The acquisition sequence for the ComStar satellite.

Comstar is spinning in transfer orbit. When the demonstration starts it is at orbit normal. The acquisition sequence has the following phases:

1. Despin to the DST angular rate
2. DST with nutation damping
3. Pitch estimation
4. Pitch acquisition
5. Normal mode

Phases 2-4 make use of the tach loop

Since version 2.
-------------------------------------------------------------------------
See also DSTCrit, PtchLoop, SSA, SpinREst, StatePrp, FGs, NPlot,
ComStar, PitchEst, Q2Eul, Constant, Plot2D, TimeGUI, RK4
-------------------------------------------------------------------------

Global for the TimeGUI
Constants
Database inputs
Input parameters
The acquisition sequence has four phases:
Compute an acceptable spin rate prior to the dual spin turn
Initialize the Spin rate controller
Design the tach loop
Get the pitch and tach loop controllers
Set up the pitch Kalman Filter
Design the thruster pitch controller
The main simulation loop
Initialize the time display

%-------------------------------------------------------------------------------
%	 Copyright 1994-1998 Princeton Satellite Systems, Inc. All rights reserved.
%-------------------------------------------------------------------------------

Global for the TimeGUI

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

Constants

%----------
rPSToRPM   = Constant('Rad/Sec to RPM');
rPMToRPS   = Constant('RPM to Rad/Sec');
degToRad   = Constant('Deg to Rad');
radToDeg   = Constant('Rad to Deg');

Database inputs

%----------------
inrMWA     = ComStar('MWA Inertia');
inr        = ComStar('TO Inertia');
wMWATarg   = ComStar('DST MWA Target');
uMWA       = ComStar('U MWA');
uDamper    = ComStar('U Damper');
cDamper    = ComStar('C Damper');
inrDamper  = ComStar('Damper Inertia');

invInr     = inv(inr);
hMWA       = inrMWA*wMWATarg;

Input parameters

%-----------------
w          = [0;0;4.5]*rPMToRPS;
nSim       = 4000;
nPMax      = 10;
dTSim      = 0.25;                  % Control period
x          = [[1;0;0;0];w;0;0];
esaLimit   = 8.0*degToRad;

The acquisition sequence has four phases:

%------------------------------------------
% 1. Despin to the DST angular rate
% 2. DST with nutation damping
% 3. Pitch estimation
% 4. Pitch acquisition
% 5. Normal mode
% Phases 2-4 make use of the tach loop

Compute an acceptable spin rate prior to the dual spin turn

%------------------------------------------------------------
[wZMax,wZMin,wYMax] = DSTCrit(inrMWA,inr(2,2),inr(1,1),inr(3,3),hMWA);

Initialize the Spin rate controller

%------------------------------------
wC             = wZMin + 0.2*(wZMax-wZMin);
wY             = -(wC*inr(3,3)-hMWA)/inr(2,2);
phase          = 'Despin';
xSpinRateEst   = x(7);
kSpinRateEst   = 0.5;
pulsewidth     = 0;
pulsewidthMax  = 0;
accelNom       = -6/inr(3,3);  % Need to update this
wError         = 0.01*rPMToRPS;
fprintf('Minimum pre  DST z-axis spin rate         = %8.2f rpm \n',wZMin*rPSToRPM);
fprintf('Maximum pre  DST z-axis spin rate         = %8.2f rpm \n',wZMax*rPSToRPM);
fprintf('Maximum post DST y-axis spin rate         = %8.2f rpm \n',wYMax*rPSToRPM);
fprintf('Pre  DST z-axis spin rate                 = %8.2f rpm \n',wC*rPSToRPM);
fprintf('Post DST y-axis spin rate                 = %8.2f rpm \n',wY*rPSToRPM);

Minimum pre  DST z-axis spin rate         =     0.45 rpm 
Maximum pre  DST z-axis spin rate         =     1.80 rpm 
Maximum post DST y-axis spin rate         =     1.80 rpm 
Pre  DST z-axis spin rate                 =     0.72 rpm 
Post DST y-axis spin rate                 =    -0.36 rpm

Design the tach loop

%---------------------
zeta         = 0.7071;
wN           = 1.0;
tSamp        = 0.25;
zetaPL       = 0.7071;
wNPL         = 0.1;
beta         = 0.0;
fprintf('Tach loop damping ratio                   = %8.2f         \n',  zeta);
fprintf('Tach loop undamped natural freq           = %8.2f rad/sec \n',    wN);
fprintf('Tach loop sampling period                 = %8.2f sec     \n', tSamp);
fprintf('Pitch loop damping ratio                  = %8.2f         \n',zetaPL);
fprintf('Pitch loop undamped natural freq          = %8.2f rad/sec \n',  wNPL);

Tach loop damping ratio                   =     0.71         
Tach loop undamped natural freq           =     1.00 rad/sec 
Tach loop sampling period                 =     0.25 sec     
Pitch loop damping ratio                  =     0.71         
Pitch loop undamped natural freq          =     0.10 rad/sec

Get the pitch and tach loop controllers

%----------------------------------------
[aM,bM,cM,dM,aP,bP,cP,dP] = PitchLoop(inr(2,2),inrMWA,beta,zeta,zetaPL,wN,wNPL,tSamp,'Delta');

Set up the pitch Kalman Filter

%-------------------------------
pPitchEst            = [pi^2 0;0 (0.1*pi/30)^2];
xPitchEst            = zeros(2,1);
rPitchEst            = (0.01*degToRad)^2;
qPitchEst            = (6*0.01)^2; % in-lbf 1 percent thruster torque uncertainty
esaPitchValid        = 8*degToRad;
covarianceThreshold  = 4.0;

Design the thruster pitch controller

%-------------------------------------
zetaTPL = 0.7071;
wNTPL   = 0.02;
fprintf('Thruster Pitch loop damping ratio         = %8.2f         \n',zetaTPL);
fprintf('Thruster Pitch loop undamped natural freq = %8.2f rad/sec \n',  wNTPL);

kTPL           = inr(2,2)*wNTPL^2;
tauTPL         = 2*zetaTPL/wNTPL;
pitchThreshold = 4*degToRad;

Thruster Pitch loop damping ratio         =     0.71         
Thruster Pitch loop undamped natural freq =     0.02 rad/sec

The main simulation loop

%-------------------------
nPlot         = nSim/nPMax;
xPlot         = zeros(9,nPlot);
xPlotEst      = zeros(1,nPlot);
esaPitchPlot  = zeros(1,nPlot);
phasePlot     = zeros(1,nPlot);
tPlot         = zeros(1,nPlot);
xPlotPitchEst = zeros(2,nPlot);
pPlotPitchEst = zeros(2,nPlot);
thrusterPlot  = zeros(3,nPlot);
plotPitch     = zeros(1,nPlot);
t             = 0;
nP            = 0;
kP            = 0;
uSun          = [1;0;0];
uSunBodyOld   = uSun;
TLast         = -1;
T             = 2*pi/x(7);
tThruster     = [0;0;0];
pitchSat      = 0;
e             = [0;0;0];
pulseLeft     = 0;

phases        =  ['Despin        ';...
                  'Dual Spin Turn';...
                  'Estimate Pitch';...
                  'Acquire Pitch '];

Initialize the time display

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

for k = 1:nSim;

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

  % Sun sensor
  %-----------
  [cEP,dTCEP,uSunBodyOld] = SSA(x(1:4),uSun,uSunBodyOld,dTSim);

  % The gyro
  % --------
  yawRate = x(7);

  % The tachometer
  % --------------
  wSpeed = x(8);

  % Earth sensor
  %-------------
  e          = Q2Eul(x(1:4),e);
  pitch      = -e(3);
  if abs(pitch) > esaLimit & pitchSat == 0,
    esaPitch = sign(pitch)*esaLimit;
    pitchSat = 1;
  elseif abs(pitch) < esaLimit,
    esaPitch = pitch;
    pitchSat = 0;
  end

  % Store plot data
  %----------------
  if nP == 0,
    kP                  = kP + 1;
    xPlot(:,kP)         = x;
    tPlot(kP)           = t;
    xPlotEst(kP)        = xSpinRateEst;
    xPlotPitchEst(:,kP) = xPitchEst;
    pPlotPitchEst(:,kP) = [pPitchEst(1,1);pPitchEst(2,2)];
    thrusterPlot (:,kP) = tThruster;
    esaPitchPlot(kP)    = esaPitch;
    plotPitch(kP)       = pitch;
    if     ( strcmp(phase,'Despin'        ) == 1 ),
      phasePlot(kP) = 1;
    elseif ( strcmp(phase,'Dual Spin Turn') == 1 ),
      phasePlot(kP) = 2;
    elseif ( strcmp(phase,'Estimate Pitch') == 1 ),
      phasePlot(kP) = 3;
    else
      phasePlot(kP) = 4;
    end
	nP = nPMax - 1;
  else
    nP = nP - 1;
  end

  %-----------------------------------
  % The controller
  %-----------------------------------

  % Phase transition control
  %-------------------------
  if( strcmp(phase,'Despin') == 1 )

    if( abs(xSpinRateEst - wC) < wError )
      phase     = 'Dual Spin Turn';
      xTachLoop = 0;
      wYawOld   = yawRate;
      wYawMax   = 0;
      wNutLimit = 2*degToRad;
    end

  elseif( strcmp(phase,'Dual Spin Turn') == 1 )

    wYawMax = max(wYawMax,abs(yawRate));
    if yawRate*wYawOld < 0,
      if wYawMax < wNutLimit,
        phase  = 'Estimate Pitch';
      end
      wYawMax = 0;
    end
  	wYawOld  = yawRate;

  elseif ( strcmp(phase,'Estimate Pitch') == 1 ),

    if( pPitchEst(1,1) < covarianceThreshold ),
      phase = 'Acquire Pitch';
    end

  end

  % Control System
  %---------------
  if( strcmp(phase,'Despin') == 1 )
    tMWA = 0;
    if( cEP == 1 )
	  if( TLast ~= -1 )
	    T             = t - dTCEP - TLast;
      xSpinRateEst  = SpinREst(accelNom, kSpinRateEst, xSpinRateEst, T, pulsewidth);
      pulsewidthMax = abs(2*pi/xSpinRateEst);
	    rateError     = wC-xSpinRateEst;
      pulsewidth    = min(pulsewidthMax,abs(rateError/accelNom));
	    tThruster     = sign(rateError)*[0;0;6];
	    pulseLeft     = pulsewidth - dTSim;
	  end
	  TLast = t - dTCEP;
	else
	  pulseLeft     = pulseLeft - dTSim;
	end

	if ( pulseLeft < 0),
	  tThruster = [0;0;0];
	end

  elseif ( strcmp(phase,'Dual Spin Turn') == 1 ),
	wSDemand = wMWATarg;

  elseif ( strcmp(phase,'Estimate Pitch') == 1 ),
    [xPitchEst,pPitchEst] = PitchEst(xPitchEst,pPitchEst,dTSim,inr(2,2),qPitchEst,rPitchEst,...
	                                    tThruster(2),esaPitch,esaPitchValid);

  elseif ( strcmp(phase,'Acquire Pitch') == 1 ),
    tThruster = [0;-kTPL*(tauTPL*xPitchEst(2) + xPitchEst(1));0];
    [xPitchEst,pPitchEst] = PitchEst(xPitchEst,pPitchEst,dTSim,inr(2,2),qPitchEst,rPitchEst,...
	                                    tThruster(2),esaPitch,esaPitchValid);

  end

  % Tach loop
  %----------
  if (strcmp(phase,'Despin') == 0),
    [tMWA,xTachLoop] = StatePrp(aM,bM,cM,dM,xTachLoop,[wSpeed; wSDemand],'Delta');
  else
    tMWA = 0;
  end

  %-----------------------------------
  % The simulation
  %-----------------------------------

  x = RK4('FGs',x,dTSim,t,inr,invInr,tThruster,[inrMWA inrDamper],[uMWA uDamper],[tMWA 0],[0 cDamper]);
  t = t + dTSim;

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

end

j = 1:kP;

tPlot = tPlot(j);

Plot2D(tPlot,xPlot(5:8,j),'Time (sec)',['X and Z Rates (rad/sec)';...
    'MWA Speed (rad/sec)    '; 'Y-Axis Rate (rad/sec)  '],'Body Rates',...
    'lin',['[1,3]';'4    ';'2    ']);

Plot2D(tPlot,xPlotEst(j)-xPlot(7,j),'Time (sec)',...
    'Spin Rate Estimator error (rad/sec)','Estimator');

Plot2D(tPlot,[xPlotPitchEst(1,j)-plotPitch(j);xPlotPitchEst(2,j)-xPlot(6,j)]*radToDeg,...
    'Time (sec)', ['Pitch Error (deg)         ';...
    'Pitch Rate Error (deg/sec)'],'Pitch Control');

Plot2D(tPlot,[esaPitchPlot(j);plotPitch(j);xPlotPitchEst(1,j)]*radToDeg,...
    'Time (sec)', ['ESAPitch (deg)'; 'Pitch (deg)   '; 'Estimate (deg)'],'Pitch');

Plot2D(tPlot,pPlotPitchEst(1:2,j),'Time (sec)', ['Pitch Covariance     ';...
    'Pitch Rate Covariance'],'Pitch Covariance');

Plot2D(tPlot,thrusterPlot(:,j),'Time (sec)','Thruster torque (inlb)','Thruster Torque');

NPlot(phases,phasePlot(j),tPlot,'Time (sec)','Phase')

TimeGUI('close');

%--------------------------------------
% PSS internal file version information
%--------------------------------------

The acquisition sequence for the ComStar satellite.

Contents

Global for the TimeGUI

Constants

Database inputs

Input parameters

The acquisition sequence has four phases:

Compute an acceptable spin rate prior to the dual spin turn

Initialize the Spin rate controller

Design the tach loop

Get the pitch and tach loop controllers

Set up the pitch Kalman Filter

Design the thruster pitch controller

The main simulation loop

Initialize the time display