# Re: Nyquist by hand

*From*: AsimV <asimvod@xxxxxxxxx>*Date*: Sat, 14 Jun 2008 08:47:03 -0700 (PDT)

Jerry Avins wrote:

Jerry Avins wrote:

parrishc@xxxxxxxxx wrote:

Can someone PLEASE direct me to a resource which explains the

construction of Nyquist plots by hand? The threads I looked at in

this forum do not concern this specifically. I have been in the dark

on this matter for longer than I care to discuss. Gratefully yours.

Chris Parrish

Check out http://tinyurl.com/4vxxvz

A Nyquist plot is a polar plot of frequency and phase response.

Magnitude -- linear, not dB --is the radius and phase is the angle.

What I meant: A Nyquist plot is a polar plot of amplitude vs. phase

response with frequency as a parameter. Magnitude -- linear, not dB --

is the radius and phase is the angle.

For a chosen frequency, place a dot in the right place on polar paper.--

(I write the frequency as a label.) Plot enough dots to see the

curvature -- more where the curve bends more sharply, then connect the

dots.

Jerry

Engineering is the art of making what you want from things you can get.

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Jerry, I believe that is so called Nichols plot. Nichols plot gives

amplitude vs phase chart. That is different from Nyquist plot.

For example if feedback transfer functions is T = G/(1+GH), usually in

order to determine stability of a system, its Nyquist plot is drawn

for GH and observed if it encircles point (-1,0) and how many times.

Nyquist plot represents simple graphical form of GH(s) mapping. Since

s = a+jw, GH(s) maps that complex domain into new complex variable

domain u+jv. Nyquist plot represents Im{GH(s)} vs Re{GH(s)} plot or

"v" vs "u" plot.

Procedure to draw it by hand can be very tedious and with many

software pacjkages available today, I'm surprised that someone ask

this question.

However there are some formal rules that can be used when drawing

Nyquist plot for simple systems.

Usually you devide GH(s) into portions for s = jw. Then you observed

how portion from w = 0+ to w = +inf is mapped. Then you try and see

how portion from w = +inf to w = -inf is mapped.

You do this by findind limit values (lim).

Nyquist plot is always symmetrical around x (Real) axis.

Like I said, constructing Nyquist plot by hand is very complex and

difficult for most but few simple examples. I usually use tables with

graphical plots or some powerful software tools such Matlab or Scilab.

I would recommend Scilab, because it is very powerful and entirely

free alternative to expensive Matlab.

Best regards,

Asim Vodencarevic

.

**Follow-Ups**:**Re: Nyquist by hand***From:*dave y .

**Re: Nyquist by hand***From:*Jerry Avins

**References**:**Nyquist by hand***From:*parrishc

**Re: Nyquist by hand***From:*Jerry Avins

**Re: Nyquist by hand***From:*Jerry Avins

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