Nyquist Plot – 나이퀴스트 선도

A Nyquist plot is used in automatic control and signal processing for assessing the stability of a system with feedback. It is represented by a graph in polar coordinates in which the gain and phase of a frequency response are plotted. The plot of these phasor quantities shows the phase as the angle and the magnitude as the distance from the origin. This plot combines the two types of Bode plot — magnitude and phase — on a single graph, with frequency as a parameter along the curve. The Nyquist plot is named after Harry Nyquist, a former engineer at Bell Laboratories.

Assessment of the stability of a closed-loop negative feedback system is done by applying the Nyquist stability criterion to the Nyquist plot of the open-loop system (i.e. the same system without its feedback loop). This method is easily applicable even for systems with delays which may appear difficult to analyze by means of other methods.

Nyquist and related plots are classic methods of assessing stability, but have been supplemented or supplanted by computer-based mathematical tools in recent years. Such plots remain a convenient method for an engineer to get an intuitive feel for a circuit.

< MATLAB 함수 설명 >

  – nyquist(sys) : plots the Nyquist response of an arbitrary LTI model sys.

  – nyquist(sys,w) : explicitly specifies the frequency range or frequency points to be used for the plot.
                                 To focus on a particular frequency interval, set w = {wmin,wmax}

  – nyquist(sys1,sys2,…,sysN) or nyquist(sys1,sys2,…,sysN,w)
                : superimposes the Nyquist plots of several LTI models on a single figure.
                  You can also specify a distinctive color, linestyle, and/or marker for each system plot
                   with the syntax nyquist(sys1,’PlotStyle1′,…,sysN,’PlotStyleN’)

      When invoked with left-hand arguments return the real and imaginary parts of the frequency
      response at the frequencies w (in rad/sec)
             [re,im,w] = nyquist(sys)   or   [re,im] = nyquist(sys,w)

< 예제 코드 및 출력 결과>

    – Plot the Nyquist response of the system
사용자 삽입 이미지      Code: >> H = tf([2 5 1],[1 2 3])                           >> nyquist([2 5 1], [1 2 3])
               >> nyquist(H)                       또는             >> grid
               >> grid

* 참고: http://en.wikipedia.org/wiki/Nyquist_plot

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