Attitude ControlWeek-14

Fundamentals of Spacecraft Attitude Determination

and Control

F. Landis Markley • John L. Crassidis1

Magnetic Torque Attitude Control• Magnetic torque is used for detumbling, initial

acquisition, precession control, nutation damping, andmomentum control.

• One of the main uses of magnetic torquers is to dumpexcess momentum induced bu external disturbances.

• This is typically required to insure that wheels do not saturate.

• Wheels only redistribute a S/C angular momentum since they are internal body mechanism.

• External disturbance torques would lead to saturationof momentum capacity of the reaction wheels.

• Either mass expulsion (thrusters) or magnetic controltorques are needed to dump excess wheel angularmomentum.

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Magnetic Torque Attitude Control

• Magnetic torquers use the Earth’smagnetic field to produce a torque.

• Magnetic control torques are typicallyon the order of 10-5 to 10-4 N.m forLEO.

• Torques are constrained to lie in a 2-D plane orthogonal to magnetic field.

• So only two out of three axes can be controlled at a given time instant.

• Full three-axis control is availableprovided that S/C orbital plane doesnot coincide with the geomagneticequatorial plane and does not containmagnetic poles.

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Magnetic Torque Attitude Control

m

L

B

𝐋 = 𝐦× 𝐁

Torque generated by magnetic torquers

m is commanded magnetic dipole moment generated by torquersB is local geomagnetic dipole moment field expressed in body-frame coordinates

B=ARVector R depends on S/C orbital positionA is attitude matrix between reference frame and body frame

NASA 4

• The control is effected by commanding a magnetic dipolemoment.

• 𝐦 =𝑘

𝐁𝛚× 𝐛

• 𝐛 =𝑩

𝐁

• 𝛚 is angular velocity• k is scalar positive gain

• This gives a control torque perpendicular to b

• 𝐋 =𝑘

𝐁𝛚× 𝐛 × 𝐁 = −𝑘 𝐈𝟑 − 𝐛𝐛𝐓 𝛚

• If no angular information is available, use:• ሶ𝐁 = 𝐀 ሶ𝐑 − 𝛚 × 𝐁

• Initial stages ሶ𝐑 ≪ ሶ𝐁

• 𝐦 = −𝑘𝐁

ሶ𝐁

• B is the field sensed by onboard magnetometers.

• Example 1:

Detumbling with Magnetic Torque AttitudeControl

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Momentum Dumping with Thrusters

• Excess momentum is usually built up in the spacecraft through external disturbances, which are non-conservative.

• A periodic disturbance torque along one spacecraft axis results in a cyclic variation in the angular velocity along that axis, while a constant (secular) disturbance results in a linear increase in angular velocity, where the wheel is accelerated at a constant rate in order to transfer the excess momentum from the external disturbance to the wheel.

• Eventually saturation of the wheels will occur due to the excess momentum, which can only be dumped through external torques.

• Example 2:

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Momentum Dumping withMagnetic Torquers

• A common approach to design a magnetic torquercontrol law for momentum dumping is to commanda magnetic dipole moment:

• 𝐦 =𝑘

𝐁𝐡 × 𝐛

• The resulting torque is:• 𝐋 = −𝑘 𝐈𝟑 − 𝐛𝐛𝐓 𝐡

Example 3:

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TLE

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TLE

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TLE

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Example 4: