Simulate various single degree of freedom gyros.

Simulates a rate gyro and a rate integrating gyro.
Both are simulated using SDG and the RHS FSDG. They are
configured by setting the appropriate parameters.

------------------------------------------------------------------------
See also Plot2D, TimeGUI, RK4, SDG
------------------------------------------------------------------------

Contents

%--------------------------------------------------------------------------
%   Copyright (c) 1996 Princeton Satellite Systems, Inc.
%   All rights reserved.
%--------------------------------------------------------------------------
%   Since version 1.

Global for the time GUI

%------------------------
global simulationAction
simulationAction = ' ';

To make a rate integrating gyro set k = cD/h and k.*kF./cD << 1

%-----------------------------------------------------------------
h    = 1;
u    = [1;0;0];
cD   = 1;
kSG  = cD/h;
kF   = 0.0001;
bias = 0;
nU   = 0;
nV   = 0;
nE   = 0;

[a,b,c,d] = SDG( u, h, cD, kSG, kF );
eig(a)

ans =
   1.0e-04 *
  -1.000000000000000
                   0
                   0

Run the simulation

%-------------------
dT   = 0.05;
nSim = 100;
x    = zeros(3,nSim);
w    = [0.01;0;0];
t    = dT*(0:(nSim-1));
y    = zeros(1,nSim);

Initial output

%---------------
[~,y(1)] = SDG( u, h, cD, kSG, kF, w, x(:,1), bias, nU, nV, nE );

Initialize the time display

%----------------------------
[ ratioRealTime, tToGoMem ] =  TimeGUI( nSim, 0, [], 0, dT, 'TGyro' );

for k = 2:nSim

  % Display the status message
  %---------------------------
  [ ratioRealTime, tToGoMem ] = TimeGUI( nSim, k, tToGoMem, ratioRealTime, dT );

  x(:,k)          = RK4('FSDG', x(:,k-1), dT, t(k-1), u, h, cD, kSG, kF, w, bias, nU, nV, nE);
  [dontCare,y(k)] = SDG( u, h, cD, kSG, kF, w, x(:,k), bias, nU, nV, nE );

  % Time control
  %-------------
  switch simulationAction
    case 'pause'
      pause
      simulationAction = ' ';
    case 'stop'
      return;
    case 'plot'
      break;
  end

end

j = 1:k;
y = [y-w(1)*t;y;x];

Plotting

%---------
yLabel = ['Error  ';...
          'Output ';...
          'State 1';...
          'State 2';...
          'State 3'];

Plot2D( t(j), y(:,j), 'Time (sec)',yLabel,'Rate Integrating Gyro');

To make a rate gyro set kF = h and kSG*kF/cD >> 1

%--------------------------------------------------
h    = 1;
kF   = h;
cD   = 1;
u    = [1;0;0];
kSG  = 10;
bias = 0;
nU   = 0;
nV   = 0;
nE   = 0;

[a,b,c,d] = SDG( u, h, cD, kSG, kF );
eig(a)

ans =
   -10
     0
     0

Run the simulation

%-------------------
dT   = 0.05;
nSim = 100;
x    = zeros(3,nSim);
w    = [0.01;0;0];
t    = dT*(0:(nSim-1));
y    = zeros(1,nSim);

Initialize the time display

%----------------------------
tToGoMem.lastJD        = 0;
tToGoMem.lastStepsDone = 0;
tToGoMem.kAve          = 0;
[ ratioRealTime, tToGoMem ] =  TimeGUI( nSim, 0, tToGoMem, 0, dT, 'TGyro' );

Initial output

%---------------
[dontCare,y(1)] = SDG( u, h, cD, kSG, kF, w, x(:,1), bias, nU, nV, nE );

for k = 2:nSim

  % Display the status message
  %---------------------------
  [ ratioRealTime, tToGoMem ] = TimeGUI( nSim, k, tToGoMem, ratioRealTime, dT );

  x(:,k)          = RK4('FSDG', x(:,k-1), dT, t(k-1), u, h, cD, kSG, kF, w, bias, nU, nV, nE);
  [dontCare,y(k)] = SDG( u, h, cD, kSG, kF, w, x(:,k), bias, nU, nV, nE );

  % Time control
  %-------------
  switch simulationAction
    case 'pause'
      pause
      simulationAction = ' ';
    case 'stop'
      return;
    case 'plot'
      break;
  end

end

Shorten the arrays in case the user stopped the sim

%----------------------------------------------------
j = 1:k;
y = [y-w(1)*t;y;x];

Plotting

%---------
yLabel = ['Error  ';...
          'Output ';...
          'State 1';...
          'State 2';...
          'State 3'];

Plot2D( t(j), y(:,j), 'Time (sec)',yLabel,'Rate Gyro');


%--------------------------------------

Published with MATLAB® R2019a