Download - Attitude Determination and Control
Attitude Determination and Control
Dr. Andrew Ketsdever
MAE 5595
Outline• Introduction
– Definitions– Control Loops– Moment of Inertia Tensor– General Design
• Control Strategies– Spin (Single, Dual) or 3-Axis
• Disturbance Torques– Magnetic– Gravity Gradient– Aerodynamic– Solar Pressure
• Sensors– Sun– Earth– Star– Magnetometers– Inertial Measurement Units
• Actuators– 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
– Rate Requirements (e.g. Slew)– Stationkeeping Requirements– Disturbing Environment– Mass and Volume– Power– Reliability– Cost and Schedule
Introduction
Velocity Vector
X
Y
Z
Nadir
Control Loops
Spacecraft Dynamics - Rigid Body - Flexible Body (non-rigid)
AttitudeControl
Task
AttitudeActuators
Commands
e.g. increaseWheel speed 100rpm
DesiredAttitude
e.g. +/- 3 degRam pointing
AttitudeSensors
AttitudeDetermination
Task
ActualAttitude
e.g. – 4 degRam pointing
EstimatedAttitudee.g. – 3.5 degRam pointing
Disturbance Torques
Mass Moment of Inertia
IH
z
y
x
zzzyzx
yzyyyx
xzxyxx
z
y
x
III
III
III
H
H
H
H
where H is the angular momentum, I is the mass moment of inertia tensor, and is the angular velocity
where the cross-term products of inertia are equal (i.e. Ixy=Iyx)
Mass Moment of Inertia
• For a particle
• For a rigid body
m
r
O
O
dm
m
r
O
O
I r mO 2
I r dm r dmm
2 2
I r dVV
2
Mass MOI
dmyzI
dmxzI
dmxyI
dmyxI
dmzxI
dmzyI
yz
xz
xy
zz
yy
xx
22
22
22
jiijIE 2
1
Rotational Energy:
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
z
y
x
I
I
I
I
00
00
00
IH
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.
I I md 2
O
O
CM
d
r
r’
m
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 satellitesBest 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
1T
S
I
I
S
T
S
T
1T
S
I
I
UNSTABLE STABLE
Satellite Precession• Spinning Satellite• Satellite thruster is fired to
change its spin axis• During the thruster firing, the
satellite rotated by a small angle
• Determine the angle F
F
R
H
2
)(2
;)(2
I
FRtI
tFR
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
Orbital Altitude (au)
Tor
que
(au)
SolarPress.
Drag
Gravity
Magnetic
LEO GEO
NOTE: The magnitudes of the torques isdependent on the spacecraft design.
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
FrT
IHT
Gravity Gradient Torque
2sin
2
33 yzg II
RT
where:
verticalfromaway deviation maximum
inertia of moments mass S/C ,
radiusorbit
parameter nalgravitatio sEarth'
gradientgravity maximum
zy
g
II
R
T
z
y
Magnetic Torque
where:
BxmTm
meters radiusorbit
m tesla10 7.96moment magnetic sEarth'
poles theabove pointsfor 2
equator theabove pointsfor
field magnetic sEarth' ofstrength
mAmp dipole magnetic residual S/C
torqueedisturbanc magnetic
315
3
3
2
R
M
R
MR
M
B
m
Tm
*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
where:
gpaa ccFT
2
2
1AvCF D
gravity ofcenter C
pressure catmospheri ofcenter C
velocity
area sectional-cross
2.5 - 2 are valuesS/C typical drag oft coefficien
density catmospheri
torqueedisturbanc caerodynami
g
pa
v
A
C
T
D
a
Solar Pressure Torque
where:
gpssrp ccFT
iAc
FF s
s cos1
angle incidencesun
S/Cfor 0.6 value typical1,0factor ereflectanc
surface dilluminate of area
light of speed
m
Wdensity flux solar
gravity ofcenter c
pressureradiation solar ofcenter
torqueedisturbanc presureradiation solar
2
g
i
A
c
F
c
T
s
s
ps
srp
FireSat Example
Disturbing Torques
• All of these disturbing torques can also be used to control the satellite– 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 Sun Sensor Star Tracker
Sensor Accuracies Comments
IMU Drift: 0.0003 – 1 deg/hr 0.001 deg/hr nominal
Requires updates
Star Sensor 1 arcsec – 1 arcmin (0.0003 – 0.001 deg)
2-axis for single star Multiple stars for map
Sun Sensor 0.005 – 3 deg 0.01 deg nominal
Eclipse
Earth Sensor GEO LEO
< 0.1 – 0.25 deg
0.1 – 1 deg
2-axis
Magnetometer 0.5 – 3 deg < 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
ActuatorsActuator Accuracy CommentGravity 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