Magnetorquer Control

Magnetorquer Control (space-systems/adcs/magnetorquer-control)

Use when the task is spacecraft magnetic attitude control: computing the magnetic dipole moment that produces a commanded torque through the cross-product torque = m x B, B-dot detumbling of body rates, torque authority limits, or torque rod coil sizing.

Domain quick reference

• A magnetorquer (torque rod) is a coil that produces a magnetic dipole moment m (A m^2); the magnetic field B of the Earth exerts the control torque torque = m x B (N m) on the spacecraft.
• The torque is always perpendicular to B: m x B is orthogonal to B, so a magnetorquer can only produce torque about axes perpendicular to the local field. The torque component along B is unachievable, which is the underdetermined-axis limit of magnetic control.
• Required dipole: the minimal dipole that produces a torque demand perpendicular to B is m = (B x torque) / |B|^2. The component of the demand along B is returned as an underdetermined-axis warning.
• Achievable torque magnitude: |m x B| = |m| |B| sin(theta) where theta is the angle between m and B; the maximum for a given dipole magnitude is |m| |B|, reached when m is perpendicular to B.
• Torque authority: the largest torque a magnetorquer of dipole limit m_max can exert in a field B is m_max * |B|. Authority is weakest near the magnetic poles and strongest near the equator.
• B-dot detumbling law: damp the body rate omega by commanding m = gain * (omega x B), which equals -gain * Bdot because the body frame field derivative is Bdot = -omega x B. The resulting torque opposes the rate component perpendicular to B and damps it.
• Orbit-averaged authority: over one orbit the mean of m_max * |B| over the sampled field vectors estimates the average torque capability available for momentum dumping and pointing.
• Coil sizing: the dipole of a torque rod is N * I * A, the product of the number of turns, the drive current, and the coil area. Required current for a dipole demand is m / (N * A).
• Units: dipole moment in A m^2, field in T, torque in N m, rate in rad/s, coil current in A, area in m^2.
• Magnetic attitude control follows ECSS-E-ST-60 ADCS practice.

Workflow

1. Get the torque demand vector (from the attitude controller or the detumbling law) and the local magnetic field vector B in the body frame.
2. Compute the required dipole m = (B x torque) / |B|^2 and check the underdetermined-axis warning: torque along B is not producible.
3. For detumbling, compute the B-dot dipole m = gain * (omega x B) from the measured body rate and field.
4. Compare the demanded dipole and the resulting achievable torque magnitude |m x B| against the magnetorquer torque authority limit m_max * |B|; clip the dipole to m_max when it exceeds the limit.
5. Size the torque rods: current per coil I = m / (N * A) for the selected turns and area; verify the coil current is within the driver limit.
6. Estimate the orbit-averaged torque authority from the field samples along the orbit to confirm the capability budget.

Pitfalls

• Demanding torque along B: m x B can never produce it; detect the underdetermined axis and report it instead of returning a meaningless dipole.
• Dividing by a zero field: |B| = 0 makes the dipole formula singular; raise instead of returning nan.
• Forgetting that |m x B| depends on the angle: a dipole parallel to B produces zero torque even at full authority.
• Using B-dot gain with the wrong sign: m = gain * (omega x B) must oppose the rate, otherwise the law spins the spacecraft up.
• Sizing coils without the driver current limit: the required current m / (N * A) must be within what the electronics can supply.
• Treating the orbit-averaged authority as instantaneous capability: the average hides the per-axis gaps where B is nearly parallel to the demand.

Behavior contract (gate 3)

The dipole computation, B-dot law, authority, and coil sizing logic is exercised by the gate 3 contract test: scripts/test_magnetorquer_control.py against scripts/magnetorquer_control_logic.py (stdlib unittest, offline). Run: python3 scripts/test_magnetorquer_control.py

Compliance

• ECSS (European Cooperation for Space Standardization) standards are freely downloadable, copyright ESA; cite the source and paraphrase. This leaf cites ECSS as reference only per standards-map.yaml; the logic here is generic magnetic attitude control physics (torque = m x B, B-dot damping), not ECSS text.
• compliance: STANDARDS-REF, gated: false.