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时滞状态反馈控制系统的稳定性增益区域 被引量：8

STABLE REGION OF THE FEEDBACK GAINS IN A CONTROLLED SYSTEM WITH DELAYED FEEDBACK
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摘要 研究了一阶时滞微分方程的状态反馈P控制、PI控制问题,目的是确定反馈增益的范围使得系统的平衡态是渐近稳定的.对P控制状态反馈控制模型,利用Lambert W函数的主分支给出了确定反馈增益的显式判据以及系统的最优反馈增益;在PI状态反馈控制模型中,运用稳定性切换原理并结合D-划分法确定了在反馈增益平面上系统的稳定性区域,并利用Lambert W函数采用数值方法给出了系统的最优增益曲线.和现有方法相比较,本文方法更直观、计算更简单. The problem of P and PI feedback control to a time delay system was investigated,with the emphasis on the determination of the feedback gains that ensured the asymptotical stability of the delayed system. By means of Lambert W function,the feedback gain of P control can be expressed explicitly,so that the optimal feedback gain can be easily obtained. For the system under a PI control,the stable region of the feedback gains was determined on the basis of stability switches and D-subdivision,and the optimal f...
作者 王京祥 王在华
机构地区 解放军理工大学理学院
出处 《动力学与控制学报》 2008年第4期301-306,共6页 Journal of Dynamics and Control
基金 全国优秀博士学位论文作者专项基金资助~~
关键词 时滞 反馈增益 P/PI控制 稳定性切换 D-划分法 Lambert W函数 time delay feedback gain P/PI control stability switch D-subdivision Lambert W function
分类号 TP13 [自动化与计算机技术—控制理论与控制工程]
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参考文献18

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同被引文献103

  • 1陈丽萍.振动主动控制技术的研究进展[J].现代机械,2005(2):52-55. 被引量：12
  • 2徐鉴,裴利军.时滞系统动力学近期研究进展与展望[J].力学进展,2006,36(1):17-30. 被引量：66
  • 3Hu Haiyan, Wang Zaihua. Dynamics of controlled mechanical systems with delayed feedback[M]. Berlin: Springer-Verlag, 2002.
  • 4Wang Zaihua, Hu Haiyan. Stability switches of time delayed dynamic systems with unknown parameters [J]. J Sound and Vibration, 2000, 233 (2): 215-233.
  • 5Xu Xu, Hu Haiyan, Wang Huailei. Stability switches, Hopf bifurcation and chaos of a neuron model with delay-dependent parameters[J]. Physics LetterA, 2006, 354(1): 126-136.
  • 6Xu Xu, Hu Haiyan, Wang Huailei. Stability, bifurcation and chaos of a delayed oscillator with negative damping and delayed feedback control[J]. Nonlinear Dynamics, 2007, 49(1): 117-129.
  • 7Hu Haiyan, Wang Zaihua. Singular perturbation methods for nonlinear dynamic systems with time delay[J/OL]. Chaos, Solitons and Fractals, doi: 10.1016/j .chaos .2007.07.048.
  • 8Xu Jian, Chung K W, Chan C L. An efficient method for studying weak resonant double Hopf bifurcation in nonlinear systems with delayed feedback[J]. SlAM Journal on Applied Dynamical Systems, 2007, 6: 29-60.
  • 9Wang Zaihua, Hu Haiyan. An energy analysis of nonlinear oscillators with time-delayed coupling [J]. International Journal of Bifurcation and Chaos, 2006, 16: 2275-2292.
  • 10Wang Zaihua, Hu Haiyan. An energy analysis of the local dynamics of adelayed oscillator near a Hopf bifurcation [J]. Nonlinear Dynamics, 2006, 46: 149-159.

引证文献8

二级引证文献22

动力学与控制学报
2008年 第4期

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