摘要
为解决无人机在滚转运动中的横向稳定性，本文研究了随机激励下飞行器滚转运动系统的随机分岔控制。首先建立带有分数阶PID控制器的色噪声激励的滚转运动系统，借助幅值包络随机平均法计算得出FPK方程和振幅响应的平稳概率密度函数。其次，根据奇异性理论，推导了带有该控制器时系统发生随机P分岔所满足的条件。最后，经过数值验证发现，分数阶PID控制器的微分数，积分数及其系数都可以诱导系统发生随机P分岔。即该控制器对系统的随机分岔可以进行预期的控制。
关键词： 滚转运动；色噪声；随机平均法；P分岔；分数阶PID控制
Abstract
In order to solve the lateral stability of UAV in rolling motion, the random bifurcation control of UAV rolling motion system under random excitation is studied in this paper. Firstly, the rolling motion system with color noise excitation with fractional order PID controller is established, and the stationary probability density function of FPK equation and amplitude response is calculated by means of amplitude envelope random average method. Secondly, according to the singularity theory, the conditions for random P-bifurcation with the controller are derived. Finally, through numerical verification, it is found that the differential number, integral number and coefficient of fractional order PID controller can induce random P-bifurcation. That is, the controller can control the random bifurcation of the system in anticipation.
Key words： Rolling movement, Color noise, Stochastic averaging, P-bifurcation , Fractional order PID control
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