关键词: 柔性结构, 振动, 边界控制, Lyapunov 函数, 稳定性

Abstract:

In order to avoid control spillover and implement real-time control of the system, a proportional-deriva-tive (PD) boundary controller is proposed for the active vibration control of a flexible beam with unknown boundary disturbance and varying tension. The proposed controller, which is based on the infinite-dimensional distributed pa-rameter model of the flexible beam, employs the boundary control technique and Lyapunov's direct method to re-duce the beam vibration. With the proposed boundary control method, uniform boundary and exponential stabilityare both achieved under external disturbances. The proposed PD controller is simple and is independent of the pa-rameters of the flexible beam system. Moreover, it ensures the real-time and robust control of the system. Simula-tion results indicate that the proposed control method effectively suppresses the vibration of the beam and reduces the vibration amplitude as well.

Key words: flexible structures, vibration, boundary control, Lyapunov functions, stability