bsf08 spacecraft attitude determination and control v1 0

Basics of Spaceflight

S f A i dSpacecraft Attitude D t i ti d C t lDetermination and Control

dachwald@fh‐aachen de

Prof. Dr.‐Ing. Bernd Dachwald

Aerospace Technology DepartmentHohenstaufenallee 6, 52064 Aachen, Germany

dachwald@fh aachen.de

FH Aachen University of Applied Sciences/Winter 2009 / 2010

v1.0

What is Spacecraft Attitude … and Why Do We Have to Control It?Overview and Introduction

• The orientation of the spacecraft in space is called its attitude• Most spacecraft have instruments and/or antennas that must be

d f d l b d hpointed into specific directions. Solar arrays must be pointed into the sun. The thruster must be pointed into the required direction during thrust maneuversthrust maneuvers

• To control the attitude, the spacecraft operators (or the spacecraft's computer, in case of an autonomous system) must have the ability to1. Determine the current attitude2. Determine the error between the current and the desired attitude3. Apply torques to remove the error

• Therefore, the spacecraft needs an attitude determination and control system (ADCS)system (ADCS)

• Attitude determination requires sensors• Attitude control requires actuators

FH Aachen / Winter 2009/10 / v1.0 2Prof. Dr.‐Ing. Bernd Dachwald Spacecraft Attitude Determination and Control

• Attitude control requires actuators

Attitude Determination & Control ProcessOverview and Introduction

Attitude Requirements:Antenna must point

Thruster must point into thrust direction

ActuatorsActuators

TorqueDemandsTorque

Demands TorquesTorques

Antenna must point into Earth direction

ExternalDi t b T

InternalDisturbance

On‐boardOn‐board

Disturbance Torques‐ Aerodynamic‐ Gravity‐Gradient‐Magnetic‐ Solar Radiation Pressure

stu ba ceTorques

On boardComputerOn boardComputer

MeasuredAttitudeMeasuredAttitude

AttitudeAttitude

Solar arraymust pointinto sund

Sensor mustpoint intotarget direction

Solar Radiation Pressure

„Real“Attitude„Real“Attitude

GroundGround

ControlCommandsControl

Commands

direction

AttitudeSensorsAttitudeSensors

ControlControl


Measured AttitudeMeasured Attitude

Disturbing Forces and Torques Acting on SpacecraftDisturbing Forces and Torques Overview

• Aerodynamic force / torque from planetary atmospheres, at Earth: altitude / 500 km

• Gravity gradient torque• Gravity gradient torque from planetary gravity fields, ∝ 1/R3, at Earth: altitude ≈ 500‐35000 km

• Magnetic torque g qfrom planetary magnetic fields, ∝ 1/R3, at Earth: altitude ≈ 500‐35000 km

• Solar radiation pressure force / torque i th i l t 1/ 2 t E th ltit d ' 600 kin the inner solar system, ∝ 1/r2, at Earth: altitude ' 600 km

• Force / torque from micrometeorite and debris impactsat all altitudes

• Spacecraft generated forces / torques e.g. from mass movements (mechanisms, propellant, astronauts), at all altitudes

• Their relative importance is a generally a function of spacecraft size, mass,mass distribution, altitude, and design

R: Distance from Earth (center)


R: Distance from Earth (center)r: Distance from sun

Aerodynamic Torque (simplified)AerodynamicDisturbing Forces and Torques

Aerodynamic drag (simplified):

1 2³ v´

FA =1

2ρCDA⊥v

2³−v

v

´FA: Aerodynamic force

A⊥

v FA

CP

FA: Aerodynamic forceρ: Atmospheric densityCD: Aerodynamic (drag) coefficientA⊥: Area normal to the

vr

FA

CM

A⊥: Area normal to thespacecraft velocity vector

v: Spacecraft velocity vector

TD = r × FA

Aerodynamic torque:

TD r × FA

TD: Aerodynamic torquer: Vector from the center of mass (CM) to the center of pressure (CP)


r: Vector from the center of mass (CM) to the center of pressure (CP)

Typical Magnitude of Disturbing TorquesDisturbing Forces and Torques Comparison

AltitudeDiagrams like this are strongly dependent on the shape and

100 000design of the spacecraft

R di ti P

10 000

Radiation Pressure

10 000Gravity Gradient

1 000Magnetic Effects

Aerodynamic Effects

100 Torque


Description of Spacecraft AttitudeAttitude Description

Spacecraft attitude is characterized by the orientation of a spacecraft‐ fixed coordinate system with respect to a reference

Example: orbit‐defined coordinate system Roll, Pitch, Yaw:

coordinate system

p y– Yaw axis is directed toward nadir (i.e. Earth center)– Pitch axis is directed toward the south orbit normal– Roll axis is perpendicular to yaw and pitch axis

Yaw rotation

Roll rotation


Pitch rotation

Attitude Determination

Attitude Determination Objective and Sensors

• Objective: To determine the attitude, or orientation, or pointing direction of a spacecraft‐fixed reference frame with respect to a known (usually inertial) reference framereference frame.

• Attitude determination requires two or more attitude sensors like

M– Magnetometersmeasure the magnitude and direction of the magnetic field

Sun sensors– Sun sensors measure the position of the sun

– Earth sensorsEarth sensors measure the position of the Earth or the attitude with respect to the horizon

– Star sensors compare some image of the sky with a build‐in library

– Gyroscopes


measure the rotation of spacecraft without external references

Simple Sun SensorsSun SensorsAttitude Sensors

SunlightS li ht

gSunlight

Sensors

Sensors

ElectronicsSignal


Sun SensorsSun SensorsAttitude Sensors

• Accuracy limit of a sun sensor is about several arcseconds (0.1 – 0.01 deg) for precise sensors and 0.5 deg for coarse sensorsO t d t i th l t ttit d b t l• One sun sensor measurement does not give the complete attitude but only a direction (only two degrees of freedom of the vector are sensitive to the attitude).

• Two measurements are required to determine the attitude:– by a second independent sensor– by the same sensor but separated significantly in time– by the same sensor but separated significantly in time.

?FH Aachen / Winter 2009/10 / v1.0 10Prof. Dr.‐Ing. Bernd Dachwald Spacecraft Attitude Determination and Control

?

Star SensorsStar SensorsAttitude Sensors

• Starlight strikes the CCD of a camera

• By determining the y gdirection to twodifferent stars in the picture, the

Star 1

Star 2

complete attitude can be determined

• Star sensors are very accurate (typically 1‐3 arcsec, some up to0.001 arcsec) …

• … but they generally do not function well at angular rates above some deg/s (due to their small field of view)⇒ a coarse sensor is


also required for high angular rates

Typical Attitude Control TasksAttitude Control Tasks

High angular rateArbitrary orientation

Tumbling S/C after separation

Low angular rateArbitrary orientation

Slow‐down angular speed

Low angular rateSun‐pointingLow accuracy

Attain safe attitude (power, thermal)

Low angular rateOperational orientation

Attain operational attitude (payload operations)

Low accuracy

Low angular rateSlew to support orbit operations

pHigh accuracy

o a gu a ateOriented to support orbit maneuverLarge disturbances

S e to suppo t o b t ope at o s


Reaction JetsReaction JetsAttitude Control

• By expelling a mass (for the spacecraft ) with a velocity c, a thruster exerts a force onto the spacecraft

mF = mc

m < 0

• If the thruster has a moment arm r with respect to the spacecraft‘s center of mass (CM), it exerts a torque about CM:

• A single thruster also changes the spacecraft‘s linear momentum

T = r × FA single thruster also changes the spacecraft s linear momentum p, because(this is typically not desired

F = mcF = p

( yp ybecause it also changesthe orbit of the spacecraft)

r

CM


Reaction JetsReaction JetsAttitude Control

• Therefore, thrusters are used in pairs, so that

T1 + T2 = 2(r × F)

• Depending on the actual thruster, one can have a very high

F1 + F2 = 0

Depending on the actual thruster, one can have a very high control authority– Cold gas:

F1 = mc1up to 10 N– Hydrazine:

up to 10 kN r1

F1 = mc1

CM

up to 10 kN– Ion thrusters:

10 mN down to < 1 mN

r1

r2

F2 = mc2


F2 = mc2

Reaction WheelsReaction WheelsAttitude Control

• Rotating the spacecraft does not necessarily require thrusters (conservation of angular momentum!))

• Reaction wheels (RWs) are a common choice for active attitude controlRW id i k d l• RW provide quick and accurate control

• Internal torque only (external torque is still required for de‐saturating the wheels, when they q g , yhave reached their maximum rotation speed)

• Three RWs are necessary for three‐axis control but four wheels are usually used for redundancybut four wheels are usually used for redundancy (tetrahedron mounting)

• Control logic is simple for three independent axes but can get complicated with redundancy

• Static and dynamic imbalances can produce vibrations (attitude jitter)


vibrations (attitude jitter)• Typical torque is 0.1 − 1 Nm

Basic Concept of Feedback ControlAttitude Control System Design

• Satellite attitude is measured and compared with a desired value ⇒ Attitude error

• Attitude error is used to determine corrective torque to be applied by onboard actuators ⇒ New attitudeC l ti i d fi it l b• Cycle continues indefinitely because– disturbance torques occur– attitude measurement is imperfectattitude measurement is imperfect– attitude correction is imperfect


ReferencesReferences

[Ro08] Lucy Rogers:It’s ONLY Rocket Science. An Introduction in Plain English.Springer, 2008

[Sw08] Graham Swinerd:How Spacecraft Fly. Spaceflight Without Formulae.Springer 2008Springer, 2008

[Se05] Jerry Jon Sellers:Understanding Space. An Introduction to Astronautics.Third Edition. McGraw‐Hill, 2005

[Gr04] Michael D. Griffin, James D. French: Space Vehicle Design.p gSecond Edition. AIAA Education Series, 2004


bsf08 spacecraft attitude determination and control v1 0

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