The generalized Nyquist criterion and robustness margins with applications
The generalized Nyquist criterion and robustness margins with applications
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广义奈奎斯特准则和鲁棒性裕度及其应用
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
R. Kosut
中科院分区：
文献类型：
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作者：
A. Emami;R. Kosut
多变量奈奎斯特本征轨迹提供了一个更丰富的家庭相比，SISO的情况下的曲线。在许多简单的情况下，eigeloci可以象征性地计算。广义奈奎斯特特征轨迹图的检查允许的多变量增益裕度（GM），相位裕度（PM），和复杂的裕度（CM）的精确值的确定。因此，没有必要从灵敏度和互补灵敏度函数的奇异值计算GM和PM的估计，因为它们通常是非常保守的。此外，复裕度允许计算最小的加性等对角复扰动，以及驱动系统不稳定的相关联的乘性复扰动。所有的计算都反映了SISO的情况。这些想法被应用到半导体晶圆制造过程控制和航空航天的例子。
Multivariable Nyquist eigenloci provide a much richer family of curves as compared to the SISO case. The eigeloci may be computed symbolically in many simple cases. Inspection of the generalized Nyquist eigenloci plot allows the determination of the exact values of the multivariable gain margin (GM), phase margin (PM), and the complex margin (CM). Hence there is no need to compute estimates of GM and PM from the singular values of the sensitivity and the complementary sensitivity functions as they are usually very conservative. Furthermore, the complex margin allows the computation of the minimum additive equal diagonal complex perturbation, and the associated multiplicative complex perturbation that drives the system unstable. All the computations mirror the SISO case. The ideas are applied to semiconductor wafer manufacturing process control and aerospace examples.