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Within engineering control theory, the magnitude condition is a constraint that is satisfied by the locus of points in the s-plane on which closed-loop poles of a system reside. In combination with the angle condition, these two mathematical expressions fully determine the root locus. Let the characteristic equation of a system be , where . Rewriting the equation in polar form is useful. where are the only solutions to this equation. Rewriting in , and representing each factor and by their vector equivalents, and , respectively, may be rewritten. Simplifying the characteristic equation,

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  • Magnitude condition (en)
  • 量值條件 (zh)
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  • 量值條件（magnitude condition）是自動控制的根軌跡圖中，有關量值的限制條件，根軌跡圖中的點和閉迴路極點、零點組成向量的量值會滿足量值條件。量值條件和角度條件可以完全確定根軌跡圖。 令系統的特徵方程為，其中。 將改寫為各因式相乘的形式 量值條件即是 也就是 若將控制方程改為極坐標表示： 其中，這些是方程式所有的解。 將每一個因子及都用等效的向量及來表示，因此 可以再作整理。 簡化特徵方程式。 因此可以推導出另一個形式的量值條件： 也可以用類似的方式推導角度條件。 (zh)
  • Within engineering control theory, the magnitude condition is a constraint that is satisfied by the locus of points in the s-plane on which closed-loop poles of a system reside. In combination with the angle condition, these two mathematical expressions fully determine the root locus. Let the characteristic equation of a system be , where . Rewriting the equation in polar form is useful. where are the only solutions to this equation. Rewriting in , and representing each factor and by their vector equivalents, and , respectively, may be rewritten. Simplifying the characteristic equation, (en)
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  • Within engineering control theory, the magnitude condition is a constraint that is satisfied by the locus of points in the s-plane on which closed-loop poles of a system reside. In combination with the angle condition, these two mathematical expressions fully determine the root locus. Let the characteristic equation of a system be , where . Rewriting the equation in polar form is useful. where are the only solutions to this equation. Rewriting in , and representing each factor and by their vector equivalents, and , respectively, may be rewritten. Simplifying the characteristic equation, from which we derive the magnitude condition: The angle condition is derived similarly. (en)
  • 量值條件（magnitude condition）是自動控制的根軌跡圖中，有關量值的限制條件，根軌跡圖中的點和閉迴路極點、零點組成向量的量值會滿足量值條件。量值條件和角度條件可以完全確定根軌跡圖。 令系統的特徵方程為，其中。 將改寫為各因式相乘的形式 量值條件即是 也就是 若將控制方程改為極坐標表示： 其中，這些是方程式所有的解。 將每一個因子及都用等效的向量及來表示，因此 可以再作整理。 簡化特徵方程式。 因此可以推導出另一個形式的量值條件： 也可以用類似的方式推導角度條件。 (zh)
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