Feedback and Control Systems

Inverted Penululm Project

[Parameters]

% Double Pendulum Parameters (Tentative:  There are two pendulums with different parameters.  I'm not sure which these go to.)

% Run parameters
%f = input('Control Frequency (Hz) = ');
%crad = input('Pole Radius (1/s) = ');
%psi = input('Spreading Angle (deg) = ');
%eta = psi*pi/180;
%obshift = input('Observer Shift = ');
%Trun = input('Run Time (s) = ');
f=130;
crad=19;
psi=10;
eta=psi*pi/180;
obshift=2;
Trun=60;

kmax = round(f*Trun);
T = 1/f;
Maxpos = 0.25;              % Max carriage travel +- 0.25 m
Maxangle = 0.175;           % Max rod angle -- 10 deg
Maxvoltage = 20;            % Max motor voltage, V
pstart = 0.005;             % Carriage position starting limit, m
astart = 1*pi/180;          % Angle starting limit, rad

g = 9.81;                   % m/s^2     Gravitational constant

% SYSTEM PARAMETERS
% Measured Mechanical Parameters
d1 = 0.323;    % m            Length of pendulum 1 (long)
d2 = 0.079;         % m            Length of pendulum 2 (short)
%mp1 = 0.0208;        % kg        Mass of pendulum 1
mp1 = 0.0318;
%mp2 = 0.0050;        % kg        Mass of pendulum 2
mp2 = 0.0085;
m = 0.3163;            % kg        Mass of carriage
rd = 0.0254/2;      % m            Drive pulley radius
md = 0.0375;         % kg        Mass of drive pulley (cylinder)
%mc1 = 0.0036;        % kg        Mass of clamp 1*
%mc2 = 0.0036;        % kg        Mass of clamp 2*
mc1 = 0.0085;
mc2 = mc1;

% *Clamp Dimensions
%  Rectangular 0.0254 x 0.01143 m
%  The pivot shaft is 0.00714 m from the end

% Motor Parameters (Data Sheet)
Im = 43e-7;     % kg m^2/rad    Rotor moment of inertia
R = 4.09;       % ohms            Resistance
kt = 0.0351;    % Nm/A            Torque constant
ke = 0.0351;    % Vs/rad        Back emf constant

% Derived Mechanical Parameters

                                % kg m^2/rad    Moment of inertia, clamp 1
%Ic1 = mc1*(0.01143^2 + 0.0254^2)/12 + mc1*(0.0127-0.00714)^2;
Ic1 = mc1*(0.0098^2 + 0.0379^2)/12;
Ic2 = Ic1;                      % kg m^2/rad    Moment of inertia, clamp 2
Id = md*(rd^2)/2;               % kg m^2/rad    Moment of inertia, drive pulley
Imd = Im + Id;                  % kg m^2/rad    Moment of inertia, combined

J1 = Ic1 + mp1*(d1^2)/3;        % Total moment of inertia, pendulum 1 (long)
J2 = Ic2 + mp2*(d2^2)/3;        % Total moment of inertia, pendulum 2 (short)
Jd = Im + Id;                   % Total moment of inertia, motor drive
Mc = m + mc1 + mc2;             % Total carriage mass

% Friction Test Data
%   Carriage Slope = 19 deg;  Terminal Velocity xdotss = 0.312 m/s; From
%        twincarriage.m; formula b = m g sin(theta)/xdotss
%   Pendulum 1 (long) Exponent a1 = 0.0756 1/s;  From longfit.m
%   Pendulum 2 (short) Exponent a2 = 0.2922 1/s; From shortfit.m
%        formula b = 2 a J

%alpha = 19;
alpha = 12.2;
%xdotss = 0.312;
xdotss = 0.4852;
%a1 = 0.0756;
%a2 = 0.2922;
a1 = 0.0185;
a2 = 0.012;
                        % Ns/m    Viscous friction of carriage system
b = (Mc + mp1 + mp2)*g*sin(alpha*pi/180)/xdotss;
b1 = 2*a1*J1;            % Nms/rad    Viscous friction of pendulum 1 (rotational)
b2 = 2*a2*J2;            % Nms/rad    Viscous friction of pendulum 2 (rotational)

scale = [rd*2*pi/4096  2*pi/4096 -0.05/250];


T = 1/f;