旋转梁的动力学建模及其反馈控制

Dynamic Modeling and Feedback Control of Rotating Beam

利用哈密尔顿原理 ,推导了刚柔耦合形式的旋转欧拉 伯努利梁的动力学方程 ,并在小转速的假设下 ,给出了线性化近似方程的解析解 ;讨论了由直流电机和压电陶瓷组成的控制系统 ,并从动力学稳定的角度出发 ,利用Lyapunov第一方法设计系统的反馈控制实现了动力学稳定性。最后通过计算机仿真证明控制策略的有效性。

Based on the Hamilton's extended principle, the dynamical equation of a rigid flexible rotating beam is developed in this paper. The coupling between bending and rigid modes has been considered in these equation. A discretized model suited for those kinds of low speed rotation of beam is presented. The control system consists of two actuators: One is a DC servo motor at the joint and the other is a distributed piezoelectric film actuator bonded on the surfaces of the beam. A feedback control law has been developed via Lyapunov's direct method to reach dynamic stablity. Numerical simulation has been done and the results are of good efficiency.