# Attitude Determination and Control by nikeborome

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```									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
–   Aerodynamic
–   Solar Pressure
•   Sensors
–   Sun
–   Earth
–   Star
–   Magnetometers
–   Inertial Measurement Units
•   Actuators
–   Dampers
–   Magnetic Torque Rods
–   Wheels
–   Thrusters
INTRODUCTION
Introduction
• Attitude Determination and Control
– 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
Z

Y

X

Velocity Vector
Control Loops
Disturbance Torques

Desired                                                                                    Actual
Attitude                                          Commands
Attitude                            Attitude           Attitude
Control       e.g. increase         Actuators
e.g. +/- 3 deg                                                                             e.g. – 4 deg
Ram pointing
Ram pointing
100rpm

Attitude                 Attitude
Estimated        Determination              Sensors
e.g. – 3.5 deg
Ram pointing                                             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                  I xy       I xz   x 
                                                   
H   H y    I yx               I yy        I yz   y 
 H z    I zx
                             I zy       I zz    z 
 
where the cross-term products of inertia are equal (i.e. Ixy=Iyx)
Mass Moment of Inertia
• For a particle     O

IO  r m     2
r

m

O

• For a rigid body
O

I   r 2 dm   r 2 dm
r
dm                       m

m            I   r 2  dV
O                        V
Mass MOI

I xx   y  z dm
2        2

I yy     x   2
z   2
dm   Rotational Energy:

I zz     x
2
y   2
dm           1
E  I ij i  j
2
I xy    xy dm

I xz    xz dm

I yz    yz dm
Mass MOI
• Like any symmetric
tensor, the MOI            I x   0    0
tensor can be              0
I       Iy   0 
reduced to diagonal
form through the
appropriate choice of      0
      0    Iz 

axes (XYZ)
• Diagonal components              
are called the
Principle Moments of
H  I
Inertia
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
r’
d                     I  I  md   2

r

O
Control Strategies
• Deploy gravity
• Coarse roll and
pitch control
• No yaw control
surface
• Limited to near
Earth satellites
Best to design such that Ipitch > Iroll > Iyaw
Spin Stabilization
• Entire spacecraft
vertical axis
• Spinning sensors
• Cylindrical
geometry and solar
arrays
Spin Stability
UNSTABLE                    STABLE
S

S

T

T

IS                           IS
1                           1
IT                           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                                   Dy H
F
• Determine the angle Dy                        

2 FR(Dt )      Df                  Df
Dy            ; 
I          Dt
R
2 FR(Df )
Dy 
I 2                        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
• Cylindrical geometry and
solar arrays
3-Axis Stabilization
• Active stabilization of all three
axes
– Thrusters
– Momentum (Reaction) Wheels
• Momentum dumping
– No de-spin required for
– Accurate pointing
– Complex
Disturbance Torques
External Disturbance Torques
NOTE: The magnitudes of the torques is
dependent on the spacecraft design.
Drag
Torque (au)

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

        
  I
T H
  
T  r F
3                                   z
Tg     3
I z  I y sin 2 
2R
where:
y
  Earth's gravitational parameter
I y , I z  S/C mass moments of inertia
  maximum deviation away from vertical 
Magnetic Torque
Tm  m xB
where:
Tm  magnetic disturbance torque

m  S/C residual magnetic dipole Amp  m 2   
B  strength of Earth's magnetic field
M
  3
for points above the equator
R
2M
 3 for points above the poles
R

M  Earth's magnetic moment 7.96  1015 tesla  m 3   

*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  c g 
1
where:          F  C D Av 2
2
Ta  aerodynamic disturbance torque
  atmospheric density
C D  coefficient of drag typical S/C values are 2 - 2.5
A  cross- sectional area
v  velocity
C pa  center of atmospheric pressure
Cg  center of gravity
Solar Pressure Torque
Tsrp  F c ps  c g 

As 1    cosi
Fs
where:
F
c
Tsrp  solar radiation presuredisturbance torque
c ps  center of solar radiation pressure
c g  center of gravity
W
Fs  solar flux density  2 
m 
c  speed of light
As  area of illuminate d surface
  reflectance factor 0    1, typical value 0.6 for S/C
i  sun incidence angle
FireSat Example
Disturbing Torques
• All of these disturbing torques
can also be used to control the
satellite
–   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

IMU                     Drift: 0.0003 – 1 deg/hr      Requires updates
0.001 deg/hr nominal
Star Sensor                  1 arcsec – 1 arcmin      2-axis for single star
(0.0003 – 0.001 deg)      Multiple stars for map
Sun Sensor                      0.005 – 3 deg                Eclipse
0.01 deg nominal
Earth Sensor
GEO                     < 0.1 – 0.25 deg                    2-axis
LEO                       0.1 – 1 deg
Magnetometer                     0.5 – 3 deg                 < 6000 km
Difficult for high i
Actuators
Attitude Control
• Actuators come in two types
– Passive
•   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

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