Analyze the flexible solar array on the ComStar Spacecraft.

ComStar is a hypothetical geosynchronous communications satellite. This model includes the orbit rate and nutation modes. Creates the files FlexM00 and FlexM90 used by ComStarSK.

------------------------------------------------------------------------- See also LoadFlex, GetModes, ComStar, FResp, FindDirectory, Rename, DupVect, SkewSymm, VXPhi, Geo -------------------------------------------------------------------------

Contents

%--------------------------------------------------------------------------
%   Copyright (c) 1995-1998 Princeton Satellite Systems, Inc.
%   All rights reserved.
%--------------------------------------------------------------------------
%   Since version 2.
%--------------------------------------------------------------------------

Constants

%----------
degToRad = pi/180;
radToDeg = 180/pi;
g        = 9.80655;
wo       = Geo;

Inputs

%-------
nSAAngle  = [0 90]*degToRad;
sSAAngle  = [0 90]*degToRad;
zetaFlex  = 0.015;
useModes  = [1 2]; % List the modes to be used in the array

Database

%---------
inr  = ComStar('MO Inertia');
cM   = ComStar('MO CM');
rNSA = ComStar('North Solar Array Base');
rSSA = ComStar('South Solar Array Base');
hW   = ComStar('U MWA')*ComStar('MWA Inertia')*ComStar('Nominal MWA Rate');
mass = ComStar('MO M');

Cantilevered flex model

%------------------------
[phi,omega,rNode,mNode,nodeID,nNodes] = LoadFlex( 'ComstarSA.txt' );

[phi,omega] = GetModes(phi,omega,useModes,nNodes);
nModes      = length(useModes);
nFlexDOF    = 4*nModes;

for k = 1:2
  clear a b c d

  % Transformation matrices from the solar array frame to the body
  %---------------------------------------------------------------
  bNSA = [ cos(nSAAngle(k)),0,sin(nSAAngle(k));...
               0        1      0;...
          -sin(nSAAngle(k)),0,cos(nSAAngle(k))];

  bSSA = [ cos(sSAAngle(k)),0,sin(sSAAngle(k));...
               0        1      0;...
		  -sin(sSAAngle(k)),0,cos(sSAAngle(k))];

  % Must flip the sign of the y component for the north array
  %----------------------------------------------------------
  dNSA   = DupVect(rNSA-cM,nNodes) + bNSA*[rNode(1,:);-rNode(2,:);rNode(3,:)];
  dSSA   = DupVect(rSSA-cM,nNodes) + bSSA*rNode;
  mDNSA  = dNSA.*DupVect(mNode,3)/g;
  mDSSA  = dSSA.*DupVect(mNode,3)/g;
  phiNSA = bNSA*phi;
  phiSSA = bSSA*phi;
  genInr = [inr,VXPhi(mDNSA,phiNSA),VXPhi(mDSSA,phiSSA)];
  genInr = [genInr;genInr(1:3,4:(3+2*nModes))',eye(2*nModes)];

  %--------------------
  % The state matrix is
  % [w;eta;etaDot];
  % The input matrix is
  % [T;F];
  %--------------------
  mM = DupVect(mNode,3);
  for j = 1:nModes
    phiM              = phi(:,((j-1)*nNodes+1):(j*nNodes));
    mPhi              = sum((phiM.*mM)');
    b(j+3,       4:6) = mPhi*bNSA/mass;
    b(j+3+nModes,4:6) = mPhi*bSSA/mass;
  end
  b(1:3,1:3) = eye(3);

  % This is just the dynamics part
  %-------------------------------
  a = [SkewSymm(hW),zeros(3,4*nModes);...
       zeros(2*nModes,3),-diag([omega.^2,omega.^2]),-2*zetaFlex*diag([omega,omega])];
  a = genInr\a;
  b = genInr\b;
  a = [a(1:3,1:(3+4*nModes));...
       zeros(2*nModes,3+2*nModes),eye(2*nModes);...
	   a(4:(3+2*nModes),1:(3+4*nModes))];

  b = [b(1:3,1:6);zeros(2*nModes,6);b(4:(3+2*nModes),1:6)];

  % Add the attitude. Include orbit rate dynamics
  %----------------------------------------------
  b     = [zeros(3,6);b];
  [n,m] = size(a);
  aAtt  = [0 0 wo;0 0 0;-wo 0 0];
  a     = [aAtt,eye(3),zeros(3,m-3);zeros(n,3), a];
  [n,m] = size(a);

  % Display eigenvalues
  %--------------------
  s = eig(a);
	DispWithTitle(s,'Eigenvalues');

  % The state is [qX;qY;qZ;wX;wY;wZ;modes]
  %---------------------------------------
  d     = zeros(3,6);
  c     = [eye(3), zeros(3,n-3)];
  angle = sSAAngle(k)*180/pi;
  w      = logspace(-6,1,500);
  FResp(a,b,c,d,1,1,w);
  Rename( sprintf('Roll with arrays at %2i deg',angle) )
  FResp(a,b,c,d,2,2,w);
  Rename( sprintf('Pitch with arrays at %2i deg',angle) )
  FResp(a,b,c,d,3,3,w);
  Rename( sprintf('Yaw with arrays at %2i deg',angle) )

  file = sprintf('save FlexM%2.2i a b c d',sSAAngle(k)*180/pi);

  c0 = cd;
  cd(FindDirectory('SCMat'))
  eval(file)
  cd(c0)

end


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

Eigenvalues
  0.000000000000000 + 0.000000000000000i
  0.000000000000000 + 0.000000000000000i
  0.000000000000000 + 0.000072921158553i
  0.000000000000000 - 0.000072921158553i
 -0.094708992131515 + 6.277675975513406i
 -0.094708992131515 - 6.277675975513406i
 -0.000000000010592 + 0.033505063031180i
 -0.000000000010592 - 0.033505063031180i
 -0.046529080815352 + 3.078742045893070i
 -0.046529080815352 - 3.078742045893070i
 -0.093645867653167 + 6.242349503207746i
 -0.093645867653167 - 6.242349503207746i
 -0.045846170833088 + 3.056067523247761i
 -0.045846170833088 - 3.056067523247761i
Eigenvalues
  0.000000000000000 + 0.000000000000000i
  0.000000000000000 + 0.000000000000000i
  0.000000000000000 + 0.000072921158553i
  0.000000000000000 - 0.000072921158553i
 -0.000000000008575 + 0.033505068312684i
 -0.000000000008575 - 0.033505068312684i
 -0.046366732440016 + 3.073366795926412i
 -0.046366732440016 - 3.073366795926412i
 -0.095040605993570 + 6.288654499226072i
 -0.095040605993570 - 6.288654499226072i
 -0.045846258311683 + 3.056070438215320i
 -0.045846258311683 - 3.056070438215320i
 -0.093645688968815 + 6.242343549075905i
 -0.093645688968815 - 6.242343549075905i

Published with MATLAB® R2019a