Parameters

Inverted Penululm Project

Below is some Octave or Matlab code with the parameters of one of the pendulums.

% 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)


        % It appears that the labels on the pendulum for positive x
        % and negative x are backwards, and it appears that the angle 
        % for theta is also backwards.  It is really CW is positive,
        % not CCW.  A positive pwm value to the motor moves the pendulum
        % toward what is marked as NEG x (to the right).
        % I made the scales below reflect that to correct the sign problems
        % with the measured variables.  You must correct the motor voltage
        % in your code.


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


T = 1/f;

Pendulum Hardware Control

Here is a pendulum hardware control script that should help with yours. You basically need to modify tcpdemo4 (immediately below) with your control code in the appropriate place.

% tcpdemo4 - demo script to communicate with new pendulum interface
%
% Syntax:
%    tcpdemo4
%
% cnt is number of packets to receive
% srate is sample rate in Hz
%
% communication with the new ctrlbox is by the ctrlbox.m library
%
% receive data:
%    [long_pend_angle, short_pend_angle, motor_shaft_angle, knob_angle]
%    pendulum and motor shaft angles are 4096 counts/rev
%
% Pwm values are +/-32767 for full scale motor voltage.
% A positive pwm value causes the carriage to move in +X direction.
% Encoder data is 32 bit raw counts, clockwise is positive.
% Encoders are zeroed when "PROG" button is pressed on Spartan3 board.
% Leave long pendulum hanging down when zeroing, then rotate up 180 degrees
% when starting.  Subtract pi/2 from long_pend_angle to remove offset.
%
% Protocol is send pwm value, then read encoders.  Sampling in ctrlbox is
% done according to a hardware sample clock.
%
pkg load sockets control;
ctrlbox;            % load ctrlbox comm functions

cnt=4000;            % number of times through loop
srate = 400;            % sample rate in Hz

store = zeros(cnt,5);
rdata = [0,0,0,0];        % receive data

% Connection must first be established with the ctrlbox.

try
    ctrlbox_init();

    disp('finished init');

    % send sample period
    period = 1000000./srate;
    
    ctrlbox_send(0,0,period);

    disp('finished send');

    x = 1:cnt;
    tic;
        for c=1:cnt
        % read encoder values
        rdata = ctrlbox_recv();

        %
        % your control law goes here
        %

        % example control law pwm generation
        pwm = (30000 * sin(6.28*8*double(c)/min(cnt,1000))) - rdata(1);

        % write pwm values and enable motor
        ctrlbox_send(pwm, 1, 0);

        % force matlab to check for interrupts and flush event queue
        drawnow;
           
        % save data
        store(c,:) = [rdata,pwm];
    end
    runtime = toc;
    fprintf('transactions=%d seconds=%d transactions/sec=%f\n',
        c, runtime, c/runtime);
    drawnow;

catch
    % if something failed, display error and loop count
    fprintf('c=%d\n',c);
    disp(lasterror.message);
end
% disable motor and disconnect
ctrlbox_shutdown();

The function ctrlbox which is used above is given below for your edification.

% ctrlbox.m
%
%    Functions for communication with the inverted pendulum
%    ctrlbox interface via ethernet.
1;
%
% ctrlbox_init - initialize connection to ctrlbox
%
function rval = ctrlbox_init()
    global ctrlbox_con;

    ctrlbox_con = socket();
    sinfo = struct("addr","169.254.0.100", "port", 47820);
    rval = connect(ctrlbox_con,sinfo);

    return;
endfunction
%
% ctrlbox_send(cmdval,enable,period)
%  - send command value, enable, and sample period to ctrlbox
%    - cmdval = -32768 to +32767, where 32767=100% of DC bus voltage
%    - enable = 0 or 1
%    - period in usec
%
%  - future: measure time avg of pwm value, shutoff motor
%    if excessive.
function rval = ctrlbox_send(cmdval,enable,period)
    global ctrlbox_con;

    pwm = min(max(cmdval,-32000),32000);
    data = [pwm, 0, enable, period];
    send(ctrlbox_con, typecast(int32(data(1:4)),'uint8'));

    rval = 0;
    return;
endfunction
%
% ctrlbox_recv - receive an array of four values from ctrlbox
%
function data = ctrlbox_recv()
    global ctrlbox_con;

    [rdata,len] = recv(ctrlbox_con,16);

    if (len ~= 16)
        fprintf('short data: %d\n', len);
    end

    data = double(typecast(rdata,'int32'));
    return;

endfunction

%
% ctrlbox_shutdown - shutdown connection to ctrlbox
%
function ctrlbox_shutdown()
    global ctrlbox_con;

    % turn off motor
    send(ctrlbox_con,typecast(int32([0,0,0,0]),'uint8'));

    disconnect(ctrlbox_con);
endfunction