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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”, 2nd Ed. 1978

[2] Wiley J. Larson & James R. Wertz, “Space Mission Analysis and Design”, 2nd Ed. 1992

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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

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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

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Impact of Mission Requirements and Other Subsystems on ADCS

1. Spinner vs. Active vs. Passive2. Attitude determination (On-orbit or Ground)3. Sensor selection4. Actuator selection5. Computational architecture

Special thermal maneuvers required ?

Data processing capability

Antenna pointing accuracy ?

1. ADCS load2. Special regulation

1. Solar array pointing requirement ?

1. Center of mass constraints2. Inertia constraints3. Flexibility constraints4. Thruster location5. 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

Mission Power

Power

Structures

Thermal

Propulsion

Communications

1. Thruster size2. Propellant load

Command & Data Handling

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ADCS Design Process

Step Inputs Outputs1a) Define control mode1b) 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

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ADCS Design Process (Cont.)-Typical ADCS Modes

Mode Description

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.

AcquisitionInitial determination of attitude and stabilization of spacecraft. Also may be used to recover from power upsets or emergencies.

NormalUsed for the vast majority of the mission. Requirements for this mode should derive system design.

Slew Reorienting 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.

SpecialRequirement may be different for special targets or time period, such as eclipse.

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ADCS Design Process (Cont.)-Typical ADCS Requirements

Determination Definition Examples/Comments

AccuracyHow 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

RangeRange of angular motion over which accuracy must be met

Any attitude within 30 deg of nadir

Control Definition Examples/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

RangeRange of angular motion over which control performance must be met

All attitude, within 50 deg of nadir, within 20 deg of Sun

JitterA 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

DriftA 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 TimeSpecifies allowed time to recover from maneuvers or upsets

2 deg max motion; may be used to limit overshoot or nutation

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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.

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ADCS Design Process (Cont.) - ADCS Control Methods and their Capabilities

TypePointing Options

Attitude Maneuverabilit

y

Typical Accuracy

Lifetime Limit

Gravity Gradient Earth local vertical only

Very limited +/- 5o No limit

Passive Magnetic Earth local vertical only

Very limited +/- 5o No limit

Spin Stabilization Inertially fixed (any direction)

High propellant usage to move stiff momentum vector

+/- 0.1o ~ +/- 1.0o (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

+/- 0.1o ~ +/- 1.0o

Propellant (if applies)Life of sensor and wheel bearing

Zero Momentum Bias(Thruster)

No constraints No constraintsHigh rates possible

+/- 0.1o ~ +/- 5.0o

Propellant

Zero Momentum Bias(Three wheels)

No constraints No constraints +/- 0.001o ~ +/- 1.0o

Life of sensor and wheel bearing

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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

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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

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-ADCS Design Process (Cont.) Typical ADCS Sensors

SensorsTypical

PerformanceWeight

(kg)Power(Watt)

Gyro Drift rate: 0.003o/hr ~ 1o/hr

3 ~ 25 10 ~ 200

Sun sensor Accuracy: 0.005o ~ 3o 0.5 ~ 2 0 ~ 3

Star sensor Accuracy: 0.0003o ~ 0.01o 3 ~ 7 5 ~ 20

Horizon sensor

Accuracy: 0.1o ~ 1o 2 ~ 5 0.3 ~ 10

Magnetometer Accuracy: 0.5o ~ 3o 0.6 ~ 1.2 0 ~ 1

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ADCS Design Process (Cont.) -Typical ADCS Actuators

ActuatorsTypical

PerformanceWeight

(kg)Power(Watt)

Thrusters

• Hydrazine

• Cold gas

0.5 ~ 9000 N*< 5

VariableVariable

N/AN/A

Reaction Wheel0.4 ~ 400 Nms (momentum)0.01 ~ 1 Nm (torque)

2 ~ 20 10 ~ 110

Control moment gyro

25 ~ 500 Nm (torque) > 40 90 ~ 150

Magnetic torquer 1 ~ 4000 Am2 0.4 ~ 50 0.6 ~ 16

* Multiply by moment arm (typical 1 or 2 m) to get torque

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Spacecraft Coordinate Systems

Spacecraft body Coordinates Earth-Centered Earth-Fixed (ECEF) Coordinates

Local Vertical Local Horizontal (LVLH) Coordinates Earth Centered Inertial (ECI) Coordinates

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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 = [ n1*sin( /2) n2*sin( /2) n3*sin( /2) cos( /2) ]

– N [ n1 n2 n3 ]

cossin0

sincos0

001

cos0sin

010

sin0cos

100

0cossin

0sincos

),,(123R

321 nnnN

X X’

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Spacecraft Dynamic & Kinematical Equations

• Dynamic Equation (3x1) to be stabilized:

– I: Spacecraft moment of inertia

– N: External torque (Thruster & Environment)

– Hw: Wheel angular momentum

– w: Spacecraft angular velocity

• Kinematical Equation (4x1):– Q: Spacecraft quaternion

)( ww HIww

dt

dHN

dt

dwI

4

3

2

1

4321

0

0

0

0

2

1

2

1

q

q

q

q

www

www

www

www

Q

qqqqQ

QwQ

zyx

zxy

yxz

xyz

T

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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.

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RequirementSpecified

Performance

Pointing Knowledge

2 in Roll2 in Pitch2 in Yaw

Pointing Accuracy

5 in Roll2 in Pitch5 in Yaw

Position Knowledge 100 m

FORMOSAT-3 Design Example- Requirements for ADCS

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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#3Thruster#4

Thruster#1 & #2

Location change

Legend:

FORMOSAT-3 Design Example- ADCS Component Locations

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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

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Mode Launch Stabilize Safehold Nadir Nadir -Yaw Thrust

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 Reset While tumbling ARS diverged

Nadir error > expected value

, or ARS converged

Nadir error <= expected value

, or ARS converged

Ground command

ExitSolar 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 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 value3. 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

Spacecraft is tumbling

ARS has diverged or no GPS

FORMOSAT-3 Design Example- Control Modes & Requirements Definition Flow Chart

23Orbit Plane

Earth Magnetic Field

FORMOSAT-3

FORMOSAT-3 Design Example- Spacecraft Orientation in Stabilize/Safehold Mode

24Orbit Plane

ROCSAT-3

FORMOSAT-3 Design Example- Spacecraft Orientation in Nadir/Nadir-Yaw Mode

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Mode Controller Sensors Actuators

Launch none Switch on / No used Switch on / No used

Stabilize B-dotMagnetometer, Coarse Sun Sensor (CSS)

Magnetic Rod

Safehold B-dot Magnetometer, CSS Magnetic Rod

Nadir PDGPS, Magnetometer

CSS, Earth SensorMagnetic Rod, Wheel

Nadir-Yaw PDGPS, Magnetometer

CSS, Earth SensorMagnetic Rod, Wheel

Thrust PID + PWMGPS, Magnetometer

CSS, Earth SensorThruster

FORMOSAT-3 Design Example- Modes Controller and Component Utilization

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-3

-2

-1

0

1

2

3

4

0 1 2 3 4 5 6 7 8 9

Time (orbits)

S/C Rates: Degree/s

RollPitchYaw

-15

-10

-5

0

5

10

15

0 1 2 3 4 5 6 7 8 9

Time (orbits)

Command Magnetic Dipole : A-m2

MxMyMz

0

20

40

60

80

100

120

140

160

180

0 1 2 3 4 5 6 7 8 9

Time (orbits)

Angle between Body Z and Earth Magnetic Field (Degree)

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

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-3

-2

-1

0

1

2

3

4

0 1 2 3 4 5 6 7 8 9

Time (orbits)

S/C Rates: Degree/s

RollPitchYaw

-150

-100

-50

0

50

100

150

0 1 2 3 4 5 6 7 8 9

Time (orbits)

S/C attitude errors : Degree

xyz

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5 6 7 8 9

Time (orbits)

Wheel Momentum: N-m-s

xyz

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

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-15

-10

-5

0

5

10

15

0 1 2 3 4 5 6 7 8 9

Time (orbits)

Command Magnetic Dipole : A-m2

MxMyMz

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6 7 8 9

Time (orbits)

Error Angle between Body Z and Nadir (Degree)

Magnetic Dipole

Angle between body +Z and Nadir

FORMOSAT-3 Design Example- Nadir-Yaw Mode Simulation (Cont.)

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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.