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Topic: Nyquist plot

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	Analog Insydes
		The Nyquist plot is a parametric plot of the real and imaginary part of a transfer function in the complex plane as the frequency parameter sweeps through a given interval.
		Nyquist plots are particularly useful for stability analysis in control system design because one can immediately check whether a negative feedback loop meets Nyquist's stability criterion: If the Nyquist curve of the open-loop system wraps around the point -1 on the real axis, then the corresponding closed-loop system is unstable.
		A Nichol plot is similar to a Nyquist plot, but it shows gain on a logarithmic scale (dB) vs. phase on a linear scale (degrees) with an axis origin at the point (0 dB, -180°).
	library.wolfram.com /examples/AnalogInsydes/AnalogInsydes_lnk_4.html (402 words)

	Bode plot
		A Bode magnitude plot is a graph of log(magnitude) against log(frequency) often used in signal processing to show the transfer function of a system.
		The magnitude and phase Bode plots can seldom be changed independently of each other—if you change the amplitude response of the system you will most likely change the phase characteristics as well and vice versa.
		A typical application of a Bode plot is to show the frequency response of a filter.
	www.ebroadcast.com.au /lookup/encyclopedia/bo/Bode_plot.html (220 words)

	Nyquist plot - Wikipedia, the free encyclopedia (via CobWeb/3.1 planet03.csc.ncsu.edu) (Site not responding. Last check: 2007-09-19)
		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.
		An application of Cauchy's Argument principle to the open loop transfer function, the Nyquist plot identifies singularities in the semicircle of infinite radius in the right half of the s-plane, the presence of which indicates instability in the feedback system.
	en.wikipedia.org.cob-web.org:8888 /wiki/Nyquist_plot (261 words)

	Nyquist Plots (via CobWeb/3.1 planetlab2.cs.umd.edu) (Site not responding. Last check: 2007-09-19)
		Bode' plots use frequency as the horizontal axis and use two separate plots to display amplitude and phase of the frequency response.
		Nyquist plots display both amplitude and phase angle on a single plot, using frequency as a parameter in the plot.
		Nyquist plots have properties that allow you to see whether a system is stable or unstable.
	www.facstaff.bucknell.edu.cob-web.org:8888 /mastascu/eControlHTML/Freq/Freq6.html (2535 words)

	Stability analysis using Nyquist Plots
		Polar plots are not used exclusively because,without powerful computing facilities, they can be difficult to generate at a detailed level and they do not directly yield frequency values.
		As identified in the page on frequency response Frequency response The nyquist plots are based on using open loop performance to test for closed loop stability.
		Nyquist Plots A number of typical nyquist plots are shown below to illustrate the various shapes.
	www.roymech.co.uk /Related/Control/Nyquist.html (759 words)

	Nyquist Stability
		Bode' plots are really log-log plots, so they collapse a wide range of frequencies (on the horizontal axis) and a wide range of gains (on the vertical axis) into a viewable whole.
		Bode' plots are widely used, designers are used to them, and measures of stability are more easily computed on Bode' plots than they are on Nyquist plots.
		For this plot, the red is the magnitude plot, and the blue is the phase plot.
	www.facstaff.bucknell.edu /mastascu/eControlHTML/Freq/Nyquist3.html (1235 words)

	Web-Based Control System Analysis and Design (Site not responding. Last check: 2007-09-19)
		A Bode plot shows the relationship between the magnitude and phase values of the open-loop transfer function G(j*w) and input frequency(when the input frequency w goes from zero to infinity).
		A Nyquist plot is a representation of open-loop transfer function G(j*w) in s plane.
		The functions below can be used to plot the Bode plot, Nyquist plot, and Nichols chart, to claculate the gain and phase margin of a system or to calculate the value of open-loop transfer function over a given frequency vector.
	www.softintegration.com /chhtml/toolkit/control/FDAnaly.html (203 words)

	ProSoundWeb \| The Nyquist Plot
		The Nyquist plot can be used in sound system work, where in acoustics the real part is particle pressure and the imaginary part is particle velocity (near a boundary or in a standing wave) and in impedance measurements where the real part is the resistance and the imaginary part is the reactance.
		Note that in the diagram the cursor is set at the point where the reverse rotation begins, the cursor coordinates being indicated to the lower left of the plot.
		The Nyquist plot, as embodied in contemporary acoustic analyzers, usually computes at the bottom of the screen the values for frequency, real part, imaginary part, phase, and magnitude for a given cursor position on the screen.
	www.prosoundweb.com /install/sac/n26_4/nyquist/nyquist.shtml (707 words)

	Nyquist stability criterion - Wikipedia, the free encyclopedia
		The Nyquist stability criterion, named for Harry Nyquist, provides a simple test for stability of a closed-loop control system by examining the open-loop system's Nyquist plot.
		The Nyquist Contour mapped through the open-loop transfer function F(s) yields a Nyquist plot for F(s).
		By the Argument Principle, the number of clock-wise encirclements of the origin must be the number of zeros of F(s) in the right-half complex plane minus the poles of F(s) in the right-half complex plane.
	en.wikipedia.org /wiki/Nyquist_stability_criterion (665 words)

	CTM: Frequency Response Tutorial, Nyquist
		The Nyquist diagram is basically a plot of G(j* w) where G(s) is the open-loop transfer function and w is a vector of frequencies which encloses the entire right-half plane.
		command plots the Nyquist diagram using a logarithmic scale and preserves the characteristics of the -1 point.
		Remember from the Cauchy criterion that the number N of times that the plot of G(s)H(s) encircles -1 is equal to the number Z of zeros of 1 + G(s)H(s) enclosed by the frequency contour minus the number P of poles of 1 + G(s)H(s) enclosed by the frequency contour (N = Z - P).
	www.engin.umich.edu /group/ctm/freq/nyq.html (2092 words)

	Bode Step Toolbox: MATLAB functions for control systems design
		Using the plot of the lag margin allows to pay attention to only a small area of the plot where the gain response crosses the 0-dB level, and to read there the value of the guard-point phase lag margin.
		Calculating and plotting the phase shift of the plant when only the plant gain has been estimated or measured (since the measurements of the plant gain are often less time-consuming then the measurements of the phase shift).
		Plot of the phase lag margin is shown by a dashed line.
	www.luriecontrol.com /BodestepToolbox.htm (1584 words)

	nyquist (Function Reference)
		superimposes the Nyquist plots of several LTI models on a single figure.
		H = tf([2 5 1],[1 2 3]) nyquist(H) The nyquist function has support for M-circles, which are the contours of the constant closed-loop magnitude.
		This figure shows the nyquist plot with a data marker.
	www-rohan.sdsu.edu /doc/matlab/toolbox/control/ref/nyquist.html (342 words)

	NOVA Examples
		Plots include magnitude and phase of the frequency response function, as well as coherence.
		The lower plots are the magnitude and phase for comparison.
		The orbit plot has the two similar sensors 90 degrees apart so the ideal plot is a circle.
	www.hemdata.com /Products/Nova/examplesold.htm (574 words)

	Nyquist Example #5 (Site not responding. Last check: 2007-09-19)
		Note the effect that the placement of the poles and zeros (left-half or right-half plane) has on the shape of the Nyquist plot, the beginning and ending points of the plot, and the closed-loop stability.
		The solid lines in the plots are for positive frequencies, and the dashed lines are for negative frequencies.
		Again, note the effect that the placement of the poles and zeros (left-half or right-half plane) has on the shape of the Nyquist plot, the beginning and ending points of the plot, and the closed-loop stability.
	bass.gmu.edu /~gbeale/ece_421/nyquist_05.html (229 words)

	Fundamentals of Electrochemical Impedance Spectroscopy
		Notice that in this plot the y-axis is negative and that each point on the Nyquist plot is the impedance at one frequency.
		The impedance is plotted with log frequency on the x-axis and both the absolute value of the impedance (Z) and phase-shift on the y-axis.
		On a Bode plot, the Warburg impedance exhibits a phase shift of 45°.
	www.gamry.com /App_Notes/EIS_Primer/EIS_Primer.htm (5447 words)

	CTM: Frequency Response Tutorial
		To plot the frequency response, we create a vector of frequencies (varying between zero or "DC" and infinity) and compute the value of the plant transfer function at those frequencies.
		Since G(jw) is a complex number, we can plot* both its magnitude and phase (the Bode plot) or its position in the complex plane (the Nyquist plot).
		We can also read off the plot that for an input frequency of 0.3 radians, the output sinusoid should have a magnitude about one and the phase should be shifted by perhaps a few degrees (behind the input).
	www.krellinst.org /UCES/archive/classes/control/freq/freq.html (2512 words)

	Enhanced View Plugin: ETC, Spectrogram, Nyquist Plot ...
		Example of Nyquist plot (Selections A and B) The 2 following figures show an example of Nyquist Plot of a loop-back impulse response before and after Pink Filtering.
		Some tests can be performed by pressing the "Plot First and Peak Slices" button: the slice centered at t=0 and the slice centered at the time location of the Impulse Response peak will be plotted.
		When you are satisfied with the result, the "Plot ALL" option can be checked and finally, pressing the "Plot WHOLE Spectrogram" button, the whole spectrogram will be plotted.
	www.purebits.com /appnote15.html (873 words)

	[No title]
		It is the oldest of the four methods we discuss and is based on the polar plot of the loop transmission transfer function.
		These two functions are plotted separately and are used not only to check for stability, but also to find the gain and phase crossover frequencies, and the bandwidth frequency, which is the frequency at which the closed-loop magnitude response is equal to —3 dB.
		Although checking for stability with bode plots is not difficult, again we note that stability is not immediately obvious as in the case of the root locus or Nyquist.
	www.msu.edu /user/baragar1/Control_Systems.doc (2092 words)

	iiplot
		Local Nyquist plots allow a local evaluation of the quality of the fit.
		plots give a summary of the same information for all the frequency response functions and all poles.
		This plots can be used to visualize the phase scatter of identified residues.
	www.sdtools.com /help/iiplot.html (438 words)

	nyquist (System Identification Toolbox)
		produces a Nyquist plot on the screen, that is, a graph of the frequency response's imaginary part against its real part.
		If the argument indicating standard deviations is given as in `sd+5', a confidence region is plotted for every 5:th frequency, marking the center point by `+'.
		For time-series models (no input channels) the Nyquist plot is not defined.
	www.weizmann.ac.il /matlab/toolbox/ident/nyquist.html (415 words)

	sigma
		These options are available only for square systems, i.e., with the same number of inputs and outputs.
		To superimpose the singular value plots of several LTI models on a single figure:
		All systems must have the same number of inputs and outputs, but may otherwise be a mix of continuous and discrete systems.
	grove.ufl.edu /matlab_help/toolbox/control/sigma.html (220 words)

	Review of Classical Control Theory
		A Nyquist plot is a plot of the image of this path with respect to the open-loop transfer function
		In generating the plots "small" and "large" radii 0.2π and 20π were used.
		The Nyquist stability criterion is that the number of closed-loop poles in the right-half plane (RHP),
	classes.engr.arizona.edu /ame558/public_html/topic1/page5.html (405 words)

	CTM: Function lnyquist1
		By taking the log of the magnitude, the magnitude scale is compressed and the overall shape of the Nyquist plot is easier to see on the screen.
		We use log base 2 and add one to the magnitude so as to preserve the key attributes of the -1 point for the Nyquist plot.
		Furthermore, this function outputs the number of open-loop right hand plane poles, the number of anti-clockwise encirclements, and the number of closed-loop right half plane poles onto your screen.
	www.engin.umich.edu /group/ctm/extras/lnyquist1.html (514 words)

	sigma (Control System Toolbox)
		plots the singular values of the frequency response of an arbitrary LTI model
		These options are available only for square systems, that is, with the same number of inputs and outputs.
		To superimpose the singular value plots of several LTI models on a single figure, use
	www.tau.ac.il /cc/pages/docs/matlab/help/toolbox/control/sigma.html (251 words)

	PID Controller laboratory
		Should always be at least 2, which means that the Nyquist plot should cross the negative real axes at the right side from the value -1/2=-0.5.
		Should always be at least 60', which means that the Nyquist plot should cross the unit circle at the right side from the point with phase shift 60'.
		Summarizing the design specifications 1)-4) : The Nyquist plot should always pass at the right side from control points Gm and Pm and should not enter the protected area given by M-circles as it is shown on the previous picture.
	www.pidlab.com /design.php (1598 words)

	CTMS: Function nyquist1
		% % NYQUIST1(NUM,DEN) produces the Nyquist plot for the polynomial % transfer function G(s) = NUM(s)/DEN(s) where NUM and DEN contain % the polynomial coefficients in descending powers of s.
		vector W which must contain the frequencies, in radians/sec, % at which the Nyquist response is to be evaluated.
		No plot is drawn on the % screen.
	www.library.cmu.edu /ctms/ctms/extras/nyquist1.htm (359 words)

	Bode and Nyquist Using Excel
		The first plot is a plot of log modulus (in decibels) versus frequency.
		The second plot is the phase shift (in degrees) versus frequency.
		Since the frequency will be plotted in logarithmic scale, you can use a column to include numbers ranging linearly from -1 to 1, e.g.
	www.chem.mtu.edu /~tbco/cm416/freqexcel.html (239 words)

	nyquist
		calculates the Nyquist frequency response of LTI systems.
		Nyquist plots are used to analyze system properties including gain margin, phase margin, and stability.
		The frequency points are chosen automatically based on the system poles and zeros.
	grove.ufl.edu /matlab_help/toolbox/control/nyquist.html (206 words)

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