Optimal Control for Footbridges' Vibration Reduction Based on Semiactive Control Through Magnetorheological Dampers

A footbridge is a structure designed for pedestrians or animals to cross roads, water or railways, safely. Modern ones are designed as slender and light structures to be more aesthetic and economic, but may lack enough stiffness and damping that might produce excessive vibrations under service conditions, overpassing comfort limits for users and compromise structural integrity. This work presents the synthesis of a nonlinear optimal control strategy for reducing vibrations in footbridges by means of using magnetorheological dampers. The proposed optimal controller considers both, the footbridge linear dynamics and the damper nonlinear dynamics, as the complete system to be controlled. For analysis purposes, the continuous structure of a footbridge is conveniently idealized as an [Formula: see text]-degrees-of-freedom discretized model, such that it can be handled as an [Formula: see text]-order system. Parameters from an actual footbridge are used to propose a discretized model system of 11 translational degrees of freedom and to analyze the system response as a case study. The dynamical response involves displacement, velocity and acceleration for different number of pedestrians crossing in groups. The investigation rests on comparing the structural response over time for two different conditions: with no control device installed and with one magnetorheological damper installed at the span center. Results obtained with the use of the proposed optimal controller show to be an effective way of reducing the structural motion response.