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  rF
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 factor0    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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–
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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
•
•
•
•
Gravity Gradient Booms
Dampers
Yo-yos
Spinning
– Active
•
•
•
•
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