module a_attitude control review

8/7/2019 Module A_Attitude Control Review

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Royal Military College

of Canada

R.F. Vincent

The content of this

presentation is for

educational use only

The following slides are from PHE 354 Space Systems

offered by the Royal Military College of Canada

Attitude Control

Part 1:Attitude Dynamics

Part 2:Sensors and Actuators



Part 1

Attitude Dynamics



Attitude Control

Attitude Control Design Objectives

� Stabilize the spacecraft against external torques

Small environmental effects that will cause the

satellite to drift from its desired attitude

� Point housekeeping sensors in specific directions

Antennas for Telemetry, Tracking and Control (TT&C)

need to point at the ground station

� Point payload sensors in designated directions

e.g. Remote sensing payloads need to point at a

specific point on the surface

Need to meet sensor pointing accuracy requirements

Dependent on mission objectives

� Point spacecraft in the correct direction when applying

thrust for orbital changes



Pointing Accuracy

Typically, attitude control requirements are stated in terms

of pointing accuracy , ] , and rate of attitude change� Slew rate is the angular speed in rad/s that a spacecraft

can change its attitude

D ! hTarget diameter (m)

Target distance (m)

Pointing accuracy (rads)

D

]h

The requirement for spacecraft pointing depends on the

subject and the sensor¶s field-of-view

� At 500 km altitude, a spacecraft would need a pointing

accuracy of 0.115r to hit a 1 km target on Earth



Roll, Pitch, Yaw

When describing the motion of an object we use a

coordinate system In the case of attitude control the motion is rotational

� Coordinates are determined in degrees or radians

Space vehicle attitude is described in terms of roll, pitch

and yaw around the axes of the body frame



For vehicles like the Space

Shuttle, a right-hand

coordinate system is used:

� X-direction points out of the

nose

� Y-direction points out of theleft wing

� Z-direction completes the

right-hand rule

For spacecraft without a noseor wings, designers pick

convenient, preferred

directions through the center of

mass to define the body frame

Roll, Pitch, Yaw



Since the motion is rotational for attitude control weneed to know something about the mechanics of a

rotating object:

� Rotational Kinematics

� Moment of Inertia

� Center of Mass

� Angular Momentum

� Torque

Rotational Motion

z-axis

v

R



;! Rv

Every point on a rigid rotating object

has the same angular speed, ;, but notthe same tangential speed, v

dt

d U!;

Rotational Kinematics - Review

Acceleration

ERat !dt

d ;

!E2

;! Rar 22

r t aaa !

Angular Tangential Radial Total Linear

R

Direction of ;

is obtained

using the right

hand rule

;



Rotational Kinematics - Review

t if E;!;

2

2

1t t iif EUU ;! )(2

22

if if UUE ;!;

2

2

1;! I K

R

Kinetic Energy of a Rotating Mass:

Rotational Kinematic Equations:

t if if )(2

1 ;;!UU

Moment of Inertia (see next slide)



´! dmr I 2

Moment of Inertia is the tendency of a body to resist

angular acceleration

May be difficult to calculate if these conditions are not met

� Use the parallel-axis theorem if the axis of rotation does

not coincide with the axis of symmetry

See next slide

Moment of Inertia

Relatively easy to calculate for a symmetric object provided

that the axis of rotation

coincides with the axis of

symmetry



A simple way of calculating I is the parallel-axis theorem

� Where I CM is the moment of inertia through the center of

mass (CM) of the object, M is the mass of the objectand D is the distance for a parallel axis from I CM

See next slide for

center of mass

explanation

2MDI I

C M !

Parallel Axis Theorem



There is a special point in a system or object, called thecenter of mass ( CM), that moves as if all of the mass of

the system is concentrated at that point

The center of mass is the point about which a solid will

freely rotate if it is not constrained� The system will move as if an external force were

applied to a single particle of mass M located at the

center of mass

M is the total mass of the system

Center of Mass

´´´ !!! z dmM

z ydmM

yxdmM

xC M C M C M

111

x,y,z coordinates of center of mass for a solid object



ICM for Various Objects



Momentum

vmp !

Linear momentum is the

amount of resistance an objectin motion has to changes in

speed or direction Linear momentum

(kg·m·s-2)

Mass (kg)

Velocity

(m·s-1)

;! I H

Angular momentum

(kg·m2·s-2)

Moment of Inertia(kg·m2)

Angular Velocity

(rad·s-1)

Angular momentum isthe amount of resistance

a spinning object has to

changes in spin rate or

direction

Angular momentum keeps a

spinning top upright



vmRI H v!;!

We can also describe angular momentum in terms of a

cross-product

� H is perpendicular to both R and v

� Can find the direction of H by usingthe right-hand rule

Position Vector

Angular Momentum

By imparting spin to a spacecraft wecan use angular momentum to help

maintain stability

� Higher angular momentum will have

greater resistance to externaltor ues

v

H

Spin

R



Bringing in the dumbbells

will decrease the moment

of inertia In order for H to be

conserved, the angular

velocity must increase

Aman sits on a rotating stool holding out two dumbbells.

What happens if he brings the dumbbells towards his body?

Conservation of Angular Momentum

The angular momentum of an isolated system remains

constant in both magnitude and direction� Momentum is a vector quantity IH !

H H



Conservation of Angular Momentum

The sum of the angular momenta of the parts of an isolated

system is constant� If one part of the system is given an angular momentum

in a given direction, then some other part or parts of the

system must simultaneously be given exactly the same

angular momentum in the opposite direction

heel

;wheel;wheel

Hwheel

Hperson

;person

Aman on a rotatable stool holds a spinning wheel

What happens if the wheel is turned over ?Hwheel

;wheel ;wheel

Hwheel

Hperson

;person

If the wheel is turned over,

its angular momentum isnow downward

The man and the stool will

rotate with angular

momentum twice that of the

wheel



Fd rF !| J sinT

moment arm

Torque

The moment arm, d , isthe perpendicular

distance from the axis

of rotation to a line

drawn along thedirection of the force

� d = r sin



� The only component of F that causes rotation is

F sinJ , which is perpendicular to the axis O

� The F cosJ component is parallel to the horizontal

axis and has no tendency to produce a rotation

Torque

Torque facts� Units are

Force v Length = N·m

� Torque is not a force

but a consequence of force and the moment

arm



Torque

FR T v!Distance from the center of mass to where the force is applied (m)

Torque (N·m) Applied force (N)

To find the direction of

torque we use the right-

hand rule

According to this

relationship, more torquecan be achieved with the

same force by applying the

force further from the

center of rotation

Torque as a vector product:



Torque

Recall that force is the time rate of change of linear

momentump

pdF !!

dt

HHd

T !!

d t

Similarly, torque is the time rate of change of angular

momentum

When torque is zero, angular momentum is constant

If a torque is applied to a free-floating object, it willspin faster

� It will experience angular acceleration

IT !!



Angular

Acceleration

E

Attitude Dynamics

To determine a spacecraft attitude, described by an angle

U, we must look at how long it accelerates and how long itmoves at some angular velocity

� By adding torque to the spacecraft, we create angular

acceleration which leads to a change in attitude

Torque

TSpacecraft

I

Angular

Velocity

;Integrate

dt

Integrate

dt

Angular

Position

U

An important result of the interaction between a spinningobject and applied torque is gyroscopic stiffness

� The faster an object spins, the more stable it becomes

e.g. Rifle bullets, spiral football pass, Earth



Attitude Dynamics

When torque is applied to a non-spinning spacecraftthe results are easily predicted

If a spacecraft is spinning when we apply a torque,

the dynamics become more complicated

� If a torque is applied parallel

to the angular momentum

direction, it causes angular

acceleration

� If a torque is applied in a

direction other than parallel,precession may occur

Rotation of the spacecraft

around a precession axis

Precession



Attitude Dynamics

When torque is applied to the spinning disk shown below

it begins to precess by rotating around an axisperpendicular from both the torque and angular

momentum axes

� Precession vector [

For a constant torque, the precession rate is constant Precession behaviour depends on the distribution of

mass (I) of the spinning object

Knowing how a spacecraft

gains angular velocity andprecesses helps to determine

how to apply forces in order to

adjust its attitude

External Torque

[

H ;



Disturbance Torques

Why can¶t we put a satellite in space with the desired

attitude and forget about it?

� Environmental effects called disturbance torques drive

a spacecraft from its original attitude

Most of these torques are extremely small, but over

time they can rotate even the largest spacecraft

Four main sources of disturbance torques include:

� Gravity gradient

� Solar radiation pressure

� Earth¶s magnetic field

� Atmospheric drag



Disturbance Torques

Solar Radiation Pressure

� Light photons strike exposed surfaces and cause thespacecraft to rotate

Momentum transfer from the photons to the spacecraft

The force can be calculated as:

I cosr 1Ac

FF s

s !

Solar constant (1358 W/m2

at the Earth¶s orbit)

Angle of incidence

to the Sun

Reflectance (1 for a perfect

reflector, 0 for a perfect absorber)Illuminate surface area

Speed of light

A spacecraft with perfect reflectance and a surface area of

10 m2 would only experience about 9 v10-5 N of force

� Can still cause problems for spacecraft with precise

pointing requirements

Solar Radiation Pressure



Disturbance Torques

Magnetic Torque

� Because of the impact of charged particles in space,

the surface of a spacecraft

can develop a charge of its

own, giving it a distinct dipole

N orth and a south like a

compass

� Just as a compass needle

rotates to align with the

Earth¶s magnetic field, thedipole-charged spacecraft will

attempt to do the same when

it passes through the

magnetic field

Magnetic Torque



Disturbance Torques

Magnetic Torque (continued)

� The magnitude of themagnetic torque depends on

the spacecraft¶s effective

magnetic dipole and the local

strength of the Earth¶s

magnetic field

� This is a significant concern

for small satellites in low,

polar orbits

� The effect far less noticeablefor large satellites in

geostationary orbit

Magnetic Torque



Disturbance Torques

Aerodynamic Drag

� In low Earth orbit, the atmosphere applies a drag forceto the vehicle

� Since parts of a spacecraft may have different drag

coefficients (e.g. large solar panels), drag forces on

different parts of the spacecraft may also differ

This creates a drag torque

� Spacecraft designers can do little to prevent drag

torque, so the attitude control system has to deal with it

ACv

2

1F D

2

drag !

Atmospheric density Coefficient of drag

Velocity

Impacted areaDrag force

Aerodynamic Drag



Part 2

Sensors and Actuators



Spacecraft Attitude Sensors

When pilots fly an aircraft the easiest way to determine

altitude is to look out the window� Ground is down, and the sky is up

� The same principle can be used for a spacecraft

For a spacecraft there are three classes of out the

window sensors1. Earth Sensors

2. Sun Sensors

3. Star Sensors

By themselves, these sensors can accuratelymeasure attitude in only two dimensions

Only two of pitch, roll and yaw

Need to combine information from multiple

sensors sensors to get all three dimensions

Out of Window




Earth Sensors

� In LEO the Earth fills a significant portion of the sky,so a sensor would have to focus on a small portion

of the Earth for greater accuracy

� In GEO the angular radius of the Earth is 10r, so a

sensor that can locate the Earth is at least accurate

to within that amount

� Sensors that scan for the

Earth horizon can be as

much more accurate

Detect EM radiation

emitted by CO2 to

determine the horizon

Scanning Technique for

an Earth horizon sensor

E arth Sensors




Sun Sensors

� Finds the Sun and determines itsdirection with respect to the

spacecraft

� Most widely used spacecraft

attitude sensor

Star Sensors

� Compares the pattern of stars seen

by the sensor to a star catalog and

uses astrometry to determine wherethe sensor is pointed

� More accurate than a Sun sensor

� By using two or more star sensors, attitude can be

determined in 3-dimensions

Star and Sun Sensors



Accuracy xy/z axis 18/122 arcseconds

Size (Length x Width x Height) 80 x 100 x 180 mm

Weight 1.1 kg

Power Supply Voltage Range 9 to 18 VDCPower consumption 2.5 W


Star Sensor Example (Vectronic Aerospace)

Company Description

With a focal length of 50 mm the sensor¶s FOV is around 14°x14° whichguarantees at least 10 visible stars independent of the current attitude.

After the first acquisition, which takes not more than 900 ms, the sensor

operates with an adjustable update rate in the range from 4 Hz to 8 Hz.

The probability of attitude acquisition at spacecraft angular rates lower

than 0.6 deg/sec is better than 99.7% over the full sky.




Spacecraft attitude can also be determined by sensors

that do not require visible references, including:1. Gyroscopes

Mechanical

Ring Laser

Fibre Optic

2. Magnetometers

3. Global Positioning System (GPS)

I nternal




Mechanical Gyroscope

� The simplest type of gyroscope is a spinning mass� With no torque applied it will always point in the same

direction in inertial space

Higher moment of inertia (I) and higher angular

velocity (;) will result in greater stability Higher angular momentum (H)

Gyroscopes

;!I

Agyroscope will point in a fixed direction in inertial space




Mechanical Gyroscope (continued)

� With torque applied, a mechanical gyroscopes will precessin a predictable direction with a predictable magnitude

� There are two methods to measure spacecraft rotation due

to external torques using a mechanical gyroscope

1. Isolate the gyroscope from external torques bymounting it on a gimbal

Measure spacecraft rotation with respect to the

stationary gyroscope

2. Mount the gyroscope directly to the spacecraft frame

When the spacecraft rotates the gyroscope will

precess in a predictable fashion

By measuring the precession angle and rate, the

system can compute the amount and direction of the

spacecraft¶s rotation

Gyroscopes




Ring Laser Gyroscope

� Consists of a circular cavitycontaining a closed path,

through which two laser beams

shine in opposite directions

�A

s the spacecraft rotates thepath lengths traveled by the

beams change, causing a shift

in the interference pattern

Gyroscopes

Beam traveling against the rotation experiences a slightly

shorter path than the other beam

� By measuring the frequency shift of the interference pattern,

changes in the vehicle¶s orientation can be determine

No moving parts

Better accuracy & reliability than mechanical gyroscope



Fibre Optic Gyroscope

� Uses the interference of light to detect mechanicalrotation

Same principle as ring laser gyroscope

� The sensor is a coil of as much as 5 km of optical fibre

� Two light beams travel along the fibre in oppositedirections

Beam traveling against the rotation experiences a

slightly shorter path than the other beam

The resulting phase shift of the interference patternindicates vehicle rotation

The intensity of the combined beam indicates the

rotation rate of the device

Spacecraft Attitude Sensors Gyroscopes




Magnetometers

� A magnetometer functions as a highly accurate compassthat measures the direction and strength of the local

magnetic field

� By comparing this measurement to a model of the Earth¶s

field it can determine an accurate estimation of the

spacecrafts attitude

Work best in LEO where the field strength is highest

Need an accurate model of the Earth¶s magnetic field

Offer a relatively cheap independent reference that

can be compared to other sensors

Magnetometers




Global Positioning System

� GPS is a constellation of 24 satellitesin MEO that can provide position,

velocity and time information

� By placing two GPS receivers some

distance apart on a spacecraft andcomparing the phase of the signals,

it is possible to determine attitude

� Accuracy limited by:

�Reflected signals from spacecraft

� Accuracy of phase measurements

� Antenna separation

� Can only receive GPS signals if you

are below the constellation (i.e. LEO)

GPS



Spacecraft Attitude Sensors - Example

BRITE (20 ×20 × 20 cm): Attitude determination with an

accuracy of 10 arcseconds for BRITE (20 ×20 × 20 cm) is

made possible with a magnetometer, six sun sensors and a

star tracker. The GPS is used for position information.



Spacecraft Attitude Actuators

Once the spacecraft attitude is determined, we need to

know how to change it if required Actuators provide torque on demand to rotate a spacecraft

as needed to take pictures, downlink data or meet other

mission requirements

Passive Actuators� Gravity-gradient stabilization

� Spin stabilization

� Dampers

Active Actuators

� Thrusters

� Magnetic Torquers

� Momentum Control Devices

Commonly

use more

than one

type of actuator

for attitude

control

Require

little or

no input

Require

continuous

feedback and

adjustment




Gravity-Gradient Stabilization

� Takes advantage of the gravity-gradientdisturbance discussed earlier

� Can exploit this free torque to keep a spacecraft

oriented in a vertical orientation

Cheap and simple

Passive

Pitch and roll only (no yaw)

Limited accuracy depending

on spacecraft¶s mass

distribution (s

5r)

LEO only

Example: GeoSat Radar Altimeter

Launched in 1985 to measure sea surface height

Used gravity gradient to keep radar altimeter pointing at the Earth




Spin Stabilization

� Takes advantage of angular momentum to maintain aconstant inertial orientation of one of its axes

� Spin stabilization isn¶t useful for Earth pointing missions

since they will not point at the Earth for part of the orbit

Passive




Spin Stabilization Examples

� Explorer 6 (1959)

Designed to study trapped

radiation

Spin stabilized at 168 rpm

� Geostationary Operational

Environmental Satellite (GOES)

GOES 1 to 7 (1975 to 1987)

were spin stabilized at 100RPM

Visible and Infrared Spin Scan

Radiometer used the spin of

the satellite to scan the Earth

Passive




Dual-Spin Stabilization

� One way to avoid Earth-pointing limitations of spinstabilization is to use a dual-spin system

� Combines the gyroscopic stiffness of a spinning outer

section with a de-spun inner section that can point

independently at the Earth

Passive




Dual-Spin Stabilization (continued)

� The de-spun inner section does actually spin, but at amuch slower rate than the outer section

This allows for antenna and sensor pointing

� Inherently complex system, but is still a common control

option for large GEO communications satellites

Passive

Anik-C Series (1983 - 2002)Dual Spin Stabilization

Geostationary orbit, providing

pay television to Canada




Dampers

� A damper is a device that changes angular momentumby absorbing energy

Uses friction or other means to convert momentum

energy into other forms

� A simple damper consists of a ball in a circular tube filledwith a viscous fluid

As the spacecraft rotates, some of its momentum is

converted to heat through the friction of the ball in the

tube, slowing its rotation

Passive

� Dampers are used to take

unwanted wobbles in the spin axis

� Normally used in conjunction with

other types of attitude actuators




Thrusters

� Thrusters are rockets that rotate the spacecraft� By applying a balanced force with a pair of rockets on

opposite sides of a spacecraft, we can produce torque

� By varying thruster power, the satellite can be rotated

in any direction� Placing the thrusters as far from the satellite¶s center of

mass as possible allows them to exert a greater torque

Active

Can produce well-defined

torque on demand

allowing a spacecraft to

slew quickly from one

attitude to another

Amount of propellant limits

their use

S f




Magnetic Torquers

� Takes advantage of naturally occurring magnetictorques due to the Earth¶s magnetic field

� The onboard system switches electromagnets on and

off as needed

The electromagnet aligns with the Earth¶s

magnetic field, dragging the spacecraft with it

Active

Important secondary means of

attitude control for satellites in highly

inclined LEO

Cheap and simple

Use electrical power, not

propellant

Less useful in orbits higher than

LEO



S ft Attit d A t t




Momentum-Control Devices

� Vary the angular momentum of small rotating masseswithin a space craft to change its attitude

Utilize conservation of angular momentum

Small mass with a high spin rate has the same

angular velocity as a large mass with a slow spin rateSince the spinning mass is a small fraction of the

spacecraft's total mass, easily-measurable changes

in its speed provide very precise changes in angle

� Three types of momentum-control devices:

Biased momentum systems

Zero-biased systems

Control-moment gyroscopes

Active

I!

S ft Attit d A t t




Biased momentum systems

� Simplest type of momentum-control device

� Uses one or two spinning momentum wheels

� Because the wheels are always rapidly spinning, they

give the spacecraft a large angular momentum vector � Similar to spin-stabilization, except instead of

spinning the whole spacecraft only a small wheel

inside the spacecraft is spun to achieve the same

effectAchieves spin stabilization without spinning the

spacecraft

Active

S ft Attit d A t t




Zero-biased systems

� Includes three independent reaction wheels at rightangles to each other with little or no initial momentum

� When the spacecraft needs to rotate to a new attitude,

or to absorb a disturbance torque, the system spins one

or more of these wheels

Active

Provides precise attitude control and is the primary

choice for satellites requiring accurate pointing

Complex, expensive, limited operational lifetime

S ft Attit d A t t R ti Wh l



Spacecraft Attitude Actuators Reaction Wheels

In this simple single-axis example we start with a non-

rotating spacecraft that has zero angular momentum

To rotate the spacecraft in one direction, the reaction wheel

is spun up in the opposite direction

T he total angular

momentum of a spacecraft

system is the sum of the

spacecraft¶s momentum

plus the momentum of

each reaction wheel



S ft Attit d A t t A ti




Control-moment gyroscopes

� Consists of three or more spinning reaction wheels,

each mounted on gimbals that allow them to rotate

freely in all directions

� Momentum is changed by changing the magnitude

and direction of the spinning wheels

Since the angular momentum of the system must

be conserved, the spacecraft will rotate in the

opposite direction to compensate

� Provide pointing accuracy equivalent to reaction

wheels, but offer higher skew rates

Effective on large platforms

Active

3 A i St bili ti



RADARSAT-2

Attitude Determination: Sunsensors, 3-axis gyros, star trackers

Attitude Control: 3-axis stabilization

(reaction wheels), magnetic

torquers

3-Axis Stabilization

CAN-X Generic Nanosatellite Bus

Miniaturized components allow

precise attitude determination and

control. BRITE (20 × 20 × 20) uses 3

orthogonal reaction wheels and 3

orthogonal magnetorquer coils for

three-axis attitude control and

momentum dumping





Momentum Dumping

� A limitation of all momentum-control devices is that thereis a practical limit to how fast a given wheel can spin

� During operation, these systems must gradually spin

faster and faster to rotate the spacecraft and absorb

disturbance torquesWheels become saturated

� M omentum dumping is a technique for decreasing the

angular momentum of the wheel by applying a controlled

torque to the spacecraftSpacecraft needs an independent way of applying an

external torque

Magnetic torquers and/or thrusters are normally

used for momentum dumping

Comparison



Attitude

Control

Methods and

their Capabilities

Comparison

The Controller



The Controller

The controller generates commands for the actuators to

make the spacecraft point in the right direction based onmission requirements for accuracy and slew rate

To use the information from sensors and continuously

adjust actuator commands, the controller has to keep track

of:� What is happening now

� What may happen in the future

� What happened in the past

The controller combines its memory with its current

measurements and ability to predict future behaviour to

decide how to command the actuators

The Controller



The Controller

Derivative Control

� Sensors determines current attitude and compares it todesired attitude

� The difference between the measured and desired

attitude is the error signal

� The controller then sends a message to the actuators to

correct to the desired attitude

Knowing the rate of change of attitude allows more

accurate slewing

Integral Control

� Controller considers the change in angular difference

over time, (U� Controller then calculates how much torque to add in a

steady-state mode to compensate for disturbance torques

Used when highly accurate pointing is desired

The Controller



The Controller

Commands ActuatorsError Signal Controller Torques

System input: desired attitude

SensorsMeasured attitude

Spacecraft

Disturbance Torques

Physical output:

the current attitude

Derivative Control



Royal Military College

of Canada

R.F. Vincent

Attitude Control

Part 1:Attitude Dynamics

Part 2:Sensors and Actuators

module a_attitude control review

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