Lyapunov-based boundary control of a multi-span beam subjected to moving masses

This paper considers a vibration control problem for a multi-span beam under moving masses by using boundary control method. The vibration of the multi-span beam under active control is governed by both a partial differential equation (PDE) and several ordinary differential equations (ODEs) which are derived from Hamilton's principle. In order to suppress its vibration, boundary control strategy is proposed based on Lyapunov's direct method. The closed-loop system stability of the multi-span beam with the proposed boundary control is proved. It can avoid spill-over effects which may occur in those popular methods that discretise the system model through modal expansion, as it directly acts on the PDE-ODEs of the system model in control design. Moreover, the sensors and actuators in the proposed boundary control strategy can be easily placed, as they are installed at the boundary of the system. The external excitations applied in simulation are a rectangular impulse, a moving mass and two moving masses, respectively. Numerical results demonstrate the effectiveness of the proposed method and good control performance in suppressing vibration of moving mass problems. This investigation has wide applications in engineering, notably, train-bridge dynamic interaction in high-speed railways.