Line 563: |
Line 563: |
| |} | | |} |
| | | |
− | [[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 |
Line 617: |
Line 617: |
| <!-- {{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>}} |
| | | |
Line 634: |
Line 635: |
| <!-- {{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== |