Vibration mitigation of a cable-stayed beam with positive position feedback control in frequency and time domains

This study investigates the vibration mitigation of a cable-stayed beam with a Positive Position Feedback (PPF) control strategy based on Macro-Fiber Composites (MFC) actuators. To achieve this, the transfer function was derived from the frequency domain; To delve deeper into the vibration reduction effect, the method of multiple scales is employed to scrutinize the system’s performance in the time domain, and the amplitude–frequency response equation is obtained. Numerical simulations were then carried out to systematically compare the nonlinear dynamic responses of the cable-stayed beam under varying control parameters. The results reveal that vibrations among different modes significantly complicate the system’s nonlinear behavior. Moreover, an increase in control gain was found to effectively reduce response amplitudes, demonstrating the substantial impact of PPF control on vibration suppression. The study further indicates that selecting the appropriate control gains is crucial to achieve optimal control performance. It was observed that internal resonance facilitates energy transfer between modes, whereas PPF control reduces the vibration amplitude of the system, thereby suppressing vibrations. Overall, this research highlights the potential of PPF control in enhancing the performance of cable-stayed beam structures subjected to dynamic loading.