Optimal Design of Time-Delay Feedback Control in a Spring-Mass-Pendulum Vibration Reduction System

This study investigates the application of time-delay feedback active control to the anti-resonant frequency response in a Pendulum Tuned Mass Damper (PTMD) vibration reduction system. An optimization method is proposed for controlling the anti-resonant frequency response in a time-delay-coupled mass-pendulum dynamic vibration absorber system. For systems with inherent damping in the primary structure, the time-delay feedback control is employed to optimize the anti-resonant frequency response while maintaining the overall vibration reduction performance of the primary system’s amplitude-frequency response curve. First, the Cluster Treatment of Characteristic Roots (CTCR) method is applied to analyze the stability of the time-delay feedback control system, determining stable intervals for two critical parameters: time delay and feedback gain coefficient. Second, optimization criteria for the control system are established, and optimal control parameters are derived under these constraints. Finally, comparative studies with conventional models validate the effectiveness of the proposed control strategy.