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| | == Inverted Pendulum Project == |
| | #[[Parameters]] |
| | #[http://www.ee.usyd.edu.au/tutorials_online/matlab/examples/pend/invpen.html Modeling the Inverted Pendulum] |
| | #[http://engr.case.edu/merat_francis/eecs397/PLL.pdf Phase Locked Loops] |
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| == Inverted Penululm Project == | | == Octave Examples == |
| [Parameters] | | [[RLC Circuit of February 10, 2011]] |
| % Double Pendulum Parameters (Tentative: There are two pendulums with different parameters. I'm not sure which these go to.)
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| | == Links == |
| % Run parameters
| | *[https://ia700708.us.archive.org/33/items/NetworkAnalysisFeedbackAmplifierDesign/Bode-NetworkAnalysisFeedbackAmplifierDesign.pdf H. W. Bode's "Network Analysis and Feedback Amplifier Design"] |
| %f = input('Control Frequency (Hz) = ');
| | *[http://www.cds.caltech.edu/~murray/books/AM05/pdf/am08-complete_30Aug11.pdf Feedback Systems (textbook) Astrom & Murray] |
| %crad = input('Pole Radius (1/s) = ');
| | *[http://www.eolss.net/sample-chapters/c18/e6-43-13-09.pdf Bernard Friedland, Reduced Order Observer] |
| %psi = input('Spreading Angle (deg) = ');
| | *[http://www.cds.caltech.edu/~murray/books/AM05/pdf/obc-kalman_22Dec09.pdf Optimization Based Control (Murray)] |
| %eta = psi*pi/180;
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| %obshift = input('Observer Shift = ');
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| %Trun = input('Run Time (s) = ');
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| f=130;
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| crad=19;
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| psi=10;
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| eta=psi*pi/180;
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| obshift=2;
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| Trun=60;
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| kmax = round(f*Trun);
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| T = 1/f;
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| Maxpos = 0.25; % Max carriage travel +- 0.25 m
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| Maxangle = 0.175; % Max rod angle -- 10 deg
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| Maxvoltage = 20; % Max motor voltage, V
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| pstart = 0.005; % Carriage position starting limit, m
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| astart = 1*pi/180; % Angle starting limit, rad
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| g = 9.81; % m/s^2 Gravitational constant
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| % SYSTEM PARAMETERS
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| % Measured Mechanical Parameters
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| d1 = 0.323; % m Length of pendulum 1 (long)
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| d2 = 0.079; % m Length of pendulum 2 (short)
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| %mp1 = 0.0208; % kg Mass of pendulum 1
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| mp1 = 0.0318;
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| %mp2 = 0.0050; % kg Mass of pendulum 2
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| mp2 = 0.0085;
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| m = 0.3163; % kg Mass of carriage
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| rd = 0.0254/2; % m Drive pulley radius
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| md = 0.0375; % kg Mass of drive pulley (cylinder)
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| %mc1 = 0.0036; % kg Mass of clamp 1*
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| %mc2 = 0.0036; % kg Mass of clamp 2*
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| mc1 = 0.0085;
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| mc2 = mc1;
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|
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| % *Clamp Dimensions
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| % Rectangular 0.0254 x 0.01143 m
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| % The pivot shaft is 0.00714 m from the end
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| % Motor Parameters (Data Sheet)
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| Im = 43e-7; % kg m^2/rad Rotor moment of inertia
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| R = 4.09; % ohms Resistance
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| kt = 0.0351; % Nm/A Torque constant
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| ke = 0.0351; % Vs/rad Back emf constant
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| % Derived Mechanical Parameters
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| % kg m^2/rad Moment of inertia, clamp 1
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| %Ic1 = mc1*(0.01143^2 + 0.0254^2)/12 + mc1*(0.0127-0.00714)^2;
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| Ic1 = mc1*(0.0098^2 + 0.0379^2)/12;
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| Ic2 = Ic1; % kg m^2/rad Moment of inertia, clamp 2
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| Id = md*(rd^2)/2; % kg m^2/rad Moment of inertia, drive pulley
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| Imd = Im + Id; % kg m^2/rad Moment of inertia, combined
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| J1 = Ic1 + mp1*(d1^2)/3; % Total moment of inertia, pendulum 1 (long)
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| J2 = Ic2 + mp2*(d2^2)/3; % Total moment of inertia, pendulum 2 (short)
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| Jd = Im + Id; % Total moment of inertia, motor drive
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| Mc = m + mc1 + mc2; % Total carriage mass
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| % Friction Test Data
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| % Carriage Slope = 19 deg; Terminal Velocity xdotss = 0.312 m/s; From
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| % twincarriage.m; formula b = m g sin(theta)/xdotss
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| % Pendulum 1 (long) Exponent a1 = 0.0756 1/s; From longfit.m
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| % Pendulum 2 (short) Exponent a2 = 0.2922 1/s; From shortfit.m
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| % formula b = 2 a J
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| %alpha = 19;
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| alpha = 12.2;
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| %xdotss = 0.312;
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| xdotss = 0.4852;
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| %a1 = 0.0756;
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| %a2 = 0.2922;
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| a1 = 0.0185;
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| a2 = 0.012;
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| % Ns/m Viscous friction of carriage system
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| b = (Mc + mp1 + mp2)*g*sin(alpha*pi/180)/xdotss;
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| b1 = 2*a1*J1; % Nms/rad Viscous friction of pendulum 1 (rotational)
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| b2 = 2*a2*J2; % Nms/rad Viscous friction of pendulum 2 (rotational)
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| scale = [rd*2*pi/4096 2*pi/4096 -0.05/250];
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| T = 1/f;
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