Attitude Determination and Control (ADCS)

57 Pages·2001·1.23 MB·English

AAttttiittuuddee DDeetteerrmmiinnaattiioonn aanndd CCoonnttrrooll
((AADDCCSS))
1166..668844 SSppaaccee SSyysstteemmss PPrroodduucctt DDeevveellooppmmeenntt
SSpprriinngg 22000011
OOlliivviieerr LL.. ddee WWeecckk
DDeeppaarrttmmeenntt ooff AAeerroonnaauuttiiccss aanndd AAssttrroonnaauuttiiccss
MMaassssaacchhuusseettttss IInnssttiittuuttee ooff TTeecchhnnoollooggyy
AADDCCSS MMoottiivvaattiioonn
(cid:1) Motivation Sensors: GPS, star trackers, limb
—
sensors, rate gyros, inertial
In order to point and slew optical
—
measurement units
systems, spacecraft attitude control
provides coarse pointing while Control Laws
—
optics control provides fine
Spacecraft Slew Maneuvers
(cid:1)
pointing
Euler Angles
—
Spacecraft Control
(cid:1)
Quaternions
—
Spacecraft Stabilization
—
Spin Stabilization
— Key Question:
Gravity Gradient What are the pointing
—
requirements for satellite ?
Three-Axis Control
—
Formation Flight
—
NEED expendable propellant:
Actuators
—
Reaction Wheel Assemblies
— (cid:127) On-board fuel often determines life
(RWAs)
(cid:127) Failing gyros are critical (e.g. HST)
Control Moment Gyros
—
(CMGs)
Magnetic Torque Rods
—
Thrusters
—
OOuuttlliinnee
Definitions and Terminology
(cid:1)
Coordinate Systems and Mathematical Attitude Representations
(cid:1)
Rigid Body Dynamics
(cid:1)
Disturbance Torques in Space
(cid:1)
Passive Attitude Control Schemes
(cid:1)
Actuators
(cid:1)
Sensors
(cid:1)
Active Attitude Control Concepts
(cid:1)
ADCS Performance and Stability Measures
(cid:1)
Estimation and Filtering in Attitude Determination
(cid:1)
Maneuvers
(cid:1)
Other System Consideration, Control/Structure interaction
(cid:1)
Technological Trends and Advanced Concepts
(cid:1)
OOppeenniinngg RReemmaarrkkss
Nearly all ADCS Design and Performance can be viewed in
(cid:1)
terms of RIGID BODY dynamics
Typically a Major spacecraft system
(cid:1)
For large, light-weight structures with low fundamental
(cid:1)
frequencies the flexibility needs to be taken into account
ADCS requirements often drive overall S/C design
(cid:1)
Components are cumbersome, massive and power-consuming
(cid:1)
Field-of-View requirements and specific orientation are key
(cid:1)
Design, analysis and testing are typically the most
(cid:1)
challenging of all subsystems with the exception of payload
design
Need a true “systems orientation” to be successful at
(cid:1)
designing and implementing an ADCS
TTeerrmmiinnoollooggyy
: Orientation of a defined spacecraft body coordinate
AATTTTIITTUUDDEE
system with respect to a defined external frame (GCI,HCI)
Real-Time or Post-Facto knowledge,
AATTTTIITTUUDDEE DDEETTEERRMMIINNAATTIIOONN::
within a given tolerance, of the spacecraft attitude
Maintenance of a desired, specified attitude
AATTTTIITTUUDDEE CCOONNTTRROOLL::
within a given tolerance
“Low Frequency” spacecraft misalignment;
AATTTTIITTUUDDEE EERRRROORR::
usually the intended topic of attitude control
“High Frequency” spacecraft misalignment;
AATTTTIITTUUDDEE JJIITTTTEERR::
usually ignored by ADCS; reduced by good design or fine
pointing/optical control.
PPooiinnttiinngg CCoonnttrrooll DDeeffiinniittiioonnss
target
target desired pointing direction
estimate true actual pointing direction (mean)
estimate estimate of true (instantaneous)
a pointing accuracy (long-term)
c
a s stability (peak-peak motion)
k knowledge error
k true
c control error
s
aa == ppooiinnttiinngg aaccccuurraaccyy == aattttiittuuddee eerrrroorr
ss == ssttaabbiilliittyy == aattttiittuuddee jjiitttteerr
Source:
G. Mosier
NASA GSFC
AAttttiittuuddee CCoooorrddiinnaattee SSyysstteemmss
(North Celestial Pole)
^
Z
GGCCII:: GGeeoocceennttrriicc IInneerrttiiaall CCoooorrddiinnaatteess
CCrroossss pprroodduucctt
GGeeoommeettrryy:: CCeelleessttiiaall SSpphheerree
^ ^ ^
Y = Z x X
h
g t
n
A r c l e
dihedral
(cid:3)(cid:3)
(cid:1)(cid:1)
^
Y
^
VVEERRNNAALL
X
EEQQUUIINNOOXX
(cid:1)(cid:1)(cid:2)(cid:2) IInneerrttiiaall CCoooorrddiinnaattee
:: RRiigghhtt AAsscceennssiioonn
(cid:3)(cid:3) SSyysstteemm
:: DDeecclliinnaattiioonn X and Y are
in the plane of the ecliptic
AAttttiittuuddee DDeessccrriippttiioonn NNoottaattiioonnss
⋅ =
{ } Coordinate system
ˆ
Z (cid:1)
A
=
P Vector
(cid:1) (cid:1)
A A =
P P Position vector w.r.t. {A}
P
z
P
y  
ˆ P
Y
x
A (cid:1)  
Px AP = P 
y
ˆ
X  
A
P 
z
1 0 0
[ ]
 
= ˆ ˆ ˆ =
Unit vectors of {A} X Y Z 0 1 0
A A A  
 
0 0 1
Describe the orientation of a body:
(1) Attach a coordinate system to the body
(2) Describe a coordinate system relative to an
inertial reference frame
RRoottaattiioonn MMaattrriixx
Zˆ {A} = Reference coordinate system
A
Jefferson Memorial
Zˆ Yˆ =
B B {B} Body coordinate system
Rotation matrix from {B} to {A}
ˆ
Y
ˆ A [ ]
X
A A = A ˆ A ˆ A ˆ
ˆ R X Y Z
X
B B B B
B
ˆ
Z Special properties of rotation matrices:
A
Jefferson Memorial
Zˆ Yˆ (1) Orthogonal:
B B
θ −
T = T = 1
R R I, R R
θ
ˆ (2) Orthonormal:
Y
A
ˆ ˆ
X X =
A B R 1
1 0 0 
(3) Not commutative
 
A =
R 0 cos -sin
B  
A B ≠ B A
R R R R
 
0 sin cos  B C C B
EEuulleerr AAnngglleess ((11))
Euler angles describe a sequence of three rotations about different
axes in order to align one coord. system with a second coord. system.
ˆ α ˆ β ˆ γ
Rotate about Z by Rotate about Y by Rotate about X by
A B C
ˆ
ˆ ˆ ˆ Z
ZA ZB Zˆ ZB Zˆ C
C
D
β γ
ˆ
Y ˆ
Y
B Yˆ D
B γ
α
ˆ
Y ˆ
ˆ A X ˆ
X B β Y Yˆ
A α C
C
ˆ ˆ
X X ˆ ˆ
X X
B C
C D
cosα -sinα 0 cosβ 0 sinβ 1 0 0 
     
A = α α B = C = γ γ
R sin cos 0 R 0 1 0 R 0 cos -sin
B   C   D  
   β β  γ γ
 0 0 1 -sin 0 cos  0 sin cos 
A = A B C
R R R R
D B C D