Path: Missions/LunarLanding
% Implements a 2nd order guidance law
Uses a 2nd order controller to provide guidance for landing.
Demonstrated in a cartesian system with x along vertical.
Includes centripetal and gravitational acceleration.
'initialize' computes the time to land from the tolerance.
'update' updates the control accelerations.
You generally want zeta to be 1. Lower omegas will reduce the control
accelerations. An omega of 0.01 gives roughly the Apollo LM landing
guidance. If it is much lower you can overshoot and then have to return
to the landing site.
Type SecondOrderGuidance for a demo. The demo is in cartesian coordinates
with gravity and centripetal acceleration along x.
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Form:
a = SecondOrderGuidance( action, x, d )
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Inputs
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action (1,:) 'initialize' or 'update'
x (6,1) State [r;v]
d (.) Data structure
.x (6,1) Target [r;v]
.tol (1,1) Tolerance for damping
.zeta (1,1) Damping ratio
.omega (1,1) Undamped natural frequency (rad/s)
.t (1,1) Time to damp
.rP (1,1) Equatorial radius
.mu (1,1) Gravitational constant
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Outputs
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a (3,:) Control accelerations
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AC: ACData/ACTConstants SC: SCData/sCTConstants Common: CommonData/Constants Common: CommonData/SwooshWatermark Common: CommonData/xSplashSmall Common: Database/Constant Common: General/CellToMat Common: General/DeBlankLT Common: General/DeleteCell Common: General/MatToCell Common: General/Watermark Common: Graphics/NewFig Common: Graphics/Plot2D Common: Graphics/PltStyle Common: Graphics/TimeLabl Common: Graphics/XLabelS Common: Graphics/YLabelS Math: Integration/RK4
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