A multiloop generalization of the circle criterion for stability margin analysis
A multiloop generalization of the circle criterion for stability margin analysis
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DOI：
10.1109/tac.1981.1102595
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发表时间：
1981-04
影响因子：
6.8
通讯作者：
M. Safonov;M. Athans
中科院分区：
文献类型：
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作者：
M. Safonov;M. Athans
为了提供一种非常适合用于表征多环反馈系统的稳定裕度（例如增益和相位裕度）的理论工具，考虑了概括圆稳定性准则的多环输入-输出稳定性结果。采用由线性动力学算子确定的具有“中心”和“半径”的广义圆锥扇区，使工程师能够指定他想要的稳定裕度，作为建模误差的频率相关凸集（包括非线性、增益变化和相位变化），系统必须能够在每个反馈环路中容忍这些稳定裕度而不会不稳定。由此产生的稳定性准则为存在此类频率相关建模误差时的闭环稳定性提供了充分的条件，即使建模误差同时出现在所有环路中；因此，例如，当环路增益和相位在其边界与频率相关的“非零测量集”中变化时，可以确保稳定性。稳定性条件产生了一个易于解释的标量度量，用于衡量多环路系统超过或低于其稳定性裕度规格的量。
In order to provide a theoretical tool well suited for use in characterizing the stability margins (e.g., gain and phase margins) of multiloop feedback systems, multiloop input-output stability results generalizing the circle stability criterion are considered. Generalized conic sectors with "centers" and "radii" determined by linear dynamical operators are employed to enable an engineer to specify the stability margins which he desires as a frequency-dependent convex set of modeling errors-including nonlinearities, gain variations, and phase variations-which the system must be able to tolerate in each feedback loop without instability. The resulting stability criterion gives sufficient conditions for closed-loop stability in the presence of such frequency-dependent modeling errors, even when the modeling errors occur simultaneously in all loops; so, for example, stability is assured as loop gains and phases vary throughout a "set of nonzero measure" whose boundaries are frequency-dependent. The stability conditions yield an easily interpreted scalar measure of the amount by which a muitiloop system exceeds, or falls short of, its stability margin specifications.