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→Inverted Pendulum
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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 | ||
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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; | |||
l = 0.314; | |||
M = 1.3; | |||
I = 0; | |||
g = 9.80665; | |||
b = 20; | |||
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]); | |||
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>}} | ||
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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(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== | ||