prove that no other form of semi-active damping can provide the better performance than the proposed one-time switching damping.

Keywords

• Analytical optimization
• Quadratic integral
• Lyapunov equation
• Pontryagin maximum principle