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Attitude Control

Why do we need ACS?

Apart from creating a DIY-minded space-craft, EQUiSat’s most salient goal is to flash an optical beacon visible to the naked eye. But the LED’s occupy only one side of the satellite, which will come tumbling into orbit. So, how does one predictably position the satellite relative to earth such that the LED’s are visible from the ground? That’s where the Attitude Control System (ACS) comes into play.

How does an ACS work?

Multiple kinds of ACS’s have been employed on spacecraft. They break into two categories: active and passive control systems. The former implies using some means of attitude determination (see Attitude Determination System) that tells the satellite its position, and then using some kind of active stabilizers to return the satellite to its desired orientation. The latter obtains attitude stabilization by means of the effect produced by a certain physical phenomenon in which no control is required by the on board computer (OBC).

EQUiSat plans on using a permanent magnet which constantly attempts to align its polarization axis with the earth’s magnetic field lines.
This choice comes largely from the compliance with one of the mission’s design drivers, which is reliability:

  • NO reliance on the attitude determination system
  • NO energy drain from the torque coils
  • NO reliance on the complex algorithms required to 1) de-tumble and 2) stabilize (remember, there won’t be any up-linking for post-launch debugging)
  • a passive attitude control system is much more within reach for ‘amateur’ satellite aficionados

EQUiSat’s passive ACS will exert two types of moments on the spacecraft:

  • Restoring Moments: aligns the desired spacecraft axis with the earth’s magnetic field lines, implemented with a powerful permanent magnet aligned with the axis perpendicular to the flash panel.
  • Damping Moments: helps de-tumble the satellite after entering orbit by converting rotational kinetic energy into thermal energy, implemented with hysteresis rods (explained in further detail below) aligned with EQUiSat’s other two axes, parallel with the flash panel.

The end result is a spacecraft with one axis oscillating +/- 15º from the earth’s magnetic field lines. This is theoretically sufficient to ensure visibility of the flash from the ground.

A numerical model has been created to ensure the visibility reliability of the passive ACS in a 300 km, 42º inclined, circular orbit (a polar orbit with the same inclination was also analyzed).

The model calculates two things: Angle of View (AOV), defined as the angle between Providence’s azimuthal axis and EQUiSat’s position vector, and Field of View, defined as the angle between earth’s magnetic field (the ideal vector of flash beam) and the payload panel’s azimuthal axis.

The following plot shows the AOV vs. the day of orbit:

According to calculations from EQUiSat’s flash visibility team, the AOV can be no greater than 40º 45° for the flash to be within visibility range. Notice that EquiSat is well within range of Providence viewers at least six times daily.
So the next question is whether EQUiSat’s flash is suitably angled with respect to the viewer (FOV) to be visible. Below is plot of EQUiSat’s FOV v. Days in orbit.

The flash will shine with an angle of +/- 60º, and will have an orientation about +/- 15º of the Earth’s magnetic field. So, EQUiSat should theoretically be visible whenever the FOV is under 45º,

From the model discussed above, it is possible to extrapolate that EQUiSat will offer a total of about10 minutes of overhead flashing during its life-time––which should be enough time to be witnessed (assuming the merciful cooperation of Providence weather).

The next model explores the efficacy of hysteresis rods to de-tumble the satellite. The explicit goal of the hysteresis rods is to reduce the satellite’s rotational motion to an oscillation +/- 15º from the Earth’s magnetic field under a two weeks after launch.

The most critical variables of hysteresis rods are the 1) material, and 2) volume. A greater magnetic permeability and volume will apply more dampening torque on the de-tumbling spacecraft but at the same time will also raise the angle of the final oscillation. Materials being considered are HyMu80 and Permanorm 5000H

In the following plots, “Mag big” specifies a 5 cm long permanent magnet, while “Mag small” specifies a 3 cm long permanent magnet (each with identical cross-section).

This first plot represents the “resolution”, or how widely the spacecraft oscillates from the magnetic field vector after de-tumbling v. volume of the rod.

Notice that a greater rod volume results in less resolution––there’s a greater oscillation or “wobble”.

Meanwhile the plot below shows the rod’s “efficiency”, or the amount of time from launch that it would take the rod to de-tumble the satellite to the final resolution “wobble” seen above.

Notice that a larger rod volume guarantees less de-tumbling time (which is, of course, dependent on initial rotational velocity). (Green line covered by red)

Brown CubeSat is still evaluating the trade-off between high resolution (smaller hysteresis rods, lower permeability) and quick de-tumbling rate (larger hysteresis rods, greater permeability).

EquiSat’s attitude determination system is planned to improve the predictability of the satellite.
Using a suite of simple sensors, the plan is to calculate if the spacecraft is in its day time, during which time the system can enter its recharge mode. It can then continue flashing when the satellite is in its night.

To increase predictability, the satellite will downlink its attitude information allowing an observer to predict whether it should be visible from earth, or whether they should go back inside.

The satellite will use a 3-axis magnetometer in addition to its five solar panels (during the day), and its 6 IR sensors (during the night) to determine its attitude.

The satellite itself will only downlink raw sensor data; all processing and calculations will occur on the ground using the TRIAD algorithm: the most simple attitude determination algorithm.

Solar Panels

During the daytime, the solar panels will help calculate attitude by comparing the current delivered by each of its five solar panels. The current of each solar panel will vary depending on how directly it faces the sun, giving solar panels the purpose of sun-sensor in addition to energy generator.

Magnetometer

The 3-axis magnetometer tells both the strength and direction of the magnetic field (like a 3 dimensional compass, that can also measure magnetic magnitude) relative to itself. It provides another vector for the TRIAD algorithm.

IR Sensors (One on each side)

During a night pass, the satellite will be able to sense the infrared radiation emitted by the Earth’s surface. By comparing the ratio of the output signals of the sensors on adjacent sides of the satellite, we can compare the angle between a certain axis of the spacecraft and the spacecraft’s position vector.