1. Attitude Determination and Control
Dr. Andrew Ketsdever
MAE 5595

2. Outline Introduction Control Strategies Disturbance Torques Sensors
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

3. INTRODUCTION

4. 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

5. 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

6. Introduction Z
Nadir Y X
Velocity Vector

7. Control Loops Disturbance Torques Spacecraft Dynamics - Rigid Body
Attitude
Control
Task
Actuators
Commands
e.g. increase
Wheel speed
100rpm
Desired
e.g. +/- 3 deg
Ram pointing
Sensors
Determination
Actual
e.g. – 4 deg
Estimated
e.g. – 3.5 deg
Spacecraft Dynamics
- Rigid Body
- Flexible Body (non-rigid)

8. Mass Moment of Inertia
where H is the angular momentum, I is the mass moment of inertia tensor, and W is the angular velocity
where the cross-term products of inertia are equal (i.e. Ixy=Iyx)

9. Mass Moment of Inertia
For a particle
For a rigid body

10. Mass MOI
Rotational Energy:

11. 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

12. 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.

13. ADCS Design

14. ADCS Design

15. ADCS Design

16. ADCS Design

17. ADCS Design

18. Control Strategies

20. Gravity Gradient Stabilization
Deploy gravity gradient boom
Coarse roll and pitch control
No yaw control
Nadir pointing surface
Limited to near Earth satellites
Best to design such that Ipitch > Iroll > Iyaw

21. Spin Stabilization Entire spacecraft rotates about vertical axis
Spinning sensors and payloads
Cylindrical geometry and solar arrays

22. Spin Stability
UNSTABLE
STABLE S S T T

23. 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
Determine the angle Dy Dy H F w Df R F

24. 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

25. 3-Axis Stabilization Active stabilization of all three axes Advantages
Thrusters
Momentum (Reaction) Wheels
Momentum dumping
Advantages
No de-spin required for payloads
Accurate pointing
Disadvantages
Complex
Added mass

26. Disturbance Torques

27. 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)

28. 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

29. Disturbing Torques

30. Gravity Gradient Torquez y q
where:

31. Magnetic Torque where:
*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

32. Aerodynamic Torque
where:

33. Solar Pressure Torque
where:

34. FireSat Example

35. 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

36. Sensors

37. 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

38. Attitude Determination

39. Actuators

40. Attitude Control Actuators come in two types Passive Active
Gravity Gradient Booms
Dampers
Yo-yos
Spinning
Active
Thrusters
Wheels
Gyros
Torque Rods

41. 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
High Mass and Power
Thrusters
0. 1º to 1º
Propellant limited, Large impulse

42. Attitude Control