随机波动优化人机倒立摆性能的可行性分析

Feasibility analysis of performance improvements for human-machine inverted pendulum with fluctuation

为分析随机波动对人机协作系统稳定性的影响,揭示特定条件下噪声的有利一面,以指尖倒立棒平衡系统为研究对象,利用Lagrangian方法建立系统动态数学模型。考虑不确定因素的影响,引入随机噪声控制项,得到系统模型的随机微分模型。为了分析系统依概率稳定的充分必要条件,应用Ito微分算子推导系统稳定条件,采用ergodic定理对密度函数求解。与相应确定系统稳定域的对比结果表明,随机噪声的存在扩大了系统控制参数的稳定范围,增强了系统稳定性。仿真结果表明,利用适当强度的随机噪声有利于提高系统响应的稳定性和快速性。

To analyze the effect of fluctuation on the stability of human-machine system and to reveal the advantages of fluctua-tion under certain conditions,the dynamic mathematical model for balancing stick on the fingertip was derived by Lagrangian equation.Considering the existence of fluctuations,the stochastic differential equation was obtained with noisy feedback control-ler.Ito operator was adopted to deal with the stochastic differential.Ergodic theorem was also introduced to obtain a probability density function.The main result that a sufficient and necessary condition was derived for the stochastic differential equation.It was suggested that the appropriate power of fluctuation enhanced the stability of the system.Simulation results showed that the appropriate power of fluctuation could be utilized to improve the stability and rapidity of the inverted pendulum.