Bsf08 Spacecraft Attitude Determination And Control V1 0

Basics of Spaceflight

Spacecraft Attitude
S f A i d
Determination and Control
D t i ti dC t l
Prof. Dr.‐Ing. Bernd Dachwald
dachwald@fh aachen.de
dachwald@fh‐aachen de
Aerospace Technology Department
Hohenstaufenallee 6, 52064 Aachen, Germany

FH Aachen University of Applied Sciences
Winter 2009 / 2010
/
v1.0

Overview and Introduction

What is Spacecraft Attitude … and Why Do We Have to Control It?

• The orientation of the spacecraft in space is called its attitude
• Most spacecraft have instruments and/or antennas that must be
pointed into specific directions. Solar arrays must be pointed into the
d f d l b d h
sun. The thruster must be pointed into the required direction during
thrust maneuvers
thrust maneuvers
• To control the attitude, the spacecraft operators (or the spacecraft's
computer, in case of an autonomous system) must have the ability to
1. Determine the current attitude
2. Determine the error between the current and the desired attitude
3. Apply torques to remove the error
• Therefore, the spacecraft needs an attitude determination and control
system (ADCS)
• Attitude determination requires sensors
• Attitude control requires actuators
Attitude control requires actuators

Prof. Dr.‐Ing. Bernd Dachwald Spacecraft Attitude Determination and Control FH Aachen / Winter 2009/10 / v1.0 2

Overview and Introduction

Attitude Determination & Control Process
Thruster must point
into thrust direction
Attitude Requirements:
Antenna must point
Antenna must point
Actuators into Earth direction

Torque Internal
Demands Torques External
Disturbance
stu ba ce
Disturbance Torques
Di t b T
Torques ‐ Aerodynamic
‐ Gravity‐Gradient
‐ Magnetic
On board
On‐board ‐ Solar Radiation Pressure
Solar Radiation Pressure
Computer
Measured Solar array Sensor must
Attitude must point point into
Attitude into sun target direction
direction
d
Control „Real“
Commands Attitude

Ground
Control Attitude
Sensors

Measured Attitude


Disturbing Forces and Torques Overview

Disturbing Forces and Torques Acting on Spacecraft
• Aerodynamic force / torque
from planetary atmospheres, at Earth: altitude / 500 km
• Gravity gradient torque
Gravity gradient torque
from planetary gravity fields, ∝ 1/R3, at Earth: altitude ≈ 500‐35000 km
• Magnetic torque
g q
from planetary magnetic fields, ∝ 1/R3, at Earth: altitude ≈ 500‐35000 km
• Solar radiation pressure force / torque
i th i l t 1/r t E th ltit d ' 600 km
in the inner solar system, ∝ 1/ 2, at Earth: altitude ' 600 k
• Force / torque from micrometeorite and debris impacts
at all altitudes
• Spacecraft generated forces / torques
e.g. from mass movements (mechanisms, propellant, astronauts), at all altitudes
• Their relative importance is a generally a function of spacecraft size, mass,
mass distribution, altitude, and design
R: Distance from Earth (center)
r: Distance from sun


Disturbing Forces and Torques Aerodynamic

Aerodynamic Torque (simplified)

Aerodynamic drag (simplified):
1 ³ v´
FA = ρCD A⊥ v 2 −
2 v A⊥
CP

F A: Aerodynamic force v FA
ρ: Atmospheric density r
CD : Aerodynamic (drag) coeﬃcient CM
A⊥ : Area normal to the
spacecraft velocity vector
v: Spacecraft velocity vector

Aerodynamic torque:
TD = r × FA

T D: Aerodynamic torque
r: Vector from the center of mass (CM) to the center of pressure (CP)


Disturbing Forces and Torques Comparison

Typical Magnitude of Disturbing Torques

Altitude
Diagrams like this are strongly
dependent on the shape and
design of the spacecraft
100 000

Radiation P
R di ti Pressure

10 000
Gravity Gradient

Magnetic Effects
1 000
Aerodynamic Effects

100 Torque


Attitude Description

Description of Spacecraft Attitude
Spacecraft attitude is characterized by the orientation of a
spacecraft‐ fixed coordinate system with respect to a reference
coordinate system
Example: orbit‐defined coordinate system Roll, Pitch, Yaw:
p y
– Yaw axis is directed toward nadir (i.e. Earth center)
– Pitch axis is directed toward the south orbit normal
– Roll axis is perpendicular to yaw and pitch axis

Yaw rotation

Roll rotation

Pitch rotation


Attitude Determination

Attitude Determination Objective and Sensors

• Objective: To determine the attitude, or orientation, or pointing direction of a
spacecraft‐fixed reference frame with respect to a known (usually inertial)
reference frame.
reference frame
• Attitude determination requires two or more attitude sensors like
– M
Magnetometers
measure the magnitude and direction of the magnetic field

– Sun sensors
Sun sensors
measure the position of the sun

– Earth sensors
Earth sensors
measure the position of the Earth or the attitude with respect to the horizon

– Star sensors
compare some image of the sky with a build‐in library

– Gyroscopes
measure the rotation of spacecraft without external references


Attitude Sensors Sun Sensors

Simple Sun Sensors

Sunlight
g
Sunlight
S li ht

Sensors

Sensors
Electronics
Signal


Attitude Sensors Sun Sensors

Sun Sensors
• Accuracy limit of a sun sensor is about several arcseconds (0.1 – 0.01 deg) for
precise sensors and 0.5 deg for coarse sensors
• O
One sun sensor measurement does not give the complete attitude but only a
td t i th l t ttit d b t l
direction (only two degrees of freedom of the vector are sensitive to the
attitude).
• Two measurements are required to determine the attitude:
– by a second independent sensor
– by the same sensor but separated significantly in time
by the same sensor but separated significantly in time.

?

Attitude Sensors Star Sensors

Star Sensors
• Starlight strikes the CCD
of a camera
• By determining the
y g
direction to two Star 1
different stars in the
Star 2
picture, the
complete attitude can
be determined
• Star sensors are very
accurate (typically 1‐3
arcsec, some up to
0.001 arcsec) …
• … but they generally do
not function well at
angular rates above
some deg/s (due to their
small field of view)
⇒ a coarse sensor is
also required for high
angular rates

Attitude Control Tasks

Typical Attitude Control Tasks

Tumbling S/C after separation High angular rate
Arbitrary orientation

Slow‐down angular speed Low angular rate
Arbitrary orientation

Attain safe attitude (power, thermal) Low angular rate
Sun‐pointing
Low accuracy
Low accuracy

Attain operational attitude (payload Low angular rate
operations) Operational orientation
p
High accuracy

S e to suppo t o b t ope at o s
Slew to support orbit operations Low angular rate
o a gu a ate
Oriented to support orbit maneuver
Large disturbances


Attitude Control Reaction Jets

Reaction Jets

m˙ ˙
m<0
• By expelling a mass     (for the spacecraft            ) with a velocity c,
F = mc
a thruster exerts a force          ˙ onto the spacecraft
• If the thruster has a moment arm r with respect to the
spacecraft‘s center of mass (CM), it exerts a torque about CM:
T=r×F
• A single thruster also changes the spacecraft‘s linear momentum
A single thruster also changes the spacecraft s linear momentum
p, because F = p ˙
F = mc
˙
(
(this is typically not desired
yp y
because it also changes r
the orbit of the spacecraft)
CM


Attitude Control Reaction Jets

Reaction Jets
• Therefore, thrusters are used in pairs, so that
T1 + T2 = 2(r × F)
F1 + F2 = 0
• Depending on the actual thruster, one can have a very high
Depending on the actual thruster, one can have a very high
control authority
– Cold gas:
F1 = mc1
˙
up to 10 N
– Hydrazine:
up to 10 kN
up to 10 kN r1
– Ion thrusters:
10 mN down to < 1 mN CM
r2

F2 = mc2
˙


Attitude Control Reaction Wheels

Reaction Wheels
• Rotating the spacecraft does not necessarily
require thrusters (conservation of angular
momentum!) )
• Reaction wheels (RWs) are a common choice for
active attitude control
• RW
RW provide quick and accurate control
id i k d l
• Internal torque only (external torque is still
required for de‐saturating the wheels, when they
q g , y
have reached their maximum rotation speed)
• Three RWs are necessary for three‐axis control
but four wheels are usually used for redundancy
but four wheels are usually used for redundancy
(tetrahedron mounting)
• Control logic is simple for three independent
axes but can get complicated with redundancy
• Static and dynamic imbalances can produce
vibrations (attitude jitter)
vibrations (attitude jitter)
• Typical torque is 0.1 − 1 Nm

Attitude Control System Design

Basic Concept of Feedback Control
• Satellite attitude is measured and compared with a desired value
⇒ Attitude error
• Attitude error is used to determine corrective torque to be
applied by onboard actuators ⇒ New attitude
• C l
Cycle continues indefinitely because
ti i d fi it l b
– disturbance torques occur
– attitude measurement is imperfect
attitude measurement is imperfect
– attitude correction is imperfect


References

References
[Ro08] Lucy Rogers:
It’s ONLY Rocket Science. An Introduction in Plain English.
Springer, 2008
[Sw08] Graham Swinerd:
How Spacecraft Fly. Spaceflight Without Formulae.
Springer, 2008
Springer 2008
[Se05] Jerry Jon Sellers:
Understanding Space. An Introduction to Astronautics.
Third Edition. McGraw‐Hill, 2005
[Gr04] Michael D. Griffin, James D. French:
Space Vehicle Design.
p g
Second Edition. AIAA Education Series, 2004


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