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Hohmann transfers are a well-known maneuver used to change the semi-major axis of an orbit. The Spacecraft Control Toolbox allows you to compute the required velocity changes, and integrate them into a full simulation.
In this demonstration, we create a 6U CubeSat that has 3 orthogonal reaction wheels and s single hydrazine thruster. The thruster is aligned with the x-axis and must be aligned with the velocity vector to do the maneuver. An ideal Hohmann maneuver is done with impulsive burns at two points in the orbit. In reality, with a thruster, we have to do a finite burn.
The simulation computes burn durations based on the thrust and the mass of the spacecraft. The maneuver is quite small, so the mass change is not important. The Hohman transfer is computed with the following Spacecraft Control Toolbox code:
rI = [-7000;0;0]
;vI = [0;-sqrt(mu/Mag(rI));0];
[dV,tOF] = OrbMnvrHohmann(Mag(rI),rF);
The first time OrbMnvrHohmann is called it generates the plot below.The attitude control system uses the PID3Axis function which is a general-purpose attitude control algorithm. The entire simulation is in a short script. The planned Hohmann transfer is shown below.
At the final orbit radius an attitude maneuver is needed to reorient for the final burn.
The spacecraft body rates, in the body frame, during the maneuver are shown below.
The reaction wheels are shown below. This does not model any particular wheel.
The wheel torques and rocket thrust are shown below. The thruster is a 0.2 lbf hydrazine thruster that is based on the Aerojet-Rocketdyne MR-103. The PID controller does not demand much torque.
The semi-major axis and eccentricity is shown below. The middle portion is during the transfer orbit.
The eccentricity is zero at the start and finish. Note the slope in both eccentricity and semi-major axis due to the finite acceleration.
This post shows how you can easily integrate attitude and orbit control. Email us for more information!. We’d be happy to share the script. We can also offer a 30 day demo to let you explore the software.