Design and test the nutation compensator.

Requires the output of ComStarRYLF.m.

Since version 2.
-------------------------------------------------------------------------
See also Gen2nd, ComStarRYLF, Series, C2DZOH, C2DelZOH, FResp, Plot2D,
Rename, WriteCM
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Contents

%-------------------------------------------------------------------------------
%   Copyright 1996 Princeton Satellite Systems, Inc.
%   All rights reserved.
%-------------------------------------------------------------------------------

Simulation parameters

%----------------------
cMatrices = 'yes'; % If yes will dump matrices to a file (RYNut) and display them

% Load in the data generated by TRYLF.m

Which supplies a, b, c, d and rYGain.

%--------------------------------------
load RYC

Connect the skew dipole and earth sensor

%-----------------------------------------
a      = aP;
b      = bP*rYGain;
c      = [1 0 0 0]; % Only roll is available
d      = 0;

w      = logspace(-6,0,400);
FResp(a,b,c,d,1,1,w);
Rename('Open Loop');

wz     = 0.008; % Adjust these parameters to change the nutation damping
zz     = 0.1;
zp     = 1;
wp     = 0.08; %

The nutation compensator

%-------------------------
[aN,bN,cN,dN]     = Gen2nd ( zz, wz, zp, wp );
w                 = logspace(-3,0,400);
FResp(aN,bN,cN,dN,1,1,w);
Rename('Nutation Compensator');

[aT,bT,cT,dT]     = Series( a, b, c, d, aN, bN, cN, dN );
FResp(aT,bT,cT,dT,1,1,w);
Rename('Open Loop with Compensator');

aCL = aT + bT*cT;

s = eig(aCL);

DispWithTitle(s,'Eigenvalues');

Eigenvalues
    -0.064909 +   0.072632i
    -0.064909 -   0.072632i
    -0.014196 +   0.023776i
    -0.014196 -   0.023776i
   -0.0017143 +          0i
  -7.6505e-05 +          0i

Simulate the nutation compensator

%----------------------------------
dT          = 0.25;
nSim        = 1000;
[aZCL,bZCL] = C2DZOH(aCL,bT,dT);
[aZOL,bZOL] = C2DZOH(a,b,dT);

xCL = [0;0;0.001;0;0;0]; % Some roll rate
xOL = xCL(1:4);

xCLPlot = zeros(2,nSim);
xOLPlot = zeros(2,nSim);

for k = 1:nSim
  xCLPlot(:,k) = xCL(1:2);
  xOLPlot(:,k) = xOL(1:2);
  xCL          = aZCL*xCL;
  xOL          = aZOL*xOL;
end

t = (0:(nSim-1))*dT;

Plot2D(t,[xCLPlot;xOLPlot],'Time (sec)',['Roll';'Yaw '],'Nutation Damping','lin',['[1 3]';'[1 4]'])

If requested save and dump the controller matrices

if( strcmp(cMatrices,'yes') )
  pData         = fileparts(mfilename('fullpath'));
  fID           = fopen(fullfile(pData,'RYNut.txt'),'w');
  [aD,bD]       = C2DelZOH(aN,bN,dT);
  cD = cN;
  dD = dN;
  WriteCM(fID,'A Matrix','fRYAMatrix',reshape(aD',1,length(aD)^2),12,20,3)
  WriteCM(fID,'B Matrix','fRYBMatrix',bD,12,20,3)
  WriteCM(fID,'C Matrix','fRYCMatrix',cD,12,20,3)
  WriteCM(fID,'D Matrix','fRYDMatrix',dD,12,20,3)
  WriteCM(fID,'K Matrix','fRYKMatrix',rYGain,12,20,3)
  fclose(fID);
  disp('Roll/yaw Matrices and Low Frequency Gain')
  disp(aD);
  disp(bD);
  disp(cD);
  disp(dD);
  disp(rYGain);
end


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

Roll/yaw Matrices and Low Frequency Gain
    -0.039405   -0.0015683
      0.24505  -0.00019735
      0.24505
     0.030836
       -15.84      -0.6336
   100
     -0.10996
      0.11454

Published with MATLAB® R2019a