含双时滞主动控制系统平凡平衡解稳定性的数值分析

Numerical Analysis for Stability of Trivial Equilibrium Solution of Active Control Systems with Double Time Delays

采用精细积分方法求解含双时滞受控系统的平凡平衡解,根据不同时滞量下系统响应的敛散性判断系统的稳定性,得到了时滞受控系统随时滞变化的稳定区域分布,避免了求解时滞系统特征方程的困难.在此基础上,分析了不同时滞量和反馈增益对系统稳定区域的影响规律,结果表明:随时滞量的变化,系统的稳定区域与不稳定区域是交替分布的,当2个反馈增益相差较大时,与较大的反馈增益相关的时滞量对系统的稳定性影响更为显著.

The characteristic equation of control systems with time-delay is a transcendental equation containing exponential function,which has infinite roots difficult to be all solved.Aiming at solving dynamic equation of control system with double time delays,a precise integration method is chosen to obtain the distribution of stable regions of system with variational time delays and avoid the difficulty for solving the characteristic equation as taking different feedback control gains.The influence of different time delays and feedback control gains on distribution of stabile regions of system is discussed.It shows the cross distribution of stable and unstable areas,and the time delay related with the feedback gains with higher absolute value,exert a significant effect on stability of system,especially for the case of two quite different feedback gains.