研究了时滞及时滞反馈控制参数对Van der Pol系统极限环幅值的影响.运用自适应的平均场近似方法给出了系统的线性化近似及系统参数Lyapunov稳定性的边界条件,同时给出了Van der Pol系统的关联时间和功率谱密度的数值模拟结果.通过与平均场近似下的解析结果比较后发现,数值模拟结果和理论结果符合.进一步讨论了时滞反馈控制参数、噪声强度以及时滞对关联时间和功率谱密度的影响.
Time delays in the feedback control often dete-riorate the control performance or even cause the instabilityof a dynamic system.This paper presents a control strategyfor the dynamic system with a constant or a slowly time-varying input delay based on a transformation,which sim-plifies the time-delay system into a delay-free one.Firstly,the relation is discussed for two existing reduction-basedlinear quadratic controls.One is continuous and the otheris discrete.By extending the relation,a new reduction-basedcontrol is then developed with a numerical algorithm pre-sented for practical control implementation.The controllersuggested by the proposed method has such a promisingproperty that it can be used for the cases of different values ofan input time delay without redesign of controller.This prop-erty provides the potential for stabilizing the dynamic systemwith a time-varying input delay.Consequently,the applica-tion of the proposed method to the dynamic system with aslowly time-varying delay is discussed.Finally,numericalsimulations are given to show the efficacy and the applica-bility of the method.
