Parameters
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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 - 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
%
% 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