Demonstrate computing angles for a sail with four vanes.

This is an underdetermined problem solved using fminsearch.

Since version 9.
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See also SolveVaneAngles, SailDisturbance, Theta0, Cone, Constant,
WaitBarManager, Plot2D, Unit, Date2JD, El2RV, SearchVaneAngles,
ConeClockToU, QSail, DisturbanceStruct, EnvironmentStruct, ProfileStruct,
SailEnvironment, SailPropsToAccel
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Contents

%--------------------------------------------------------------------------
%  Copyright 2009 Princeton Satellite Systems, Inc.
%  All rights reserved.
%--------------------------------------------------------------------------

Set up the problem

%--------------------
clear SailDisturbance; clear thetas; clear ks2;

Use a CAD model to get actual torque produced by vanes

%-------------------------------------------------------
g = load('SailWithFourVanes');

Define spacecraft properties

%-----------------------------
mass  = g.mass.mass; % spacecraft mass in kg
lSail = max(max(g.component(2).v)); % sail length along one side in m
area  = sum(g.component(2).a);
acc0  = SailPropsToAccel( area, mass );

Vane area

%-------------
areaVane = g.component(3).a; % m2

Maximum torque

%---------------
thetaMax = 80*pi/180;
Ps       = Constant('solar pressure mks');
fVane    = 2*Ps*areaVane;
Tmax     = 4*lSail*fVane*sin(thetaMax);

Environment and disturbance models

%-----------------------------------
d = struct;
d = EnvironmentStruct( d );
d = DisturbanceStruct( d );
d.aeroOn   = 0;
d.albedoOn = 0;
d.magOn    = 0;
d.radOn    = 0;

Profile: orbit, attitude

%-------------------------
jD    = Date2JD;
[r,v] = El2RV([Constant('au') 0 0 0 0 0],[],Constant('mu sun'));
uSun  = -Unit(r);
qS    = QSail( uSun, r, v );
p    = ProfileStruct;
p.q  = qS;
p.r  = r;
p.v  = v;
p.jD = jD;
% states for rotating vanes
p.body  = [2 3 4 5];
p.angle = [0; 0; 0; 0];
p.axis  = [0 0 1; 0 0 1; 0 0 1; 0 0 1]';

% Environment will be constant over this short period
env = SailEnvironment( 'sun', p, d );

Define a torque space for solving angles

%-----------------------------------------
zz = zeros(1,20);
oo = linspace(-1,1,20);
Tcommand = Tmax/10*[oo zz zz; zz oo zz; zz zz oo];

% Investigate the effect of cone angle on the three-axis torque produced

(Vanes don't produce a pure roll torque for nonzero cone angle)

%-----------------------------------------------------------------------
cone = 0;
clock = 0;
torque = zeros(3,size(Tcommand,2));
[u,qItoCC] = ConeClockToU( cone, clock, qS );
p.q  = qItoCC;

WaitBarManager( 'initialize', struct('nSamp',size(Tcommand,2),'name','Vane Search') );
for k = 1:size(Tcommand,2)
  % Initialize for roll torque
  theta0       = asin(Tcommand(1,k)./(4*lSail*fVane));
  [theta,iter] = SearchVaneAngles(Tcommand(:,k), theta0*ones(4,1), g, env, p, d);
  p.angle      = theta;
  [f, tq]      = SailDisturbance( g, p, env, d );
  torque(:,k)  = tq.total;
  thetas(:,k)  = theta;
  ks2(k)       = iter;
  WaitBarManager( 'update', k );
end
WaitBarManager( 'close' );

Plot2D(1:size(Tcommand,2),Tcommand,'Steps',{'Tx','Ty','Tz'},'Torque Demand vs. Achieved')
for j = 1:3
  subplot(3,1,j)
  hold on
  plot(1:size(Tcommand,2),torque(j,:),'r');
end
Plot2D(1:size(Tcommand,2),Tcommand-torque,'Steps','Torque Error')
Plot2D(1:size(Tcommand,2),thetas*180/pi,'Steps','Angles')
Plot2D(1:size(Tcommand,2),ks2,'Steps','Iterations')

Define a torque space for solving angles

%-----------------------------------------
% Tcommand = Tmax/10*randn(3,100);

% assign overturning torque in pairs?




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% PSS internal file version information
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Published with MATLAB® R2020a