Path: Interplanetary/Optimization
% Compute optimal planar trajectory with a phase constraint.
The specification of phase angles allows the transfer to be part of a
planned rendezvous mission. This is a fixed-time transfer. The control
variables are the angle and the constant thrust magnitude.
This is for an electric propulsion system characterized by specific
impulse, specific power, and a fuel tank fraction. The cost function is
the total mass of the vehicle. Requires the Optimization Toolbox from
Mathworks.
Specific combinations of parameters may not provide a solution. fmincon will
fail to converge in that case. The power is calculated from the thrust,
exhaust velocity, and thrust efficiency. The engine mass is calculated from
the specific power.
P = 0.5 T*uE/eta
mE = P/sigma
The total mass is
m0 = mP + (1 + f)*mF + mE
where mP is the mass of the payload, f is the fuel structural fraction, and mE
is the mass of the engine.
Type PlanarHelioRendezvousOptimal for a demo to Mars
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Form:
d0 = PlanarHelioRendezvousOptimal
[phi, thrust, t, data] = PlanarHelioRendezvousOptimal( d, maxIter, iterDisp )
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Inputs
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d (.) Data structure
.uE Exhaust velocity (km/s)
.r0 Initial radius (km)
.rF Final radius (km)
.angleOffset Initial phase angle (rad)
.angleTarget Target phase angle (rad)
.mu Gravitational parameter of the sun (km^3/s^2)
.f Fuel structural fraction
.tF Final time (s)
.eta Thrust efficiency
.sigma Specific power (W/kg)
.scale [distance; v radial; v tangential; angle]
maxIter (1,1) Maximum number of iterations
iterDisp '' Display mode, default 'iter-detailed'
thrust0 (1,1) Thrust value (default 0.9), optional
phi0 (1,:) Initial guess for control angles, optional
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Outputs
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phi (1,n) Thrust angle (rad)
t (1,n) Times (s)
thrust (1,1) Thrust (N)
data (.) Results data structure
.p (1,1) Power (W)
.mD (1,1) Dry mass (kg)
.mF (1,1) Fuel mass (kg)
.dV (1,1) Delta-V (km/s)
.dF (1,1) Final distance achieved (km)
.vF (1,1) Final velocity achieved (km/s)
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See also SimulatePlanarHelioTrajectory, PlanarHelioOptimalSlidingTime,
ThrustElectric
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Interplanetary: Optimization/RHS2DCylindricalOrbit Interplanetary: Optimization/SimulatePlanarHelioTrajectory StraightLine: ConstantAccel/ThrustElectric StraightLine: ConstantThrust/DVConstantThrust Common: Database/Constant Math: Integration/RK4 Math: Linear/Mag
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