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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 Nyquist stability criterion ： ウィキペディア英語版 Nyquist stability criterion In control theory and stability theory, the Nyquist stability criterion, discovered by Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932,〔 on ( Alcatel-Lucent website )〕 is a graphical technique for determining the stability of a dynamical system. Because it only looks at the Nyquist plot of the open loop systems, it can be applied without explicitly computing the poles and zeros of either the closed-loop or open-loop system (although the number of each type of right-half-plane singularities must be known). As a result, it can be applied to systems defined by non-rational functions, such as systems with delays. In contrast to Bode plots, it can handle transfer functions with right half-plane singularities. In addition, there is a natural generalization to more complex systems with multiple inputs and multiple outputs, such as control systems for airplanes. The Nyquist criterion is widely used in electronics and control system engineering, as well as other fields, for designing and analyzing systems with feedback. While Nyquist is one of the most general stability tests, it is still restricted to linear, time-invariant (LTI) systems. Non-linear systems must use more complex stability criteria, such as Lyapunov or the circle criterion. While Nyquist is a graphical technique, it only provides a limited amount of intuition for why a system is stable or unstable, or how to modify an unstable system to be stable. Techniques like Bode plots, while less general, are sometimes a more useful design tool. ==Background== We consider a system whose open loop transfer function (OLTF) is $G(s)$; when placed in a closed loop with negative feedback $H(s)$, the closed loop transfer function (CLTF) then becomes $\backslash frac$. Stability can be determined by examining the roots of the polynomial $1+GH$, e.g. using the Routh array, but this method is somewhat tedious. Conclusions can also be reached by examining the OLTF, using its Bode plots or, as here, polar plot of the OLTF using the Nyquist criterion, as follows. Any Laplace domain transfer function $\backslash mathcal(s)$ can be expressed as the ratio of two polynomials: $\backslash mathcal(s)\; =\; \backslash frac.$ The roots of $N(s)$ are called the ''zeros'' of $\backslash mathcal(s)$, and the roots of$D(s)$ are the ''poles'' of $\backslash mathcal(s)$. The poles of $\backslash mathcal(s)$ are also said to be the roots of the "characteristic equation" $D(s)\; =\; 0$. The stability of $\backslash mathcal(s)$ is determined by the values of its poles: for stability, the real part of every pole must be negative. If $\backslash mathcal(s)$ is formed by closing a negative unity feedback loop around the open-loop transfer function $G(s)\; =\; \backslash frac$, then the roots of the characteristic equation are also the zeros of $1\; +\; G(s)$, or simply the roots of $A(s)\; +\; B(s)=0$. 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「Nyquist stability criterion」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.