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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Angle condition ： ウィキペディア英語版 Angle condition In mathematics, the angle 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 magnitude condition, these two mathematical expressions fully determine the root locus. Let the characteristic equation of a system be $1+\backslash textbf(s)=0$, where $\backslash textbf(s)=\backslash frac$. Rewriting the equation in polar form is useful. $e^+\backslash textbf(s)=0$ $\backslash textbf(s)=-1=e^$ where $(k=0,1,2,...)$ are the only solutions to this equation. Rewriting $\backslash textbf(s)$ in factored form, $\backslash textbf(s)=\backslash frac=K\backslash frac$, and representing each factor $(s-a\_p)$ and $(s-b\_q)$ by their vector equivalents, $A\_pe^$ and $B\_qe^$, respectively, $\backslash textbf(s)$ may be rewritten. $\backslash textbf(s)=K\backslash frac\}$ Simplifying the characteristic equation, $e^=K\backslash frac\}=K\backslash frace^$, from which we derive the angle condition: $\backslash pi+2k\backslash pi=\backslash theta\_1+\backslash theta\_2+\backslash cdots+\backslash theta\_n-(\backslash phi\_1+\backslash phi\_2+\backslash cdots+\backslash phi\_m)$ where $(k=0,1,2,...)$, $\backslash theta\_1,\backslash theta\_2,\; \backslash cdots\; \backslash theta\_n$ are the angles of poles 1 to n, and $\backslash phi\_1,\backslash phi\_2,\; \backslash cdots\; \backslash phi\_m$ are the angles of zeros 1 to m. The magnitude condition is derived similarly. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Angle condition」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.