Changes

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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</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

<!-- {{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;

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;

b = 20;

c = 0;

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],

        [(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],

        [(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>}}

<!-- {{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==