Detumbling and the B-Dot Algorithm

A magnetorquer showing the copper coils.
A magnetorquer showing the copper coils.

Detumbling?

Detumbling is essential to every satellite and is the first thing that one has to do after the launch. When the satellite is launched, it spins wildly in space due to the forces exerted on it when it’s released from the rocker. Detumbling is the process of stopping the satellite from spinning so it is ready to do what it was sent out for. Detumbling is particularly important for satellites that take photos or transmit signals, but is included in all satellite systems.

The B-Dot Algorithm?

The B-Dot algorithm is one of the most common methods of detumbling in CubeSats, because of the hardware it uses. The B-Dot algorithm is the software used with a magnetorquer. The magnetorquer was invented in the 70’s and have remained largely unchanged since then. Magnetorquers produce electromagnetic fields by running a current through a solenoid to control the motion of the satellite. 

The B-Dot algorithm is the software that lets the magnetorquer control the motion using the produced magnetic fields. The magnitude of the magnetic field is measured twice with a delay between the measurements. The gradient of the magnetic field against time can be calculated from the measurements and the delay, just like a gradient of a line can be calculated given two points (the difference between the two measurements is divided by the delay between them), and can be called B-dot. It’s called B-dot because it is the time derivative of the magnetic field and the magnetic field is symbolised by B. 

The magnitude of B-Dot indicates how fast the satellite is spinning in one direction and the sign tells us which direction it’s spinning. The B-Dot algorithm uses B-Dot to control the magnitude and direction of the magnetic fields produced by the solenoids, as indicated by the name. A current is supplied to the solenoid to produce a magnetic field that is in the opposite direction to and proportional to the magnitude of B-Dot. The output is usually controlled using pulse wave modulation or PWM. This is a proportional controller because the output to the solenoid is proportional to the difference between the magnitude of B-Dot and our desired magnitude, which is 0. This can be done in all three axes to control it in all three directions, though this does require a solenoid pointing in each of the three directions.

But how does the magnetic field produced by the magnetorquer stop the satellite from spinning? The solenoids exert a magnetic field in the opposition to the Earth’s magnetic field. This magnetic field exerts a force in the opposite direction to the spin on the satellite due to the opposition with the Earth’s magnetic field and slows the motion of the satellite. By continuing to enact the B-Dot algorithm, the satellite is detumbled and is ready to perform it’s mission.