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138 bytes added ,  08:21, 29 September 2015
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   −
[[File:inverted_pendulum_new.png]]
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[[File:inverted_pendulum_new.png|Schematic drawing of the inverted pendulum.]]
    
Linearization around the point <math display="inline">\theta=\pi</math> and substitution of <math display="inline">\theta'=\theta-\pi</math> (from here on in the analysis, <math display="inline">\theta'</math> will be written as <math display="inline">\theta</math>, but it should be noted that <math display="inline">\theta</math> now
 
Linearization around the point <math display="inline">\theta=\pi</math> and substitution of <math display="inline">\theta'=\theta-\pi</math> (from here on in the analysis, <math display="inline">\theta'</math> will be written as <math display="inline">\theta</math>, but it should be noted that <math display="inline">\theta</math> 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;
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l = 0.314;
M = 1.3;
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M = 1.3;
I = 7.38e-5;
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I = 0;
g = 9.80665;
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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],
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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]);
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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]);
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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);
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bode(G1);
bode(G2);
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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]]
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[[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==
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