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)

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:

tcpdemo4.m % 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; fprintf('period: %d %x\n',period,int32(period)); 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();

ctrlbox.m % 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*32767,-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