柔性臂振动系统角速度反馈控制的最优指数衰减率问题

Optimal Exponential Decay Rate on the Flexible Beam with Angular Velocity Feedback Control

讨论柔性臂的端点角速度反馈控制问题。通过对系统特征值和特征函数的渐近表示式的进一步研究 ,用特征扰动的 Payley- Wiener稳定性理论 ,证明了该系统的最优指数衰减率可由系统的谱来确定。

The problem of angular velocity feedback control caused by a flexible beam on a vibrating system is discussed. The stability is well known, but the optimal exponential decay rate on the system is new. In order to determine the decay rate, an assistant system as a basic system is introduced, and the system is considered as a perturbation of the assistant system. By the Payley-Wiener stability theory, it is proved that a set of the eigenvectors of the system form a Riesz basis of the state space. So the spectrum of the system is determined, and the optimal decay rate can be determined by the spectrum of the system.