1. 1 Spacecraft Attitude Determination and Control Hsiu-Jen Liu 劉修任 National SPace Organization 國家太空中心 May 12, 2005 Reference: [1] James R. Wertz, “Spacecraft Attitude Determination and Control”, 2 nd Ed. 1978 [2] Wiley J. Larson & James R. Wertz, “Space Mission Analysis and Design”, 2 nd Ed. 1992

2. 2 Course Outline  Attitude Determination and Control Subsystem (ADCS) Function  Impact of Mission Requirements and Other Subsystems on ADCS  ADCS Design Process Define ADCS Control Modes Define ADCS Requirements by Control Modes Select ADCS Control Methods and their Capabilities Attitude Control Type Environmental Disturbance Analysis ADCS Sensor Type ADCS Actuator Type  Spacecraft Coordinate Systems  Spacecraft Dynamic & Kinematical Equations  FORMOSAT-3 Design Example

3. 3 ADCS Function The ADCS stabilizes the spacecraft and orients it in desired directions during the mission despite the external disturbance torques acting on it: –To stabilize spacecraft after launcher separation –To point solar array to the Sun –To point payload (camera, antenna, and scientific instrument etc.) to desired direction –To perform spacecraft attitude maneuver for orbit maneuver and payloads operation This requires that the spacecraft determine its attitude, using sensors, and control it, using actuators

4. 4 Impact of Mission Requirements and Other Subsystems on ADCS 1. Spinner vs. Active vs. Passive 2. Attitude determination (On-orbit or Ground) 3. Sensor selection 4. Actuator selection 5. Computational architecture Special thermal maneuvers required ? Data processing capability Antenna pointing accuracy ? 1. ADCS load 2. Special regulation 1. Solar array pointing requirement ? 1. Center of mass constraints 2. Inertia constraints 3. Flexibility constraints 4. Thruster location 5. Sensor mounting 1. Earth-Pointing or inertial-Pointing ? 2. Control during  V burn ? 3. Separate payload platform ? 4. Accuracy/Stability needs ? 5. Slewing requirement ? 6. Orbit ? 7. Autonomy ? 8. Mission life ? 9. On-board navigation data required ? ADCS Trades MissionPower Structures Thermal Propulsion Communications 1. Thruster size 2. Propellant load Command & Data Handling

5. 5 ADCS Design Process StepInputsOutputs 1a) Define control mode 1b) Define or derive system-level requirements by control mode Mission requirements Mission profile Type of insertion for launch vehicle List of different control mode during mission Requirement and constraints 2) Select type of spacecraft control by attitude control mode Payload, thermal & power needs Orbit, pointing direction Disturbance environment Method for stabilizing and control: three-axis control, spinning, or gravity gradient 3) Quantify disturbance environment Spacecraft geometry Orbit/Solar/Magnetic models Mission profile Environmental disturbance: forces/torques 4) Select & size ADCS hardware Spacecraft geometry Pointing accuracy Orbit conditions Mission requirements Slew rate Sensor suite: Earth, Sun, inertial, or other sensing devices Actuators: reaction wheels, thrusters, or magnetic torquer Data processing requirements 5) Define determination and control Algorithms (Design/Analysis/Simulation) All of above Algorithms, parameters, and logic for each determination and control mode 6) Iterate and document All of above Refines requirements and design Subsystem specification

6. 6 ADCS Design Process (Cont.) -Typical ADCS Modes ModeDescription Orbit Insertion Period during and after boost while spacecraft is brought to final orbit. Options include no spacecraft control, simple spin stabilization of solid state rocket, and full spacecraft attitude control. Acquisition Initial determination of attitude and stabilization of spacecraft. Also may be used to recover from power upsets or emergencies. Normal Used for the vast majority of the mission. Requirements for this mode should derive system design. SlewReorienting the spacecraft when required. Contingency, or Safe Used in emergencies if regular mode fails or is disabled. May use less power or sacrifice normal operation to meet power or thermal constraints. Special Requirement may be different for special targets or time period, such as eclipse.

7. 7 ADCS Design Process (Cont.) -Typical ADCS Requirements DeterminationDefinitionExamples/Comments Accuracy How well a vehicle’s orientation with respect to an absolute reference is known 0.25 deg, 3-sigma, all axes; may be real-time or post-processed on the ground Range Range of angular motion over which accuracy must be met Any attitude within 30 deg of nadir ControlDefinitionExamples/Comments Accuracy How well the vehicle attitude can be controlled with respect to a commanded direction 0.25 deg, 3-sigma, including determination and control errors, may be taken with respect to an inertial or Earth-fixed reference Range Range of angular motion over which control performance must be met All attitude, within 50 deg of nadir, within 20 deg of Sun Jitter A specified angle bound or angular rate limit on short-term, high-frequency motion 0.1 deg /min, 1deg/s, 1 to 20 Hz; usually specified to keep spacecraft motion from blurring sensor data Drift A limit on slow, low-frequency vehicle motion. Usually expressed as angle/time 1 deg/hr, 5deg max. Used when vehicle may drift off target with infrequent resets Setting Time Specifies allowed time to recover from maneuvers or upsets 2 deg max motion; may be used to limit overshoot or nutation

8. 8 ADCS Design Process (Cont.) - Attitude Control Type Passive Control Techniques: –Gravity-gradient control uses the inertial properties of a spacecraft to keep it pointed toward the Earth. This relies on the fact that an elongated object in the gravity field tends to align its longitudinal axis through the Earth’s center. –Passive magnetic control uses permanent magnets on board the spacecraft to force alignment along the Earth’s magnetic field. This is most effective in near-equatorial orbits where the field orientation stays almost constant. –Spin stabilization is a passive control technique in which the entire spacecraft rotates so that its angular momentum vector remains approximately fixed in inertial space. Spin-stabilized spacecraft employ the gyroscopic stability to passively resist disturbance torques about two axes. Three-axis Active Control Technique: –Spacecraft stabilized in three axes are more common today than those using passive control. –It can be stable and accurate but also more expensive, complex, and potentially less reliable. –Broadly, these system take two forms: one uses momentum bias by placing a momentum wheel along the pitch axis; the other is called zero momentum with a reaction wheel on each axis. Either option usually need thrusters or magnetic torquers for wheel momentum unloading.

9. 9 ADCS Design Process (Cont.) - ADCS Control Methods and their Capabilities Type Pointing Options Attitude Maneuverability Typical Accuracy Lifetime Limit Gravity GradientEarth local vertical only Very limited+/- 5 o No limit Passive MagneticEarth local vertical only Very limited+/- 5 o No limit Spin StabilizationInertially fixed (any direction) High propellant usage to move stiff momentum vector +/- 0.1 o ~ +/- 1.0 o (proportional to spin rate) Propellant Pitch Momentum Bias Best suited for Earth local vertical pointing Momentum vector of the bias wheel prefers to stay normal to orbit plane +/- 0.1 o ~ +/- 1.0 o Propellant (if applies) Life of sensor and wheel bearing Zero Momentum Bias (Thruster) No constraints High rates possible +/- 0.1 o ~ +/- 5.0 o Propellant Zero Momentum Bias (Three wheels) No constraints +/- 0.001 o ~ +/- 1.0 o Life of sensor and wheel bearing

10. 10 ADCS Design Process (Cont.) -Control Example: Active Attitude Control System 控制器 (Controller) 致動器 (Actuators) 衛星動態 & 衛星軌道 感測器 (Sensors) 估測器 (Estimator) 濾波器 (Compensator) 1. 衛星姿態 (Quaternion) 2. 衛星角速度 (Angular Velocity) 1. 命令 : 衛星姿態 2. 命令 : 衛星角速度 3. 命令 : 衛星角加速度 1. 迴授訊號 : 衛星姿態 2. 迴授訊號 : 衛星角速度 General Structure of a Satellite Attitude Determination and Control Subsystem Implemented by Software ADCS Hardware 太空環境 (Environment) Disturbance

11. 11 ADCS Design Process (Cont.) -Typical Environmental Disturbance Gravity-Gradient Torque: –Any nonsymmetrical object of finite dimensions in orbit is subject to a gravitational torque because of the variation in the Earth’s gravitational force over the object Solar Radiation Torque: –Radiation incident on a spacecraft’s surface produces a force which results in a torque about the spacecraft’s center of mass Aerodynamic Torque –The interaction of the upper atmosphere with a spacecraft’s surface produces a torque about the center of mass Magnetic Disturbance Torque –Magnetic disturbance torques result from the interaction between the spacecraft’s residual magnetic field and the geomagnetic field

12. 12 -ADCS Design Process (Cont.) Typical ADCS Sensors Sensors Typical Performance Weight (kg) Power (Watt) Gyro Drift rate: 0.003 o /hr ~ 1 o /hr 3 ~ 2510 ~ 200 Sun sensor Accuracy: 0.005 o ~ 3 o 0.5 ~ 20 ~ 3 Star sensor Accuracy: 0.0003 o ~ 0.01 o 3 ~ 75 ~ 20 Horizon sensor Accuracy: 0.1 o ~ 1 o 2 ~ 50.3 ~ 10 Magnetometer Accuracy: 0.5 o ~ 3 o 0.6 ~ 1.20 ~ 1

13. 13 ADCS Design Process (Cont.) -Typical ADCS Actuators ActuatorsTypical Performance Weight (kg) Power (Watt) Thrusters Hydrazine Cold gas 0.5 ~ 9000 N* < 5 Variable N/A Reaction Wheel 0.4 ~ 400 Nms (momentum) 0.01 ~ 1 Nm (torque) 2 ~ 2010 ~ 110 Control moment gyro 25 ~ 500 Nm (torque)> 4090 ~ 150 Magnetic torquer 1 ~ 4000 Am 2 0.4 ~ 500.6 ~ 16 * Multiply by moment arm (typical 1 or 2 m) to get torque

14. 14 Spacecraft Coordinate Systems Spacecraft body Coordinates Earth-Centered Earth-Fixed (ECEF) Coordinates Local Vertical Local Horizontal (LVLH) Coordinates Earth Centered Inertial (ECI) Coordinates

15. 15 Spacecraft Attitude Definition Spacecraft Attitude: the orientation of the body coordinate w.r.t. the ECI (or LVLH) coordinate system Euler angle representation: –[    ] : rotate  angle around X-axis, then rotate  angle around Y-axis, then rotate  angle around Z-axis –The transition matrix: Quaternion: rotation an angle (  ) around arbitrary axis (N) of ECI coordinate system: –Q = [ n 1 *sin(  /2) n 2 *sin(  /2) n 3 *sin(  /2) cos(  /2) ] –N  [ n 1 n 2 n 3 ] X X’

16. 16 Spacecraft Dynamic & Kinematical Equations Dynamic Equation (3x1) to be stabilized: –I: Spacecraft moment of inertia –N: External torque (Thruster & Environment) –H w : Wheel angular momentum –w: Spacecraft angular velocity Kinematical Equation (4x1): –Q: Spacecraft quaternion

17. 17 FORMOSAT-3 Design Example - Mission Requirements FORMOSAT-3 program has a goal to launch a constellation of six micro-satellites to collect atmospheric remote sensing data for monitoring weather and conducting climate, ionosphere, and gravity research.

18. 18 Requirement Specified Performance Pointing Knowledge  2  in Roll  2  in Pitch  2  in Yaw Pointing Accuracy  5  in Roll  2  in Pitch  5  in Yaw Position Knowledge100 m FORMOSAT-3 Design Example - Requirements for ADCS

19. 19 CSS#5 CSS#6 CSS#7 CSS#8 CSS#1 CSS#3 CSS#4 CSS#2 Reaction Wheel X-axis Magnetic Torquer Rod Z-axis Magnetic Torquer Rod Y-axis Magnetic Air-Core Torquer Thruster#3 Thruster#4 Thruster#1 & #2 Location change Legend: FORMOSAT-3 Design Example - ADCS Component Locations

20. 20 FORMOSAT-3 Design Example - ADCS Sensors & Actuators Sensors Actuators Earth Horizon Sensor Magnetometer Coarse Sun Sensor Solid Core Torque Rod Air Core Torquer Reaction Wheel

21. 21 ModeLaunchStabilizeSafeholdNadirNadir -YawThrust Purpose Prevent any actuation pending deployment Despin and hold with +Z along Earth Magnetic Field Temporary mode while Attitude Reference System (ARS) initializes +Z to nadir +Z to nadir and yaw to commanded angle Orbit transfer Entry ResetWhile tumblingARS diverged Nadir error > expected value, or ARS converged Nadir error <= expected value, or ARS converged Ground command Exit Solar Array deployed Earth Magnetic Field aligned with +Z for the expected value ARS converged Nadir error <= expected value, or ARS diverged, no GPS Nadir error > expected value, or ARS diverged, noGPS Thrust completed FORMOSAT-3 Design Example - Control Modes & Requirements Definition

22. 22 Thrust Mode Launch Mode Safehold Mode Nadir-Yaw Mode Spacecraft is tumbling Separation and deployment observed from EPS ARS has converged and Nadir pointing < the expected value Command from Ground Nadir pointing < the expected value ARS has diverged or no GPS ARS has converged and Nadir pointing > the expected value Stabilize Mode Nadir Mode ARS has diverged or no GPS Spacecraft is tumbling 1 Initially injected into parking orbit 2 Flight computer is rebooted 1.The argument of latitude of the north of the orbit within the expected value 2.Body rate < the expected value 3.The error angle between +Z body axis and the Earth’s magnetic field vector is less than the expected value Thrust Completed Nadir pointing > the expected value Spacecraft is tumbling ARS has diverged or no GPS FORMOSAT-3 Design Example - Control Modes & Requirements Definition Flow Chart

23. 23 Orbit Plane Earth Magnetic Field FORMOSAT-3 FORMOSAT-3 Design Example - Spacecraft Orientation in Stabilize/Safehold Mode

24. 24 Orbit Plane ROCSAT-3 FORMOSAT-3 Design Example - Spacecraft Orientation in Nadir/Nadir-Yaw Mode

25. 25 ModeControllerSensorsActuators LaunchnoneSwitch on / No used StabilizeB-dot Magnetometer, Coarse Sun Sensor (CSS) Magnetic Rod SafeholdB-dotMagnetometer, CSSMagnetic Rod NadirPD GPS, Magnetometer CSS, Earth Sensor Magnetic Rod, Wheel Nadir-YawPD GPS, Magnetometer CSS, Earth Sensor Magnetic Rod, Wheel ThrustPID + PWM GPS, Magnetometer CSS, Earth Sensor Thruster FORMOSAT-3 Design Example - Modes Controller and Component Utilization

26. 26 FORMOSAT-3 Design Example - Stabilize/Safehold Mode Simulation Attitude Rate Magnetic Dipole Angle between body +Z and Earth Magnetic Field Initial Conditions: 1.10° attitude bias for each axis 2.2°/s attitude rate for each axis

27. 27 Initial Conditions: 1.10° attitude bias for each axis 2.2°/s attitude rate for each axis Attitude Rate Attitude Bias Wheel Momentum FORMOSAT-3 Design Example - Nadir-Yaw Mode Simulation

28. 28 Magnetic Dipole Angle between body +Z and Nadir FORMOSAT-3 Design Example - Nadir-Yaw Mode Simulation (Cont.)

29. 29 Exercise 1.Define the mission requirements of your satellite. 2.According to the mission requirements, define ADCS control modes and corresponding ADCS requirements. 3.Select the proper control type for each control modes.