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| 二阶系统根轨迹的完整分析与证明 |
| Complete Analysis and Proof of Root Locus for Second‑order Systems |
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| DOI：10.16018/j.cnki.cn32-1650/n.202303009 |
| 中文关键词: 根轨迹 二阶系统 圆周 稳定性 |
| 英文关键词: root locus second-order system circle stability |
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| 摘要点击次数: 2070 |
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| 中文摘要: |
| 针对文献[1]第166-177页例4. 25系统根轨迹的复数部分(不包括实轴上的部分)是一个圆周，通过严格的数学推导和证明，不仅发现二阶系统的根轨迹形状与圆周有重要联系，而且还精确绘制了所有二阶系统的根轨迹(非概略绘制)，并通过一些仿真实例进行了验证。 |
| 英文摘要: |
| For example 4. 25 on pages 166-177 of [1], the complex part of the root locus of the system (not including the part on the real axis) is a circle. Through rigorous mathematical derivation and proof, it shows that the shape of the root locus of the second-order system has an important relation with the circle, and we plot the root locus of all second-order systems precisely, rather than sketchily. At the end of the paper, some simulation examples verify the correctness of the conclusions. |
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