Active Vibration Control of Stay Cables in the Alamillo Bridge: A Comparative Study between Finite Element Modeling and Reduced-Order PID Control
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Stay cables are highly flexible structural components with low intrinsic damping, making them susceptible to large-amplitude oscillations induced by wind-rain effects and deck excitations. In the specific case of the Alamillo Bridge in Seville, its unique asymmetric design without back-stays underscores the necessity of robust vibration mitigation strategies. This paper investigates the implementation of active vibration control on a stay cable modeled as a Multiple-Input Single-Output (MISO) system. The system considers two primary force inputs: stochastic wind loading and the corrective force applied by an active actuator positioned near the deck anchorage. The primary objective is to minimize the transverse displacement at the cable's mid-span. The research focuses on a comparative performance analysis between two modeling paradigms. First, a High-Fidelity Finite Element Method (FEM) is employed to capture the complex cable behavior, accounting for sag, tension, and boundary conditions. Second, a Reduced-Order Model (ROM) is derived to facilitate real-time control synthesis. For the vibration suppression task, a Proportional-Integral-Derivative (PID) controller is designed. The controller gains are tuned to optimize the trade-off between energy consumption and displacement reduction. Simulations are conducted within the MATLAB/Simulink environment to evaluate the efficacy of the PID law when applied to both the discretized FEM environment and the simplified ROM. Results demonstrate that while the FEM provides superior spatial accuracy, the Reduced-Order Model offers a computationally efficient framework for gain scheduling without significant loss in control performance. The findings suggest that active actuators, when driven by properly tuned PID logic, can significantly increase the effective damping ratio of the Alamillo Bridge’s cables, ensuring structural longevity and aeroelastic stability.
