EEAC解析灵敏度分析的研究

对非线性非自治运动系统,扩展等面积准则(EEAC)方法是目前惟一严格的稳定量化分析方法.对EEAC提供的稳定量化指标进行灵敏度分析具有重要意义.提出了不稳定情况下非线性非自治运动系统EEAC灵敏度分析的解析方法,首先以轨迹灵敏度分析为工具得出系统相点到达动态鞍点的时间tdsp对控制参数的解析灵敏度,进而求得EEAC稳定量化指标对控制参数的解析灵敏度.数值实例表明,所提出的EEAC解析灵敏度分析方法是正确的,丰富了EEAC灵敏度分析理论.

RESEARCH ON ANALYTICAL SENSITIVITY ANALYSIS OF EXTENDED EQUAL-AREA CRITERION (EEAC)

Extended equal-area criterion (EEAC) is the only strict quantitative stability analysis method of the nonlinear non-autonomous motion systems (NNMS) so far. It is important to do sensitivity analysis of quantitative stability index provided by EEAC to control parameters. The numerical perturbation method (NPM) is adopted for EEAC sensitivity analysis of NNMS at present. However, NPM is a kind of approximation method and not pleasing theoretically. An analytical method for EEAC sensitivity analysis is therefore proposed. This new method first gets the sensitivity of the instant tdsp when dynamic saddle point (DSP) is arrived at to control parameters by trajectory sensitivity analysis, and then based on this sensitivity, the sensitivity of quantitative stability index to control parameters under unstable case is acquired. A numerical example is given to