Why isn't Nyquist taught like this?

Clash Royale CLAN TAG#URR8PPP

up vote
1
down vote

favorite

When I learnt how to do a Nyquist plot I was taught a really long-winded method that I don't understand to this day. I realised by myself that if you are given a system like below where s=j * omega $$fracs+1s+10$$ you can just replace s with j * omega and put in several values of omega and plot these outputs on the real-imaginary axis.

Is there a problem doing it this way because I cannot understand why it would not be taught like this if it is this easy?

EDIT: added image below.

nyquist-plot

share|improve this question

edited 1 hour ago

asked 1 hour ago

CoderEH

1084

add a comment | 

up vote
1
down vote

favorite

When I learnt how to do a Nyquist plot I was taught a really long-winded method that I don't understand to this day. I realised by myself that if you are given a system like below where s=j * omega $$fracs+1s+10$$ you can just replace s with j * omega and put in several values of omega and plot these outputs on the real-imaginary axis.

Is there a problem doing it this way because I cannot understand why it would not be taught like this if it is this easy?

EDIT: added image below.

nyquist-plot

share|improve this question

edited 1 hour ago

asked 1 hour ago

CoderEH

1084

add a comment | 

up vote
1
down vote

favorite

up vote
1
down vote

favorite

When I learnt how to do a Nyquist plot I was taught a really long-winded method that I don't understand to this day. I realised by myself that if you are given a system like below where s=j * omega $$fracs+1s+10$$ you can just replace s with j * omega and put in several values of omega and plot these outputs on the real-imaginary axis.

Is there a problem doing it this way because I cannot understand why it would not be taught like this if it is this easy?

EDIT: added image below.

nyquist-plot

share|improve this question

edited 1 hour ago

asked 1 hour ago

CoderEH

1084

When I learnt how to do a Nyquist plot I was taught a really long-winded method that I don't understand to this day. I realised by myself that if you are given a system like below where s=j * omega $$fracs+1s+10$$ you can just replace s with j * omega and put in several values of omega and plot these outputs on the real-imaginary axis.

Is there a problem doing it this way because I cannot understand why it would not be taught like this if it is this easy?

EDIT: added image below.

nyquist-plot

nyquist-plot

share|improve this question

edited 1 hour ago

asked 1 hour ago

CoderEH

1084

share|improve this question

edited 1 hour ago

asked 1 hour ago

CoderEH

1084

share|improve this question

share|improve this question

edited 1 hour ago

edited 1 hour ago

edited 1 hour ago

asked 1 hour ago

CoderEH

1084

asked 1 hour ago

CoderEH

1084

asked 1 hour ago

CoderEH

1084

1084

add a comment | 

add a comment | 

2 Answers
2

active

oldest

votes

up vote
4
down vote



accepted

1. There is no problem with the method you propose. It's the one I've used for years designing real systems.


2. You were probably taught a graphical method (I'm curious as to what it is -- do you have a link?). The graphical methods were invented before digital computers, or even calculators, were ubiquitous, and were designed to make it easy for an engineer with pencil, paper, a ruler, and a slide rule to make the graphs needed to get the job done.

share|improve this answer

answered 1 hour ago

TimWescott

1,15627

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your response! This is the best thing I could find to answer you question about what method I was taught (the image I added in the edit). This is a lecture slide that explains how to choose C1 which is a contour that encircles the right-hand half of the plane. Is the graphical method still taught in most universities or are students expected just to use Matlab or something similar?
  – CoderEH
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  So, the reason that they're obsessing on a contour is because the mathematical basis of the Nyquist plot is the Method of the Argument, which tells you how many more poles than zeros are within an area on the complex plane by counting how many times the graph revolves around zero. You actually need to do that to be absolutely 100% correct -- but you also need to know exactly how many unstable zeros you have in the system. I find it easier in practice to start with a known-stable system and investigate what changes I can make that will improve it's performance while keeping it stable.
  – TimWescott
  1 hour ago
  

  
  
  
  

add a comment | 

up vote
1
down vote

As far as I know, the usual way to introduce the Nyquist plots are the one you just described. This is how it was defined in my university studies and this is what I have seen in multiple books. The slide what you attached is not an introduction or definition for Nyquist diagrams, but for some advanced methods using it.

share|improve this answer

answered 26 mins ago

Horror Vacui

1214

add a comment | 

Your Answer

StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["\$", "\$"]]);
);
);
, "mathjax-editing");

StackExchange.ifUsing("editor", function ()
return StackExchange.using("schematics", function ()
StackExchange.schematics.init();
);
, "cicuitlab");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "135"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);

 

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2felectronics.stackexchange.com%2fquestions%2f404689%2fwhy-isnt-nyquist-taught-like-this%23new-answer', 'question_page');

);

Post as a guest

Name Email

2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
4
down vote



accepted

1. There is no problem with the method you propose. It's the one I've used for years designing real systems.


2. You were probably taught a graphical method (I'm curious as to what it is -- do you have a link?). The graphical methods were invented before digital computers, or even calculators, were ubiquitous, and were designed to make it easy for an engineer with pencil, paper, a ruler, and a slide rule to make the graphs needed to get the job done.

share|improve this answer

answered 1 hour ago

TimWescott

1,15627

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your response! This is the best thing I could find to answer you question about what method I was taught (the image I added in the edit). This is a lecture slide that explains how to choose C1 which is a contour that encircles the right-hand half of the plane. Is the graphical method still taught in most universities or are students expected just to use Matlab or something similar?
  – CoderEH
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  So, the reason that they're obsessing on a contour is because the mathematical basis of the Nyquist plot is the Method of the Argument, which tells you how many more poles than zeros are within an area on the complex plane by counting how many times the graph revolves around zero. You actually need to do that to be absolutely 100% correct -- but you also need to know exactly how many unstable zeros you have in the system. I find it easier in practice to start with a known-stable system and investigate what changes I can make that will improve it's performance while keeping it stable.
  – TimWescott
  1 hour ago
  

  
  
  
  

add a comment | 

up vote
4
down vote



accepted

1. There is no problem with the method you propose. It's the one I've used for years designing real systems.


2. You were probably taught a graphical method (I'm curious as to what it is -- do you have a link?). The graphical methods were invented before digital computers, or even calculators, were ubiquitous, and were designed to make it easy for an engineer with pencil, paper, a ruler, and a slide rule to make the graphs needed to get the job done.

share|improve this answer

answered 1 hour ago

TimWescott

1,15627

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your response! This is the best thing I could find to answer you question about what method I was taught (the image I added in the edit). This is a lecture slide that explains how to choose C1 which is a contour that encircles the right-hand half of the plane. Is the graphical method still taught in most universities or are students expected just to use Matlab or something similar?
  – CoderEH
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  So, the reason that they're obsessing on a contour is because the mathematical basis of the Nyquist plot is the Method of the Argument, which tells you how many more poles than zeros are within an area on the complex plane by counting how many times the graph revolves around zero. You actually need to do that to be absolutely 100% correct -- but you also need to know exactly how many unstable zeros you have in the system. I find it easier in practice to start with a known-stable system and investigate what changes I can make that will improve it's performance while keeping it stable.
  – TimWescott
  1 hour ago
  

  
  
  
  

add a comment | 

up vote
4
down vote



accepted

up vote
4
down vote



accepted

1. There is no problem with the method you propose. It's the one I've used for years designing real systems.


2. You were probably taught a graphical method (I'm curious as to what it is -- do you have a link?). The graphical methods were invented before digital computers, or even calculators, were ubiquitous, and were designed to make it easy for an engineer with pencil, paper, a ruler, and a slide rule to make the graphs needed to get the job done.

share|improve this answer

answered 1 hour ago

TimWescott

1,15627

1. There is no problem with the method you propose. It's the one I've used for years designing real systems.


2. You were probably taught a graphical method (I'm curious as to what it is -- do you have a link?). The graphical methods were invented before digital computers, or even calculators, were ubiquitous, and were designed to make it easy for an engineer with pencil, paper, a ruler, and a slide rule to make the graphs needed to get the job done.

share|improve this answer

answered 1 hour ago

TimWescott

1,15627

share|improve this answer

share|improve this answer

answered 1 hour ago

TimWescott

1,15627

answered 1 hour ago

TimWescott

1,15627

answered 1 hour ago

TimWescott

1,15627

1,15627

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your response! This is the best thing I could find to answer you question about what method I was taught (the image I added in the edit). This is a lecture slide that explains how to choose C1 which is a contour that encircles the right-hand half of the plane. Is the graphical method still taught in most universities or are students expected just to use Matlab or something similar?
  – CoderEH
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  So, the reason that they're obsessing on a contour is because the mathematical basis of the Nyquist plot is the Method of the Argument, which tells you how many more poles than zeros are within an area on the complex plane by counting how many times the graph revolves around zero. You actually need to do that to be absolutely 100% correct -- but you also need to know exactly how many unstable zeros you have in the system. I find it easier in practice to start with a known-stable system and investigate what changes I can make that will improve it's performance while keeping it stable.
  – TimWescott
  1 hour ago
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your response! This is the best thing I could find to answer you question about what method I was taught (the image I added in the edit). This is a lecture slide that explains how to choose C1 which is a contour that encircles the right-hand half of the plane. Is the graphical method still taught in most universities or are students expected just to use Matlab or something similar?
  – CoderEH
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  So, the reason that they're obsessing on a contour is because the mathematical basis of the Nyquist plot is the Method of the Argument, which tells you how many more poles than zeros are within an area on the complex plane by counting how many times the graph revolves around zero. You actually need to do that to be absolutely 100% correct -- but you also need to know exactly how many unstable zeros you have in the system. I find it easier in practice to start with a known-stable system and investigate what changes I can make that will improve it's performance while keeping it stable.
  – TimWescott
  1 hour ago
  

  
  
  
  

Thanks for your response! This is the best thing I could find to answer you question about what method I was taught (the image I added in the edit). This is a lecture slide that explains how to choose C1 which is a contour that encircles the right-hand half of the plane. Is the graphical method still taught in most universities or are students expected just to use Matlab or something similar?
– CoderEH
1 hour ago

Thanks for your response! This is the best thing I could find to answer you question about what method I was taught (the image I added in the edit). This is a lecture slide that explains how to choose C1 which is a contour that encircles the right-hand half of the plane. Is the graphical method still taught in most universities or are students expected just to use Matlab or something similar?
– CoderEH
1 hour ago

1

1

So, the reason that they're obsessing on a contour is because the mathematical basis of the Nyquist plot is the Method of the Argument, which tells you how many more poles than zeros are within an area on the complex plane by counting how many times the graph revolves around zero. You actually need to do that to be absolutely 100% correct -- but you also need to know exactly how many unstable zeros you have in the system. I find it easier in practice to start with a known-stable system and investigate what changes I can make that will improve it's performance while keeping it stable.
– TimWescott
1 hour ago

So, the reason that they're obsessing on a contour is because the mathematical basis of the Nyquist plot is the Method of the Argument, which tells you how many more poles than zeros are within an area on the complex plane by counting how many times the graph revolves around zero. You actually need to do that to be absolutely 100% correct -- but you also need to know exactly how many unstable zeros you have in the system. I find it easier in practice to start with a known-stable system and investigate what changes I can make that will improve it's performance while keeping it stable.
– TimWescott
1 hour ago

add a comment | 

up vote
1
down vote

As far as I know, the usual way to introduce the Nyquist plots are the one you just described. This is how it was defined in my university studies and this is what I have seen in multiple books. The slide what you attached is not an introduction or definition for Nyquist diagrams, but for some advanced methods using it.

share|improve this answer

answered 26 mins ago

Horror Vacui

1214

add a comment | 

up vote
1
down vote

As far as I know, the usual way to introduce the Nyquist plots are the one you just described. This is how it was defined in my university studies and this is what I have seen in multiple books. The slide what you attached is not an introduction or definition for Nyquist diagrams, but for some advanced methods using it.

share|improve this answer

answered 26 mins ago

Horror Vacui

1214

add a comment | 

up vote
1
down vote

up vote
1
down vote

As far as I know, the usual way to introduce the Nyquist plots are the one you just described. This is how it was defined in my university studies and this is what I have seen in multiple books. The slide what you attached is not an introduction or definition for Nyquist diagrams, but for some advanced methods using it.

share|improve this answer

answered 26 mins ago

Horror Vacui

1214

As far as I know, the usual way to introduce the Nyquist plots are the one you just described. This is how it was defined in my university studies and this is what I have seen in multiple books. The slide what you attached is not an introduction or definition for Nyquist diagrams, but for some advanced methods using it.

share|improve this answer

answered 26 mins ago

Horror Vacui

1214

share|improve this answer

share|improve this answer

answered 26 mins ago

Horror Vacui

1214

answered 26 mins ago

Horror Vacui

1214

answered 26 mins ago

Horror Vacui

1214

1214

add a comment | 

add a comment | 

 

draft saved

draft discarded

 

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2felectronics.stackexchange.com%2fquestions%2f404689%2fwhy-isnt-nyquist-taught-like-this%23new-answer', 'question_page');

);

Post as a guest

Name Email

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name Email

Name Email

Name

Email

Name Email

Name

Email