Magnetic Torque Bar Array Power Model

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Description

The Magnetic Torque Bar Array Power Model is a Power Node Model that attaches to a Magnetic Torque Bar Array to model the electrical load from driving air-core coils. The model computes the current required to produce commanded dipole moments using coil physics, calculates the resulting power dissipation, and scales output commands when insufficient voltage is available.

Unlike constant power loads, magnetic torque bars are classical resistive loads where the resistance can be computed directly from the commanded dipoles without quasi-static iteration.

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Example Use Cases

• Power-Limited Actuation: Simulate realistic torque bar behavior when battery voltage drops, automatically scaling dipole outputs.
• Power Budget Analysis: Evaluate power consumption of magnetic torque bars under various dipole command profiles.
• Electrical Load Modeling: Determine current draw and resistance presented to the power bus during attitude control maneuvers.

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Module Implementation

Coil Physics

Magnetic torque bars are air-core coils driven by H-bridge electronics. The dipole moment produced by a coil is:

$$m=N\cdot I\cdot A$$

where $N$ is the number of turns, $I$ is the coil current, and $A$ is the effective cross-sectional area. The current required to produce a commanded dipole is therefore:

$$I=\frac{|m|}{N\cdot A}$$

Voltage Limiting

The coil voltage required to drive the current through the coil resistance is:

$$V_{\text{coil}}=I\cdot R_{\text{coil}}$$

If any coil requires more voltage than available ($V_{\text{coil}}>V_{\text{in}}$), all output dipole commands are scaled proportionally:

$$s=\frac{V_{\text{in}}}{V_{\text{coil,max}}}$$ $$m_{\text{out}}=s\cdot m_{\text{in}}$$

This ensures the magnetic torque bars operate within the available voltage envelope.

Power Consumption

The power dissipated in each coil follows the resistive power law:

$$P_{\text{coil}}=I^2\cdot R_{\text{coil}}$$

The total DC power draw includes driver efficiency and standby power:

$$P_{\text{DC}}=\frac{\sum P_{\text{coil}}}{\eta }+P_{\text{standby}}$$

where $\eta$ is the H-bridge driver efficiency.

Resistance Calculation

The equivalent resistance presented to the power bus is:

$$R=\frac{V_{\text{in}}^2}{P_{\text{DC}}}$$

When no power is being drawn, the resistance defaults to a large value ($10^{12}\Omega$).

Parameters

Parameter	Description	Default
CoilResistance	Resistance per torque bar coil (Ω)	10.0
CoilTurns	Number of turns per coil	400
CoilEffectiveArea	Cross-sectional area per coil (m²)	0.01
DriverEfficiency	H-bridge driver efficiency (0–1)	0.85
DriverStandbyPower	Quiescent power when idle (W)	0.2

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Assumptions/Limitations

• All torque bars in the array share the same coil parameters (resistance, turns, area).
• The model assumes ideal H-bridge behavior with constant efficiency across the operating range.
• When disabled or input voltage is zero, output dipole commands are set to zero.
• The model does not account for coil inductance or transient current dynamics.
• Thermal effects on coil resistance are not modeled.