Changes

,  15:21, 29 September 2015
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|}
−
[[File:inverted_pendulum_new.png]]
+
[[File:inverted_pendulum_new.png|Schematic drawing of the inverted pendulum.]]

Linearization around the point <math display="inline">\theta=\pi[/itex] and substitution of <math display="inline">\theta'=\theta-\pi[/itex] (from here on in the analysis, <math display="inline">\theta'[/itex] will be written as <math display="inline">\theta[/itex], but it should be noted that <math display="inline">\theta[/itex] now

Linearization around the point <math display="inline">\theta=\pi[/itex] and substitution of <math display="inline">\theta'=\theta-\pi[/itex] (from here on in the analysis, <math display="inline">\theta'[/itex] will be written as <math display="inline">\theta[/itex], but it should be noted that <math display="inline">\theta[/itex] now
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<!-- {{SyntaxHighlight| -->

<!-- {{SyntaxHighlight| -->

{{Code|Creating the transfer functions for the inverted pendulum|<syntaxhighlight lang="octave" style="font-size:14px">

{{Code|Creating the transfer functions for the inverted pendulum|<syntaxhighlight lang="octave" style="font-size:14px">
m = 0.15;
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m = 0.15;
l = 0.314;
+
l = 0.314;
M = 1.3;
+
M = 1.3;
I = 7.38e-5;
+
I = 0;
g = 9.80665;
+
g = 9.80665;
b = 20;
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b = 20;
c = 0;
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c = 20;
G1 = tf([m*l^2+I b -m*g*l],
+

[(M+m)*(m*l^2+I)-m^2*l^2 (M+m)*b+(m*l^2+I)*c -(M+m)*m*g*l+b*c -m*g*l*c 0]);
+
G1 = tf([m*l^2+I b -m*g*l],
G2 = tf([-m*l],
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[(M+m)*(m*l^2+I)-m^2*l^2 (M+m)*b+(m*l^2+I)*c -(M+m)*m*g*l+b*c -m*g*l*c 0]);
[(M+m)*(m*l^2+I)-m^2*l^2 (M+m)*b+(m*l^2+I)*c -(M+m)*m*g*l+b*c -m*g*l*c]);
+
G2 = tf([-m*l],
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[(M+m)*(m*l^2+I)-m^2*l^2 (M+m)*b+(m*l^2+I)*c -(M+m)*m*g*l+b*c -m*g*l*c]);

</syntaxhighlight>}}

</syntaxhighlight>}}
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<!-- {{SyntaxHighlight| -->

<!-- {{SyntaxHighlight| -->

{{Code|Creating Bode plots for the inverted pendulum|<syntaxhighlight lang="octave" style="font-size:14px">

{{Code|Creating Bode plots for the inverted pendulum|<syntaxhighlight lang="octave" style="font-size:14px">
bode(G1);
+
bode(G1);
bode(G2);
+
bode(G2);

</syntaxhighlight>}}

</syntaxhighlight>}}

one obtains the Bode plots of the two transfer functions.

one obtains the Bode plots of the two transfer functions.
−
[[File:bode_g1.png]]
+
[[File:bode_g1.png|Bode diagram of the cart movement transfer function.]]
−
[[File:bode_g2.png]]
+
[[File:bode_g2.png|Bode diagram of the pendulums rotation transfer function.]]

==References==

==References==
501

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