Why the angle is $-180°$ at $omega = 0$ for this system
I'm trying to plot the nyquist from the analytical expression of the system but the bode plot generated by matlab yields an angle -180 whereas the analytical expression yields zero when $omega=0$. The open-loop is
$$
G(s) = frac{s+4}{(s+2)(s-3)}
$$
The analytical expression for this system is
$$
G(jomega) = frac{-(5omega^2+24)-j(omega^3+2omega)}{omega^4+13omega^2+36}
$$
The angle is defined as follows:
$$
angle G(jomega) = tan^{-1}left(frac{omega^3+2omega}{5omega^2+24}right)
$$
the standard arctan function is defined as follows:
In my case, $x$ is always positive. Now if $omega = 0$, the angle is zero. According to the Bode plot generated by Matlab, the angle is -180 shown below
Am I missing something in here?
trigonometry linear-control
edited Dec 12 '18 at 23:11
bjcolby15
1,1921916
asked Dec 12 '18 at 22:16
CroCoCroCo
229220
add a comment |
I'm trying to plot the nyquist from the analytical expression of the system but the bode plot generated by matlab yields an angle -180 whereas the analytical expression yields zero when $omega=0$. The open-loop is
$$
G(s) = frac{s+4}{(s+2)(s-3)}
$$
The analytical expression for this system is
$$
G(jomega) = frac{-(5omega^2+24)-j(omega^3+2omega)}{omega^4+13omega^2+36}
$$
The angle is defined as follows:
$$
angle G(jomega) = tan^{-1}left(frac{omega^3+2omega}{5omega^2+24}right)
$$
the standard arctan function is defined as follows:
In my case, $x$ is always positive. Now if $omega = 0$, the angle is zero. According to the Bode plot generated by Matlab, the angle is -180 shown below
Am I missing something in here?
trigonometry linear-control
edited Dec 12 '18 at 23:11
bjcolby15
1,1921916
asked Dec 12 '18 at 22:16
CroCoCroCo
229220
add a comment |
I'm trying to plot the nyquist from the analytical expression of the system but the bode plot generated by matlab yields an angle -180 whereas the analytical expression yields zero when $omega=0$. The open-loop is
$$
G(s) = frac{s+4}{(s+2)(s-3)}
$$
The analytical expression for this system is
$$
G(jomega) = frac{-(5omega^2+24)-j(omega^3+2omega)}{omega^4+13omega^2+36}
$$
The angle is defined as follows:
$$
angle G(jomega) = tan^{-1}left(frac{omega^3+2omega}{5omega^2+24}right)
$$
the standard arctan function is defined as follows:
In my case, $x$ is always positive. Now if $omega = 0$, the angle is zero. According to the Bode plot generated by Matlab, the angle is -180 shown below
Am I missing something in here?
trigonometry linear-control
edited Dec 12 '18 at 23:11
bjcolby15
1,1921916
asked Dec 12 '18 at 22:16
CroCoCroCo
229220
I'm trying to plot the nyquist from the analytical expression of the system but the bode plot generated by matlab yields an angle -180 whereas the analytical expression yields zero when $omega=0$. The open-loop is
$$
G(s) = frac{s+4}{(s+2)(s-3)}
$$
The analytical expression for this system is
$$
G(jomega) = frac{-(5omega^2+24)-j(omega^3+2omega)}{omega^4+13omega^2+36}
$$
The angle is defined as follows:
$$
angle G(jomega) = tan^{-1}left(frac{omega^3+2omega}{5omega^2+24}right)
$$
the standard arctan function is defined as follows:
In my case, $x$ is always positive. Now if $omega = 0$, the angle is zero. According to the Bode plot generated by Matlab, the angle is -180 shown below
Am I missing something in here?
trigonometry linear-control
trigonometry linear-control
edited Dec 12 '18 at 23:11
bjcolby15
1,1921916
asked Dec 12 '18 at 22:16
CroCoCroCo
229220
edited Dec 12 '18 at 23:11
bjcolby15
1,1921916
asked Dec 12 '18 at 22:16
CroCoCroCo
229220
edited Dec 12 '18 at 23:11
bjcolby15
1,1921916
edited Dec 12 '18 at 23:11
bjcolby15
1,1921916
edited Dec 12 '18 at 23:11
bjcolby15
1,1921916
1,1921916
asked Dec 12 '18 at 22:16
CroCoCroCo
229220
asked Dec 12 '18 at 22:16
CroCoCroCo
229220
asked Dec 12 '18 at 22:16
CroCoCroCo
229220
229220
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
while $text{atan2} frac {x}{y}$ may not be defined when $omega = 0$
$lim_limits{omegato 0} text{atan2} frac {y}{x}$ exists.
$G(jomega) = frac{-(5omega^2+24)-j(omega^3+2omega)}{omega^4+13omega^2+36}$
$x = frac {-(5omega^2+24)}{omega^4+13omega^2+36}$
Which means that $x$ is always negative or $0$.
And where does that put your angle?
answered Dec 12 '18 at 22:24
Doug MDoug M
44.2k31854
Probably my mistake is the way $x$ is defined. The angle is basically in the second and fourth quadrants.
– CroCo
Dec 12 '18 at 22:48
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.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
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',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
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
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
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
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3037294%2fwhy-the-angle-is-180-at-omega-0-for-this-system%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
while $text{atan2} frac {x}{y}$ may not be defined when $omega = 0$
$lim_limits{omegato 0} text{atan2} frac {y}{x}$ exists.
$G(jomega) = frac{-(5omega^2+24)-j(omega^3+2omega)}{omega^4+13omega^2+36}$
$x = frac {-(5omega^2+24)}{omega^4+13omega^2+36}$
Which means that $x$ is always negative or $0$.
And where does that put your angle?
answered Dec 12 '18 at 22:24
Doug MDoug M
44.2k31854
Probably my mistake is the way $x$ is defined. The angle is basically in the second and fourth quadrants.
– CroCo
Dec 12 '18 at 22:48
add a comment |
while $text{atan2} frac {x}{y}$ may not be defined when $omega = 0$
$lim_limits{omegato 0} text{atan2} frac {y}{x}$ exists.
$G(jomega) = frac{-(5omega^2+24)-j(omega^3+2omega)}{omega^4+13omega^2+36}$
$x = frac {-(5omega^2+24)}{omega^4+13omega^2+36}$
Which means that $x$ is always negative or $0$.
And where does that put your angle?
answered Dec 12 '18 at 22:24
Doug MDoug M
44.2k31854
Probably my mistake is the way $x$ is defined. The angle is basically in the second and fourth quadrants.
– CroCo
Dec 12 '18 at 22:48
add a comment |
while $text{atan2} frac {x}{y}$ may not be defined when $omega = 0$
$lim_limits{omegato 0} text{atan2} frac {y}{x}$ exists.
$G(jomega) = frac{-(5omega^2+24)-j(omega^3+2omega)}{omega^4+13omega^2+36}$
$x = frac {-(5omega^2+24)}{omega^4+13omega^2+36}$
Which means that $x$ is always negative or $0$.
And where does that put your angle?
answered Dec 12 '18 at 22:24
Doug MDoug M
44.2k31854
while $text{atan2} frac {x}{y}$ may not be defined when $omega = 0$
$lim_limits{omegato 0} text{atan2} frac {y}{x}$ exists.
$G(jomega) = frac{-(5omega^2+24)-j(omega^3+2omega)}{omega^4+13omega^2+36}$
$x = frac {-(5omega^2+24)}{omega^4+13omega^2+36}$
Which means that $x$ is always negative or $0$.
And where does that put your angle?
answered Dec 12 '18 at 22:24
Doug MDoug M
44.2k31854
edited Dec 12 '18 at 22:27
answered Dec 12 '18 at 22:24
Doug MDoug M
44.2k31854
answered Dec 12 '18 at 22:24
Doug MDoug M
44.2k31854
answered Dec 12 '18 at 22:24
Doug MDoug M
44.2k31854
44.2k31854
Probably my mistake is the way $x$ is defined. The angle is basically in the second and fourth quadrants.
– CroCo
Dec 12 '18 at 22:48
add a comment |
Probably my mistake is the way $x$ is defined. The angle is basically in the second and fourth quadrants.
– CroCo
Dec 12 '18 at 22:48
Probably my mistake is the way $x$ is defined. The angle is basically in the second and fourth quadrants.
– CroCo
Dec 12 '18 at 22:48
Probably my mistake is the way $x$ is defined. The angle is basically in the second and fourth quadrants.
– CroCo
Dec 12 '18 at 22:48
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
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
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3037294%2fwhy-the-angle-is-180-at-omega-0-for-this-system%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
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
Required, but never shown
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
Required, but never shown
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
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
