Attitude Determination and Control

Dr. Andrew Ketsdever

MAE 5595

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

INTRODUCTION

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

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

Introduction

Velocity Vector

X

Y

Z

Nadir

Control Loops

Spacecraft Dynamics - Rigid Body - Flexible Body (non-rigid)

AttitudeControl

Task

AttitudeActuators

Commands

e.g. increaseWheel speed 100rpm

DesiredAttitude

e.g. +/- 3 degRam pointing

AttitudeSensors

AttitudeDetermination

Task

ActualAttitude

e.g. – 4 degRam pointing

EstimatedAttitudee.g. – 3.5 degRam pointing

Disturbance Torques

Mass Moment of Inertia

IH

z

y

x

zzzyzx

yzyyyx

xzxyxx

z

y

x

III

III

III

H

H

H

H

where H is the angular momentum, I is the mass moment of inertia tensor, and is the angular velocity

where the cross-term products of inertia are equal (i.e. Ixy=Iyx)

Mass Moment of Inertia

• For a particle

• For a rigid body

m

r

O

O

dm

m

r

O

O

I r mO 2

I r dm r dmm

2 2

I r dVV

2

Mass MOI

dmyzI

dmxzI

dmxyI

dmyxI

dmzxI

dmzyI

yz

xz

xy

zz

yy

xx

22

22

22

jiijIE 2

1

Rotational Energy:

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

z

y

x

I

I

I

I

00

00

00

IH

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.

I I md 2

O

O

CM

d

r

r’

m

ADCS Design

ADCS Design

ADCS Design

ADCS Design

ADCS Design

Control Strategies

Gravity Gradient Stabilization

• Deploy gravity gradient boom

• Coarse roll and pitch control

• No yaw control• Nadir pointing

surface• Limited to near

Earth satellitesBest to design such that Ipitch > Iroll > Iyaw

Spin Stabilization

• Entire spacecraft rotates about vertical axis

• Spinning sensors and payloads

• Cylindrical geometry and solar arrays

Spin Stability

1T

S

I

I

S

T

S

T

1T

S

I

I

UNSTABLE STABLE

Satellite Precession• Spinning Satellite• Satellite thruster is fired to

change its spin axis• During the thruster firing, the

satellite rotated by a small angle

• Determine the angle F

F

R

H

2

)(2

;)(2

I

FRtI

tFR

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

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

Disturbance Torques

External Disturbance Torques

Orbital Altitude (au)

Tor

que

(au)

SolarPress.

Drag

Gravity

Magnetic

LEO GEO

NOTE: The magnitudes of the torques isdependent on the spacecraft design.

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

Disturbing Torques

FrT

IHT

Gravity Gradient Torque

2sin

2

33 yzg II

RT

where:

verticalfromaway deviation maximum

inertia of moments mass S/C ,

radiusorbit

parameter nalgravitatio sEarth'

gradientgravity maximum

zy

g

II

R

T

z

y

Magnetic Torque

where:

BxmTm

meters radiusorbit

m tesla10 7.96moment magnetic sEarth'

poles theabove pointsfor 2

equator theabove pointsfor

field magnetic sEarth' ofstrength

mAmp dipole magnetic residual S/C

torqueedisturbanc magnetic

315

3

3

2

R

M

R

MR

M

B

m

Tm

*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

Aerodynamic Torque

where:

gpaa ccFT

2

2

1AvCF D

gravity ofcenter C

pressure catmospheri ofcenter C

velocity

area sectional-cross

2.5 - 2 are valuesS/C typical drag oft coefficien

density catmospheri

torqueedisturbanc caerodynami

g

pa

v

A

C

T

D

a

Solar Pressure Torque

where:

gpssrp ccFT

iAc

FF s

s cos1

angle incidencesun

S/Cfor 0.6 value typical1,0factor ereflectanc

surface dilluminate of area

light of speed

m

Wdensity flux solar

gravity ofcenter c

pressureradiation solar ofcenter

torqueedisturbanc presureradiation solar

2

g

i

A

c

F

c

T

s

s

ps

srp

FireSat Example

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

Sensors

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

Attitude Determination

Earth Horizon Sensor Sun Sensor Star Tracker

Sensor Accuracies Comments

IMU Drift: 0.0003 – 1 deg/hr 0.001 deg/hr nominal

Requires updates

Star Sensor 1 arcsec – 1 arcmin (0.0003 – 0.001 deg)

2-axis for single star Multiple stars for map

Sun Sensor 0.005 – 3 deg 0.01 deg nominal

Eclipse

Earth Sensor GEO LEO

< 0.1 – 0.25 deg

0.1 – 1 deg

2-axis

Magnetometer 0.5 – 3 deg < 6000 km Difficult for high i

Actuators

Attitude Control

• Actuators come in two types– Passive

• Gravity Gradient Booms• Dampers• Yo-yos• Spinning

– Active• Thrusters• Wheels• Gyros• Torque Rods

ActuatorsActuator Accuracy CommentGravity 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 0.001º to 0.1º High Mass and Power

Thrusters 0. 1º to 1º Propellant limited, Large impulse

Attitude Control