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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: