基于Lyapunov直接法的柔性梁振动控制

Vibration Control of Flexible Beam Based on Lyapunov Direct Method

为避免控制溢出和保证控制系统实时性,针对具有边界未知扰动和变张力的柔性梁振动边界控制问题,基于柔性梁无穷维分布参数模型,结合边界控制技术和Lyapunov直接法设计了比例-微分(PD)边界控制器,用于对柔性梁的振动进行主动控制.该边界控制方法可使柔性梁系统达到外界干扰下的一致有界和指数稳定;所设计的PD控制器简单且独立于柔性梁系统参数,可确保系统具有较好的实时性和鲁棒性.仿真结果表明,文中控制方法能有效地抑制柔性梁的振动,降低其振动幅值.

In order to avoid control spillover and implement real-time control of the system, a proportional-derivative （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 parameter model of the flexible beam, employs the boundary control technique and Lyapunov＇ s direct method to reduce the beam vibration. With the proposed boundary control method, uniform boundary and exponential stability are 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. Simulation results indicate that the proposed control method effectively suppresses the vibration of the beam and reduces the vibration amplitude as well.