1. Introduction to Attitude Control Systems
MAE 155A
GN/MAE155A

2. Determination & Attitude Control Systems (DACS)
Introduction
DACS Basics
Attitude Determination and Representation
Basic Feedback Systems
Stabilization Approaches
GN/MAE155A

3. Determination & Attitude Control Systems (DACS)
Control of SC orientation: Yaw, Pitch, Roll
3 Components to DACS:
Sensor: Measure SC attitude
Control Law: Calculate Response
Actuator: Response (Torque)
Example: Hubble reqts 2x10-6 deg pointing accuracy => equivalent to thickness of human hair about a mile away!
GN/MAE155A

4. Determination & Attitude Control Systems (DACS)
Introduction
DACS Basics
Attitude Determination and Representation
Basic Feedback Systems
Stabilization Approaches
GN/MAE155A

5. DACS Basics S/C Correction Attitude Errors Sensors Torquers Gyros
Thrusters
Reaction Wheels
Momentum Wheels
CMGs
S/C
Sensors
Gyros
Horizon Sensors
Sun Sensors
Correction
Attitude Errors
Computer
Control Law
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6. Determination & Attitude Control Systems (DACS)
Spinning Spacecraft provide simple pointing control along single axis (low accuracy)
Three axis stability provides high accuracy pointing control in any direction
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7. DACS Design Considerations: Mission Reqts Disturbance Calcs
DACS System Design
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8. DACS Reqts Definition Summarize mission pointing reqts
Earth (Nadir), Scanning, Inertial
Mission & PL Pointing accuracy
Note that pointing accuracy is influenced by all 3 DACS components
Pointing accuracy can range from < to 5 degrees
Define Rotational and translational reqts for mission: Magnitude, rate and frequency
Calculate expected torque disturbances
Select ACS type; Select HW & SW
Iterate/improve as necessary
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9. Torque Disturbances Internal Cyclic and secular External
Gravity gradient: Variable g force on SC
Solar Pressure: Moment arm from cg to solar c.p.
Magnetic: Earth magnetic field effects
Aero. Drag: Moment arm from cg to aero center
Internal
Appendage motion, pointing motors- misalign, slosh
Cyclic and secular
Cyclic: varies in sinusoidal manner during orbit
Secular: Accumulates with time
GN/MAE155A

10. Determination & Attitude Control Systems (DACS)
Introduction
DACS Basics
Attitude Determination and Representation
Basic Feedback Systems
Stabilization Approaches
GN/MAE155A

11. SC Attitude Determination Fundamentals
Attitude determination involves estimating the orientation of the SC wrt a reference frame (usually inertial or geocentric), the process involves:
Determining SC body reference frame location from sensor measurements
Calculating instantaneous attitude wrt reference frame
Using attitude measurement to correct SC pointing using actuators (or torquers)
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12. Basic SC Attitude Determination
Sensor
Data
State
Estimation
Attitude Calculation
Gyros
Star/Sun Sensor
Magnetometer
Batch Estimators
Least Squares
Kalman Filtering
Euler Angles
DCM
Quaternions
Control Law
Used to Determine
Required Correction
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13. Attitude Sensors
Performance requirements based on mission
Weight, power and performance trades performed to select optimal sensor
Multiple sensors may be used
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14. State Estimation Approaches
Estimate SC orientation using data measurements
Estimates typically improve as more data are collected (assuming no ‘jerk motion’)
Estimation theory and statistical methods are used to obtain best values
Least squares and Kalman filtering are most common approaches
Least squares minimizes square of error (assumes Gaussian error distribution)
Kalman filter minimizes variance
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15. SC Attitude Representation
SC frame of reference typically points SC Z axis anti-Nadir, and X axis in direction of velocity vector
Relationship between SC and inertial reference frame can be defined by the 3 Euler angles (Yaw, Pitch and Roll)
Note that both magnitude and sequence of rotation affect transformation between SC and inertial reference frame
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16. SC Attitude Representation Using Euler Rotation Angles
The Direction Cosine Matrix (DCM) is the product of the 3 Euler rotations in the appropriate sequence (Yaw-Pitch-Roll)
DCM ~ R = R * R * R3
Ref: Brown, Elements of SC Design
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17. Direction Cosine Rotation Matrix
The DCM is given by:
Note that each transformation requires substantial arithmetic and
trigonometric operations, rendering it computationally intensive
An alternative, and less computationally intensive, approach to using
DCM involves the use of Quaternions
Ref: Brown, Elements of SC Design
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18. Quaternion Definition
Euler’s theorem states that any series of rotation of a rigid body can be represented as a single rotation about a fixed axis
Orientation of a body axis can be defined by a vector and a rotation about that vector
A quaternion, Q, defines the body axis vector and the scalar rotation => 4 elements
Q = i.q1 + j.q2 + k.q3 + q4 , where i2 = j2 = k2 = -1
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19. Basic Quaternion Properties
Given the quaternion Q, where Q = i.q1 + j.q2 + k.q3 + q4 ; we have
ij = - ji = k; jk = -kj = i; ki = -ik = j
Two quaternions, Q and P are equal iff all their elements are equal, i.e., q1 = p1 ; q2 = p2 ; q3 = p3
Quaternion multiplication is order dependent, R=Q*P is given by: R = (i.q1 + j.q2 + k.q3 + q4)*(i.p1 + j.p2 + k.p3 + p4)
The conjugate of Q is given by Q*, where Q* = -i.q1 - j.q2 - k.q3 + q4
The inverse of Q, Q-1 = Q* when Q is normalized
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20. Basic Quaternion Properties
The DCM can be expressed in terms of quaternion elements as:
The quaternion transforming frame A into frame B is given by:
VB = Qab VA (Qab)*
Quaternions can also be combined as:
Qac = Qbc Qab
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21. Comparison of 3-Axis Attitude Representation
Ref: Brown, Elements of SC Design
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22. Determination & Attitude Control Systems (DACS)
Introduction
DACS Basics
Attitude Determination and Representation
Basic Feedback Systems
Stabilization Approaches
GN/MAE155A

23. Feedback Loop Systems
The control loop can use either an open or closed system. Open loop is used when low accuracy is sufficient, e.g., pointing of solar arrays.
Generic closed-loop system:
Disturbance
e = r + a
Control Law,
Actuators
Spacecraft
Dynamics
Output
Reference
Error r a a
Ref: Brown, Elements of SC Design
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24. Basic Rotation Equations Review
Angular displacement:  = 1/2  t2 = d  /dt (note ‘burn’ vs. maneuvering time)
Angular speed:  =  t
Angular acceleration:  = T/Iv Angular Momentum: H = Iv  => H = T t
Where,
 ~ rotation angle;  ~ angular acceleration T ~ torque; Iv ~ SC moment of Inertia H ~ Angular Momentum;  ~angular speed
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25. Basic Rotation Equations Review
Torque equations: T = dH/dt = Iv d /dt = Iv d2 / dt2 (Iv assumed constant) Note that the above equations are scalar representations of their vector forms (3D) Hx  Hy
Spin axis precession
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26. Determination & Attitude Control Systems (DACS)
Introduction
DACS Basics
Attitude Determination and Representation
Basic Feedback Systems
Stabilization Approaches
GN/MAE155A

27. Spin Stabilized Systems
Spinning SC (spinner): resists disturbance toques (gyroscopic effect)
Disturbance along H vector affects spin rate
Disturbance perp. to H => Precession
Adv: Low cost, simple, no propel mgmt
Disadv:- Low pointing accuracy (> 0.3 deg) I about spinning axis >> other I Limited maneuvering, pointing
Dual spin systems: major part of SC spins while a platform (instruments) is despun
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28. SC Stabilization SystemsF2
- Gravity Gradient (G2) Systems (passive):
Takes adv of SC tendency to align its long axis along g vector,
g = GM/r; r1<r2 => F1>F => Restoring Torque
-Momentum Bias: Use momentum wheel to provide inertial stiffness in 2 axes, wheel speed provides
control in 3rd axis r2 F1 r1
Stability condition: Ir r > (Ixx-Iyy) y
Pitch axis (y)
wheel SC V
Nadir
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29. SC Stabilization Systems
Reaction Wheels (RW)
Motor spins a small free rotating wheel aligned w. vehicle control axis (~low RPM)
One wheel per axis needed, however, additional wheels are used for redundancy
RW only store, not remove torques
Counteracting external torque is needed to unload the stored torque, e.g., magnetic or rxn jets (momentum dumping)
Speed of wheel is adjusted to counter torque
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30. SC Stabilization Systems
RW at high RPM are termed momentum wheels.
Also provides gyroscopic stability
Magnetic (torque) coils can be used to continuously unload wheel
Wheels provide stability during periods of high torque disturbances
Control Moment Gyro
Gimbaled momentum wheel
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31. SC Stabilization Systems (External):
Thrusters: Used to provide torque (external) on SC
Magnetic torque rods
Can be used to provide a controlled external torque on SC
Need to minimize potential residual disturbance torque T = M x B where M~dipole w. magnetic moment M B~Local Flux density
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32. Reaction Wheels
Magnetometers
Magnetic Torquers
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33. DACS Summary
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34. Conclusions
Examples
References
Discussion & Questions
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