Attitude Determination and Control
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Transcript Attitude Determination and Control
Attitude Determination and
Control
Dr. Andrew Ketsdever
MAE 5595
Outline
•
Introduction
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Definitions
Control Loops
Moment of Inertia Tensor
General Design
Control Strategies
– Spin (Single, Dual) or 3-Axis
•
Disturbance Torques
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Sensors
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Magnetic
Gravity Gradient
Aerodynamic
Solar Pressure
Sun
Earth
Star
Magnetometers
Inertial Measurement Units
Actuators
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Dampers
Gravity Gradient Booms
Magnetic Torque Rods
Wheels
Thrusters
INTRODUCTION
Introduction
• Attitude Determination and Control
Subsystem (ADCS)
– Stabilizes the vehicle
– Orients vehicle in desired directions
– Senses the orientation of the vehicle relative
to reference (e.g. inertial) points
• Determination: Sensors
• Control: Actuators
• Controls attitude despite external
disturbance torques acting on spacecraft
Introduction
• ADCS Design Requirements and Constraints
– Pointing Accuracy (Knowledge vs. Control)
• Drives Sensor Accuracy Required
• Drives Actuator Accuracy Required
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Rate Requirements (e.g. Slew)
Stationkeeping Requirements
Disturbing Environment
Mass and Volume
Power
Reliability
Cost and Schedule
Introduction
Z
Nadir
Y
X
Velocity Vector
Control Loops
Disturbance Torques
Desired
Attitude
Attitude
Control
Task
e.g. +/- 3 deg
Ram pointing
Estimated
Attitude
e.g. – 3.5 deg
Ram pointing
Attitude
Determination
Task
Commands
e.g. increase
Wheel speed
100rpm
Attitude
Actuators
Actual
Attitude
e.g. – 4 deg
Ram pointing
Attitude
Sensors
Spacecraft Dynamics
- Rigid Body
- Flexible Body (non-rigid)
Mass Moment of Inertia
H I
where H is the angular momentum, I is the mass moment of inertia
tensor, and is the angular velocity
H x I xx
H H y I yx
H z I zx
I xy
I yy
I zy
I xz x
I yz y
I zz z
where the cross-term products of inertia are equal (i.e. Ixy=Iyx)
Mass Moment of Inertia
• For a particle
O
m
• For a rigid body
IO r m
2
r
O
O
I r 2 dm r 2 dm
r
m
dm
m
O
I r 2 dV
V
Mass MOI
x
x
dm
dm
I xx y z dm
I yy
I zz
2
2
2
z
2
2
y
2
I xy xy dm
I xz xz dm
I yz yz dm
Rotational Energy:
1
E I ij i j
2
Mass MOI
• Like any symmetric
tensor, the MOI
tensor can be
reduced to diagonal
form through the
appropriate choice of
axes (XYZ)
• Diagonal components
are called the
Principle Moments of
Inertia
I x
I 0
0
0
Iy
0
H I
0
0
I z
Mass MOI
• Parallel-axis theorem: The moment of
inertia around any axis can be calculated
from the moment of inertia around parallel
axis which passes through the center of
mass.
O
m
CM
d
r
O
r’
I I md
2
ADCS Design
ADCS Design
ADCS Design
ADCS Design
ADCS Design
Control Strategies
Gravity Gradient Stabilization
• Deploy gravity
gradient boom
• Coarse roll and
pitch control
• No yaw control
• Nadir pointing
surface
• Limited to near
Earth satellites
Best to design such that Ipitch > Iroll > Iyaw
Spin Stabilization
• Entire spacecraft
rotates about
vertical axis
• Spinning sensors
and payloads
• Cylindrical
geometry and solar
arrays
Spin Stability
UNSTABLE
STABLE
S
S
T
T
IS
1
IT
IS
1
IT
Satellite Precession
• Spinning Satellite
• Satellite thruster is fired to
change its spin axis
• During the thruster firing, the
satellite rotated by a small
angle Df
• Determine the angle Dy
2 FR(Dt )
Df
Dy
;
I
Dt
2 FR(Df )
Dy
I 2
Dy H
Df
R
F
F
Dual Spin Stabilization
• Upper section does not
rotate (de-spun)
• Lower section rotates to
provide gyroscopic
stability
• Upper section may rotate
slightly or intermittently to
point payloads
• Cylindrical geometry and
solar arrays
3-Axis Stabilization
• Active stabilization of all three
axes
– Thrusters
– Momentum (Reaction) Wheels
• Momentum dumping
• Advantages
– No de-spin required for
payloads
– Accurate pointing
• Disadvantages
– Complex
– Added mass
Disturbance Torques
External Disturbance Torques
NOTE: The magnitudes of the torques is
dependent on the spacecraft design.
Torque (au)
Drag
Gravity
Solar
Press.
Magnetic
LEO
GEO
Orbital Altitude (au)
Internal Disturbing Torques
• Examples
– Uncertainty in S/C Center of Gravity (typically
1-3 cm)
– Thruster Misalignment (typically 0.1° – 0.5°)
– Thruster Mismatch (typically ~5%)
– Rotating Machinery
– Liquid Sloshing (e.g. propellant)
– Flexible structures
– Crew Movement
Disturbing Torques
T H I
T rF
Gravity Gradient Torque
3
Tg
I z I y sin 2
3
2R
z
where:
Tg maximumgravitygradient
Earth's gravitational parameter
R orbit radius
I y , I z S/C mass momentsof inertia
maximumdeviationaway from vertical
y
Magnetic Torque
Tm m xB
where:
Tm magneticdisturbance torque
m S/C residual magneticdipole Amp m 2
B strengthof Earth's magneticfield
M
for pointsabove theequator
3
R
2M
3 for pointsabove thepoles
R
M Earth's magneticmoment 7.96 1015 tesla m 3
R orbit radius meters
*Note value of m depends on S/C size and whether on-board compensation is used
- values can range from 0.1 to 20 Amp-m2
- m = 1 for typical small, uncompensated S/C
Aerodynamic Torque
Ta F c pa cg
where:
1
F C D Av 2
2
Ta aerodynamic disturbance torque
atmospheric density
C D coefficient of drag typicalS/C valuesare 2 - 2.5
A cross- sectionalarea
v velocity
C pa centerof atmospheric pressure
Cg centerof gravity
Solar Pressure Torque
Tsrp F c ps cg
where:
Fs
F
As 1 cos i
c
Tsrp solar radiat ionpresuredisturbance torque
c ps cent erof solar radiat ionpressure
c g cent erof gravity
W
Fs solar flux density 2
m
c speed of light
As area of illuminated surface
reflectance factor0 1, typicalvalue 0.6 for S/C
i sun incidenceangle
FireSat Example
Disturbing Torques
• All of these disturbing torques
can also be used to control the
satellite
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Gravity Gradient Boom
Aero-fins
Magnetic Torque Rods
Solar Sails
Sensors
Attitude Determination
• Earth Sensor (horizon sensor)
– Use IR to detect boundary between deep space &
upper atmosphere
– Typically scanning (can also be an actuator)
• Sun Sensor
• Star Sensor
– Scanner: for spinning S/C or on a rotating mount
– Tracker/Mapper: for 3-axis stabilized S/C
• Tracker (one star) / Mapper (multiple stars)
• Inertial Measurement Unit (IMU)
– Rate Gyros (may also include accelerometers)
• Magnetometer
– Requires magnetic field model stored in computer
• Differential GPS
Attitude Determination
Earth Horizon Sensor
Sensor
IMU
Star Sensor
Sun Sensor
Earth Sensor
GEO
LEO
Magnetometer
Sun Sensor
Accuracies
Drift: 0.0003 – 1 deg/hr
0.001 deg/hr nominal
1 arcsec – 1 arcmin
(0.0003 – 0.001 deg)
0.005 – 3 deg
0.01 deg nominal
< 0.1 – 0.25 deg
0.1 – 1 deg
0.5 – 3 deg
Star Tracker
Comments
Requires updates
2-axis for single star
Multiple stars for map
Eclipse
2-axis
< 6000 km
Difficult for high i
Actuators
Attitude Control
• Actuators come in two types
– Passive
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Gravity Gradient Booms
Dampers
Yo-yos
Spinning
– Active
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Thrusters
Wheels
Gyros
Torque Rods
Actuators
Actuator
Accuracy
Comment
Gravity Gradient
5º
2 Axis, Simple
Spin Stabilized
0.1º to 1º
2 Axis, Rotation
Torque Rods
1º
High Current
Reaction Wheels
0.001º to 0.1º
High Mass and Power,
Momentum Dumping
Control Moment Gyro
0.001º to 0.1º
High Mass and Power
Thrusters
0. 1º to 1º
Propellant limited,
Large impulse
Attitude Control