悬浮水轮原理及外界微扰下的系统稳定性研究

Study on the principle of suspended water wheel and the stability of the system under external disturbances

对水轮在悬浮状态下进行多向分析,判断其与水柱的相对位置关系,确定冲击点的位置。通过三种受力假设对水轮的平衡现象进行定量分析,并在合理假设参量的条件下求出其满足平衡条件的动力学方程,同时再利用冲量定理对水轮与水的平衡条件进行补充性定性分析。在抗微扰分析上,通过假设各种外部干扰进行定性分析,以判断系统的稳定性,最后再对本研究做出的条件假设进行误差校准与细致推算。

This paper aims to study the principle of suspended water wheel and its stability under external perturbation.Firstly,through the multi-direction analysis of the wheel in suspension state,the relative position relationship between the wheel and the water column is determined,and the position of the impact point is also confirmed.Secondly,the equilibrium phenomenon of water wheel is analyzed quantitatively by assuming three kinds of force systems,and the dynamic equation satisfying the equilibrium condition is obtained under the condition of reasonable assumption parameters.At the same time,the balance condition between water wheel and water is qualitatively analyzed by using impulse theorem.In anti-perturbation analysis,the stability of the system is judged by qualitative analysis based on various external disturbances.At last,we calibrate and calculate the error of the conditional hypothesis.