Digital Control Systems: Difference between revisions

From Class Wiki
Jump to navigation Jump to search
 
(One intermediate revision by the same user not shown)
Line 55: Line 55:
*[[Digital Control Octave Scripts]]
*[[Digital Control Octave Scripts]]
====MATLAB/Simulink====
====MATLAB/Simulink====
*[http://ctms.engin.umich.edu/CTMS/index.php?aux=Activities_IOpack This page shows some neat experiments you can do with the ArduinoIO package which allows you to use an Arduino from Simulink/MATLAB.] You can also control it from any terminal program, or write your own program that sends data to the Arduino via the USB serial link. It's license from Mathworks forbids its use with other software like Octave or Scilab.
*[http://ctms.engin.umich.edu/CTMS/index.php?aux=Activities_IOpack This page shows some neat experiments you can do with the ArduinoIO package which allows you to use an Arduino from Simulink/MATLAB.] You can also control an Arduino from any terminal program. It's license from Mathworks forbids its use with other software like Octave or Scilab, and probably from controlling an Arduino from your own program, unless it is for use with Mathworks software.


====Scilab/Xcos====
====Scilab/Xcos====
Scilab is a MATLAB like program. It isn't as compatible with MATLAB as octave is, but it has Xcos, which is a GUI block manipulation tool very similar to Scilab.
Scilab is a MATLAB like program. It isn't as compatible with MATLAB as octave is, but it has Xcos, which is a GUI block manipulation tool very similar to Scilab.
[https://atoms.scilab.org/toolboxes/arduino The Xcos ATOM toolbox] is very similar to ArduinoIO, but for the open source Scilab/Xcos environment. It works only on Windows at this time, but looking at the source leads me to believe that it would be easy to port it to Linux or OS X and it is fully open source.
*[https://atoms.scilab.org/toolboxes/arduino The Xcos ATOM toolbox] is very similar to ArduinoIO, but for the open source Scilab/Xcos environment. It works only on Windows at this time, but looking at the source leads me to believe that it would be easy to port it to Linux or OS X and it is fully open source.


====Pendulum Specific Scripts====
====Pendulum Specific Scripts====

Latest revision as of 15:11, 3 June 2016

Links

Textbooks

Lectures

MATLAB/Octave/Scilab

Gnu Octave

Gnu Octave is a free open source clone of MATLAB. I use it all the time in lieu of MATLAB, and it works well on my Ubuntu Linux OS.

MATLAB/Simulink

Scilab/Xcos

Scilab is a MATLAB like program. It isn't as compatible with MATLAB as octave is, but it has Xcos, which is a GUI block manipulation tool very similar to Scilab.

  • The Xcos ATOM toolbox is very similar to ArduinoIO, but for the open source Scilab/Xcos environment. It works only on Windows at this time, but looking at the source leads me to believe that it would be easy to port it to Linux or OS X and it is fully open source.

Pendulum Specific Scripts

Single Pendulum
% Double Pendulum Parameters (Tentative:  There are two pendulum setups, each with different parameters.  I'm not sure which these go to.)
% This script is for balancing only the long rod.

% Run parameters
%f = input('Control Frequency (Hz) = ');
%Trun = input('Run Time (s) = ');
%f=130;
f=1000;
Trun=30;

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=.5;
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;

% The data above comes from the fweb wiki.

M=Mc;                       %mass of cart
m=mp1;                      %mass of pendulum 1
b=b;                        %friction
l=d1/2;                     %length of pendulum
I=J1;                       %inertia of pendulum
%q=(M+m)*(l+m*l^2)-(m*l)^2;
%num=[m*l,0];                                %numerator for transfer function
%den=[q,b*(l+m*l^2),-m*g*l*(M+m),-b*m*g*l];  %denominator for transfer function
%[A,B,C,D]=tf2ss(num,den)
%A,B,C,D matricies for the state space model
% x_vec is [x,  x_dot, theta, theta_dot]'
% See the web site:  https://www.library.cmu.edu/ctms/ctms/examples/pend/invpen.htm
A=[ 0   1                                                  0                                   0;
    0   ((-(I+m*l^2)*b)/(I*(M+m)+M*m*l^2))  ((m^2*g*l^2)/(I*(M+m)+M*m*l^2))     0;
    0   0                                   0                                   1;
    0   ((-m*l*b)/(I*(M+m)+M*m*l^2))        ((m*g*l*(M+m))/(I*(M+m)+M*m*l^2))   0];
B=[ 0;
    ((I+m*l^2)/(I*(M+m)+M*m*l^2));
    0;
    ((m*l)/(I*(M+m)+M*m*l^2))];
C=[ 1   0   0   0;
    0   0   1   0];
D=[ 0;
    0];
cont_sys = ss(A,B,C,D)
rank_ctrb = rank(ctrb(A,B))
original_poles = eig(A) %poles for our system

These Pendulum Parameters and control scripts are for our hardware.

Z Transforms

Discretization

Scilab/Xcos