File:Nyquist example.svg

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Summary

DescriptionNyquist example.svg	The Nyquist Plot for a sample function $G(s)={\frac {1}{s^{2}+s+1}}$ that can be converted to frequency by replacing $s$ with $j\omega$ (imaginary frequency) and $-\infty \leq \omega \leq \infty$ . Created using Python and matplotlib.
Date	27 March 2006
Source	Own work
Author	Utkarsh Upadhyay,--Krishnavedala (talk) 20:21, 3 June 2011 (UTC) (python version)
Permission (Reusing this file)	Public Domain

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Source Code
from numpy import * from matplotlib.pyplot import * def nyquist(w): # compute the complex Nyquist response s = complex(0,w) return (1/(s*2+s+1)) fig = figure(figsize=(5,5)) ax = fig.add_subplot(111) ax.grid(True) t, N = linspace(0,5pi,200), [] # 5pi is approx. to infinity. for i in t: # compute the complex response for +ve omega N = append(N,nyquist(i)) ax.plot(real(N),imag(N),label=r"$0\leq\omega\leq\infty$") t, N = linspace(-5pi,0,200), [] for i in t: # compute the complex response for -ve omega N = append(N,nyquist(i)) ax.plot(real(N),imag(N),label=r"$-\infty\leq\omega\leq 0$") ax.legend(frameon=False) setp(ax.get_legend().get_texts(),fontsize='small') ax.set_xlabel(r"$\mathrm{Re}\left[G\left(\omega\right)\right]$") ax.set_ylabel(r"$\mathrm{Im}\left[G\left(\omega\right)\right]$") ax.text(0.6,-1.25,r"$G(s)=\frac{1}{s^2+s+1}$",\ fontsize=15) #fig.show() fig.savefig("Nyquist example.svg",bbox_inches="tight",\ pad_inches=.15)

Source Code

from numpy import * from matplotlib.pyplot import *  def nyquist(w):		# compute the complex Nyquist response 	s = complex(0,w) 	return (1/(s**2+s+1)) 	 fig = figure(figsize=(5,5)) ax = fig.add_subplot(111) ax.grid(True)  t, N = linspace(0,5*pi,200), [] # 5*pi is approx. to infinity.  for i in t:			# compute the complex response for +ve omega 	N = append(N,nyquist(i)) ax.plot(real(N),imag(N),label=r"$0\leq\omega\leq\infty$") t, N = linspace(-5*pi,0,200), [] for i in t:			# compute the complex response for -ve omega 	N = append(N,nyquist(i)) ax.plot(real(N),imag(N),label=r"$-\infty\leq\omega\leq 0$") ax.legend(frameon=False) setp(ax.get_legend().get_texts(),fontsize='small') ax.set_xlabel(r"$\mathrm{Re}\left[G\left(\omega\right)\right]$") ax.set_ylabel(r"$\mathrm{Im}\left[G\left(\omega\right)\right]$") ax.text(0.6,-1.25,r"$G(s)=\frac{1}{s^2+s+1}$",\ 	fontsize=15)  #fig.show() fig.savefig("Nyquist example.svg",bbox_inches="tight",\ 	pad_inches=.15)

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File history

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	Date/Time	Dimensions	User	Comment
current	20:10, 3 June 2011	443 × 428 (53 KB)	Krishnavedala	corrected the equation in the curve
	20:04, 3 June 2011	443 × 428 (53 KB)	Krishnavedala	a well defined curve
	20:55, 1 July 2010	1,000 × 1,000 (7 KB)	DieBucheBot	Trying to fix SVG using scour
	02:36, 27 March 2007	1,000 × 1,000 (11 KB)	Musically ut	{{Information \|Description=The Nyquist Plot for a sample function. \|Source=Octave and GNU Plot \|Date=27/03/06 \|Author=Utkarsh Upadhyay \|Permission=Public Domain \|other_versions= - }}