Attitude Determination and Control

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

2. Outline • Introduction • 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. Desired Attitude e.g. +/- 3 deg Ram pointing Actual Attitude e.g. – 4 deg Ram pointing Commands e.g. increase Wheel speed 100rpm Attitude Control Task Attitude Actuators Attitude Determination Task Attitude Sensors Estimated Attitude e.g. – 3.5 deg Ram pointing Control Loops Disturbance Torques 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 • 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. z y q Gravity Gradient Torque 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 • Gravity Gradient Booms • Dampers • Yo-yos • Spinning • Active • Thrusters • Wheels • Gyros • Torque Rods

41. Actuators

42. Attitude Control