CAJ | 학술논문

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。
위분석수궤파동대인궤협작계통은정성적영향，게시특정조건하조성적유리일면，이지첨도립봉평형계통위연구대상，이용Lagrangian방법건립계통동태수학모형。고필불학정인소적영향，인입수궤조성공제항，득도계통모형적수궤미분모형。위료분석계통의개솔은정적충분필요조건，응용Ito미분산자추도계통은정조건，채용ergodic정리대밀도함수구해。여상응학정계통은정역적대비결과표명，수궤조성적존재확대료계통공제삼수적은정범위，증강료계통은정성。방진결과표명，이용괄당강도적수궤조성유리우제고계통향응적은정성화쾌속성。
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.