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Topic: Nyquist stability criterion

	Encyclopedia: Harry Nyquist
		Johnson-Nyquist noise (sometimes thermal noise, Johnson noise or Nyquist noise) is the noise generated by the equilibrium fluctuations of the electric current inside an electrical conductor, which happens without any applied voltage, due to the random thermal motion of the charge carriers (the electrons).
		A Nyquist plot is a graph used in signal processing in which the magnitude and phase of a frequency response are plotted on orthogonal axes.
		In 1927 Nyquist determined that an analog signal should be sampled at twice the frequency of its highest-frequency component in order to be converted into an adequate representation of the signal in digital form.
	www.nationmaster.com /encyclopedia/Harry-Nyquist (975 words)

	Feedback - Wikipedia, the free encyclopedia
		Negative feedback is often deliberately introduced to increase the stability and accuracy of a system, as in the feedback amplifier invented by Harold Stephen Black.
		Harry Nyquist was an electrical engineer who contributed the Nyquist plot for determining the stability of feedback systems.
		In ancient times, the float valve was used to regulate the flow of water in Greek and Roman water clocks; similar float valves are used to regulate fuel in a carburettor and also used to regulate tank water level in the flush toilet.
	www.wikipedia.org /wiki/Feedback (1459 words)

	Harry Nyquist - Wikipedia, the free encyclopedia
		He emigrated to the USA in 1907 and entered the University of North Dakota in 1912.
		In 1927 Nyquist determined that an analog signal should be sampled at regular intervals over time and at twice the frequency of the signal's bandwidth in order to be converted into an adequate representation of the signal in digital form.
		Nyquist published his results in the paper Certain topics in Telegraph Transmission Theory (1928).
	en.wikipedia.org /wiki/Harry_Nyquist (230 words)

	Encyclopedia: Negative feedback
		Homeostasis or homoeostasis is the property of an open system, especially living organisms, to regulate its internal environment so as to maintain a stable condition, by means of multiple dynamic equilibrium adjustments controlled by interrelated regulation mechanisms.
		The stability characteristics of the gain feedback product (BA) are often displayed and investigated on a Nyquist plot (a polar plot of the gain/phase shift as a parametric function of frequency).
		The Nyquist Stability Criterion is a unique and powerfull method for determining the stability of a closed-loop control system.
	www.nationmaster.com /encyclopedia/Negative-feedback (1022 words)

	7-3 THE NYQUIST STABILITY CRITERION
		The (-1,0) point plays the same role in the Nyquist diagram as the imaginary axis does in the in the root locus diagram.
		Two quantities that measure the stability margin of a system are directly related to the proximity of the frequency response drawn on a polar plot to the (-1,0) point, are called gain margin and phase margin.
		For a stable system OA is less than 1, hence the gain margin of a stable system is positive when expressed in dBs.
	www.engr.udayton.edu /faculty/rkashani/mee527/nyq_stab/nyq_stab_margins.htm (605 words)

	Encyclopedia: Stability criterion
		The Routh Hurwitz Stability Criterion is a necessary, and frequently sufficient method to establish the stability of a Single-Input, Single-Output, Linear Time Invarient (LTI) control system.
		During the study of the phase margin of linear systems, this criterion is often suggested by students grasping for an intuitive understanding of stability.
		They continue to insist that ``[t]he Nyquist stability criterion presents this fact in a rigorous mathematical form.'' This introduction is completely wrong, and Chestnut and Mayer even provide the Nyquist plot of a perfect counterexample a mere fourteen pages later (while defining conditionally-stable nonlinear systems).
	www.nationmaster.com /encyclopedia/Stability-criterion (943 words)

	Articles - Nyquist plot (Site not responding. Last check: 2007-11-06)
		A Nyquist plot is used in automatic control and signal processing for assessing the stability of a system with feedback.
		The real use of Nyquist plot is in that the stability of the system can be easily predicted by plotting its open loop polar plot along a path that goes along the jÏ‰ axis and along a semicircle of infinite radius in the positive (real part) half of the s-plane.
		Nyquist and related plots are classic methods of assessing stability; they have been supplemented or supplanted by computer based mathematical tools in recent years.
	www.zgrey.com /articles/Nyquist_plot (274 words)

	Abstract: M2000-174
		For circular sawing machines, which are used as an example, this is the high compliance of the saw blade and the torsional weakness of the main drive as a result of the application of a complex gearbox between main motor and saw shaft.
		The conventional representation of stability behavior is the form of stability charts, in which the stability limit is plotted versus different cutting parameters.
		Stability analysis indicates the way in which these variables should be altered to achieve rapid stabilization at the highest possible material removal rate.
	www.me.gatech.edu /mechatronics2000/Abstracts/174.htm (1057 words)

	CTM: Frequency Response Tutorial, Nyquist
		The Nyquist criterion can be used for design purposes regardless of open-loop stability (remember that the Bode design methods assume that the system is stable in open loop).
		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.
		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)

	An Introduction To The Nyquist Stability CriterionNyquist Stability Criterion
		We'll consider the question of how stable a system is, and try to give an answer couched in terms of the Nyquist stability criterion, and how closely it comes to not being satisfied.
		In order to understand the Nyquist stability criterion you need to understand what a Nyquist plot is in as many different senses as may be possible.
		A frequency response plot - the Nyquist plot in particular - is a map of a function, G(s), for s values that lie on the imaginary axis in the s-plane.
	www.facstaff.bucknell.edu /mastascu/eControlHTML/Freq/Nyquist2.html (3488 words)

	Nyquist Plots
		It 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
		Nyquist plots are produced by the command NyquistPlot whose argument sequence is the same as that of BodePlot.
	documents.wolfram.com /applications/insydes/Tutorial/NyquistPlots.html (260 words)

	Nyquist Stability
		If you did the problems in the Nyquist stability lesson, you should have concluded that many Nyquist plots have many general properties in common, even for a large variety of systems.
		Clearly, we need to develop some way of measuring how stable a system is. The lesson on relative stability (Click here to open that lesson.) will help you with that.
		Once we have an idea of what we mean by relative stability, and we have precise definitions that will give numerical measures of relative stabiltiy, we are going to find that relative stability can also be best interpreted using Bode' plots.
	www.facstaff.bucknell.edu /mastascu/eControlHTML/Freq/Nyquist3.html (1235 words)

	Module and Programme Catalogue
		Define the Nyquist frequency, explain the phenomena of aliasing and hidden oscillations, and describe how the sampling frequency of a digital control system shoul d be selected.
		Use the Root-locus to calculate stability margins, and explain how it can be used as a compensation tool for simple designs, including pole/zero cancellations and dipole addition.
		Frequency-domain methods: Explain how Nyquist?s stability criterion may be adapted to the discrete-time case; define gain/phase margins; describe how the closed-loop properties of a feedback system can be inferred from its open-loop Nyquist plot (steady-state error, damping, bandwidth, etc.) and carry out simple designs in the Nyquist plane via loop shaping.
	www.leeds.ac.uk /modules/200203/ug/elec3150.htm (749 words)

	Book Review - Control Engineering, an introductory course - The IEE (Site not responding. Last check: 2007-11-06)
		It should also, for example, provide opportunities for a simple interpretation of the Nyquist stability criterion, which is never dealt with in this book, and for dealing with tan-1x.
		Determination of the Nyquist critical point of the process transfer function using the gain adjustment method of Ziegler-Nichols and the more recent relay autotuning method are then discussed and some real plant data again included.
		The M and N contours, which are of course circles on a Nyquist diagram, are mentioned for the first time.
	www.iee.org /OnComms/PN/controlauto/bookreview.cfm (2516 words)

	Read about Nyquist stability criterion at WorldVillage Encyclopedia. Research Nyquist stability criterion and learn ... (Site not responding. Last check: 2007-11-06)
		The Nyquist Criterion given > where P is the number of poles of F(s) encircled by Γ
		Note: some texts claim that any encirclements of the point (-1 + j0) causes the system to N = Z − P, only Z must be zero to ensure that the system is stable.
		A closed-loop feedback system may have a zero in the right half plane, without compromising stability.
	encyclopedia.worldvillage.com /s/b/Stability_criterion (430 words)

	A brief history of feedback control - Chapter 1
		He studied the stability of nonlinear differential equations using a generalized notion of energy in 1892 [Lyapunov 1893].
		For instance, the Nyquist, Bode, and root locus plots are in terms of the open-loop transfer function.
		Although LQR design using state feedback guarantees closed-loop stability, all the state components are seldom available for feedback purposes in a practical design problem.
	www.theorem.net /theorem/lewis1.html (8851 words)

	AT&T Labs Research - Research Forum (Site not responding. Last check: 2007-11-06)
		The heart of control theory is the Nyquist Stability Condition - first disclosed by Harry Nyquist, a retired Bell Labs engineer who retained an office in Whippany.
		From that moment on I knew that I wanted to continue my education and obtain a Ph.D. in Electrical engineering, and that I wanted to work for Bell Labs, the place where technology and science were being created by the most interesting and innovative people on the planet.
		The issue of business impact was generally not the major criterion for the work that was tackled.
	www.research.att.com /forum/archive/19981201.html (1694 words)

	Stability Analysis On the Nichols Chart and Its Application in QFT - Chen, Ballanco (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Abstract: A new stability criterion on Nichols chart is presented.
		Furthermore this result can be used to test the stability of the new nominal closed-loop system arising in QFT controller design method for nonminimum phase and unstable plants, which is difficult to test with the existing stability criterion.
		Stability analysis on the Nichols chart and its application in QFT..
	citeseer.ist.psu.edu /160667.html (376 words)

	Re: The First NFB theory
		It gives the >> > > stability criterion that all of the poles of the characterstic >> equation >> > > of the closed loop system must be located in the left half plane.
		Stability conditions for ordinary linear differential >equations with constant cofficients go back before Maxwell.
		I sometimes use a variant >of what Maxwell wrote which is that I must place all of the eigenvalues >of the system matrix inside the unit circle.
	www.cyber-spy.com /electronics-design/electro-01992-29917.html (387 words)

	Nyquist Stability Criterion - Maplesoft Application Center
		In 1932, Harry Nyquist (1889-1976), an engineer at Bell Telephone Laboratories, articulated the use of the extended principle of the argument for determining where the poles of a transfer function in a linear feedback system are located.
		If any of these poles (or eigenvalues) have postive real part, that is, if any pole is located in the right half-plane, the solution may contain exponential terms which grow without bound as time increases.
		Thus, determining whether or not there are poles of the transfer function in the right half-plane is tantamount to determining the stability of the feedback system.
	adept.maplesoft.com /Info.asp?ArticleID=92 (143 words)

	NYQUIST - SOLUTION
		From this plot it can be seen that the Nyquist diagram does not enclose -1 on the real axis, so it can be concluded that the system is stable for K=1.
		For this part of the problem the gain K is changed from 1 to 15 (in steps of 1) and we found that increasing the gain, magnifies the Nyquist diagram.
		Furthermore if we zoom the Nyquist diagram in x-y for any value of gain 0Nyquist diagram will not approach (-1 + j0) pole, so it can be concluded that the system is stable for any gain in range 0
	www.gu.edu.au /centre/icsl/vlacic/teaching/nsolution.htm (1070 words)

	ACC00-IEEE1202 (Site not responding. Last check: 2007-11-06)
		ABSTRACT: In this paper, we first derive a Nyquist stability criterion of sampled-data systems in such a form that reflects the treatment of sampled-data systems with their intersample behavior taken into account.
		We next analyze the positive realness of sampled-data systems with the direct feedthrough matrix from the disturbance input to the controlled output being zero, and show that such sampled-data systems cannot be made positive real, unless the relative degree of the system from the disturbance input to the controlled output is 1.
		All these analyses, as well as the small-gain analysis, are compared from the viewpoint of the gain margin analysis.
	nt1.rsip.lsu.edu /cebopenweb/conferences/acc2K/T-Program/program/Manuscripts/ACC00-IEEE1202.htm (145 words)

	Feedback Stability FAQ
		In 1932, Nyquist employed the theory to determine his stability criterion for feedback amplifiers.
		Nyquist Stability Criterion: tells you whether the network will be stable, but is not very useful for optimizing the compensation network, a kind of a go, no-go approach.
		So, when you read that stability requires that the loop phase remain within 180 degrees at all frequencies where the loop gain is greater than unity, it means with respect to whatever polarity the design needs in order to subtract the NFB from the input signal.
	www.triodeel.com /feedback.htm (8237 words)

	Classical Feedback Control
		Among these are the root-locus method, the detection of right-sided polynomial roots using the Routh-Hurwitz criterion, and manual calculations using the Laplace and Fourier transforms.
		These methods have been rendered obsolete by computers and are granted only a brief treatment in the book, making room for loop shaping, Bode integrals, structural simulation of complex systems, multiloop systems, and nonlinear controllers, all of which are essential for good design practice.
		From the Nyquist diagram to the Bode diagram
	www.luriecontrol.com /ClassicalFeedbackControl.htm (707 words)

	Nyquist Stability Criterion and Positive-Realness of Sampled-Data Systems (Site not responding. Last check: 2007-11-06)
		In this paper, we first derive a Nyquist stability criterion of sampled-data systems in such a form that reflects the treatment of sampled-data systems with their intersample behavior taken into account.
		We next analyze the positive-realness of sampled-data systems with D_{11} matrix (i.e., the continuous-time direct feedthrough matrix from the disturbance input w to the controlled output z) being 0, and show that such sampled-data systems cannot be made positive-real, unless the relative degree of the system from w to z is 1.
		This should be useful for the stability analysis of sampled-data systems with nonlinearities.
	peugeot.kuee.kyoto-u.ac.jp /~hagiwara/mypubs/2002/b/42102.htm (175 words)

	Control Theory
		``Frequency Domain Stability Criterion for Vibrational Control of the Bernoulli-Euler Beam," ASME J.\ Dynamic Systems, Measurement, and Control}, (Chait, Radcliffe, MacCluer), Sept.\ 1988, vol.\ 110, pp.\ 303-307.
		``A Nyquist Stability Criterion for Distributed Parameter Systems," IEEE Trans.\ Auto.\ Control}, (Chait, MacCluer, Radcliffe), vol.\ 34, no.\ 1, Jan 1989, pp.\ 90-92.
		``Bounds on the impulse response of stable rational plants," ASME J.\ DSMC}, June, 1991, pp.
	www.math.msu.edu /~maccluer/controlT.html (754 words)

	TRI-DN-97-2 Abstract and PostScript (Site not responding. Last check: 2007-11-06)
		The goal of this paper is to generalize the Robinson stability criteria, for a charged particle beam interacting with the radio-frequency cavity resonator that is responsible for accelerating it, to the case that the resonator is equipped with a delayed voltage-proportional feedback.
		We start by reviewing the Nyquist criterion and then formulating an algebraic version which is then used to give a general, exact, analytic procedure for determining whether a transcendental equation has poles/zeros in the right-half complex plane.
		The method is first applied to determining the limiting feedback gain of a resonator alone, and then to the problem of finding analogues of the Robinson criteria.
	www.triumf.ca /people/koscielniak/tridn-97-2.htm (125 words)

	Open Directory - Science: Math: Applications: Control Theory (Site not responding. Last check: 2007-11-06)
		Bode and Nyquist Using Excel - Explains how spreadsheets can be used to obtain Bode and Nyquist Diagrams, from the University of Michigan, USA.
		The Nyquist Criterion Using Bode Plots - Explains the controller stability criteria based on the Nyquist frequency response.
		Nyquist Stability - Explains the basics of the Nyquist controller stability criteria.
	www.dmoz.com /Science/Math/Applications/Control_Theory (591 words)

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