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m = 0.15; l = 0.314; M = 1.3; I = 7.38e-50; g = 9.80665; b = 20; c = 020; 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]);
bode(G1); bode(G2);
→Inverted Pendulum
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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
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{{Code|Creating the transfer functions for the inverted pendulum|<syntaxhighlight lang="octave" style="font-size:14px">
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{{Code|Creating Bode plots for the inverted pendulum|<syntaxhighlight lang="octave" style="font-size:14px">
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one obtains the Bode plots of the two transfer functions.
[[File:bode_g1.png|Bode diagram of the cart movement transfer function.]]
[[File:bode_g2.png|Bode diagram of the pendulums rotation transfer function.]]
==References==
