AE4713F15LectureonACS.pdf

AE 4713 Spacecraft Dynamics and Control

Supplemental lecture/overview on attitude control system (ACS)

Prof. Michael A. Demetriou

Aerospace Engineering

Worcester Polytechnic Institute, Worcester, MA, 01609

2015-16, A-term, Lec: M,T,W,Th,F, 10:00-10:50am

Lectures are based on material from

1. “Elements of Spacecraft Design”, C. D. Brown, AIAA 2003

Outline

ACS tasks

1. common attitude control system types

2. disturbance torques

3. attitude determination

4. attitude control hardware

2

Attitude Control Tasks

• measure attitude using attitude sensors (e.g. gyroscopes)

• correct attitude - done by torquers or actuators (e.g. thrusters)

• control law - determines magnitude and direction of torque in response to a given disturbance

3

1. common attitude control system types

The most common ACS types are as follows

• spin stabilized ; entire s/c spins around the axis with the highest moment of inertia

• dual spin stabilized ; a dual spin s/c has a spinning segment and an inertially fixed section

• three-axis stabilized ; actively controls the inertial position of all three axes

• momentum-bias; uses a momentum wheel to provide stiffness in two axes and wheel speed

to control the third axis

• gravity-gradient ; completely passive, takes advantage of the s/c tendency to align the long

axis with the gravity gradient

4

1. common attitude control system types: SPIN-STABILIZED SYSTEM

Description:

A spin-stabilized s/c takes advantage of the inherent resistance of a spinning body to disturbance

torques.

If no disturbance torques are experienced, the momentum vector remains constant in magnitude

and fixed in inertial space

If a disturbance torque occurs that is parallel to the momentum vector, the spin rate will be

affected, but not attitude. Thrusters are used to correct spin rate.

Disturbance torques perpendicular to the momentum vector will cause the spin axis to precess;

thruster force is used to remove precession

rotational maneuvers are performed by precessing the spin axis

translational maneuvers are always made parallel to the spin axis

maneuver is slow and energy-consuming process because of inherent stability of vehicle

5


Advantages:

useful in applications that require simplicity, low cost, modest pointing accuracy and minimal

maneuvering.

Stabilization about transverse axes is passive for long periods of time

sensor gyros, momentum exchange devices and onboard computers are unnecessary;

result in substantial cost and mass savings

6


Disadvantages: pointing accuracy is low, 0.3 to 1 degrees; tight control of the moments of inertia

is required.

moment of inertia about the spin axis must be substantially greater than that about the transverse

axis, or the vehicle will reverse axis; moment of inertia ratio must be greater than 1; a ratio of 1.2

is common requirement

the only location for solar arrays is the spinning body exterior; total power available is limited to

that which can be obtained from the body surface; this area is not in the sun all of the time; a

given area on a cylindrical spinning body gets only 32% of the solar intensity that would fall on a

pointed planar array; power is therefore a scarce commodity on a spinner

maneuver rate is limited; a maneuver is made by precessing the spin axis (slow process);

maneuver slew rates greater than 0.5 degrees/second indicate three-axis stabilization

body pointing of payload sensors and antenna is not possible

examples are: Explorer I, Pioneer Venus and INTELSAT I, II and III

7

1. common attitude control system types: DUAL-SPIN SYSTEM

Description:

it is a compromise design; has some of the simplicity of a spinner and some of the pointing

accuracy of a three-axis vehicle

major mass of s/c spins providing gyroscopic stiffness, while an instrument platform is despun to

point at instruments or an antenna

Advantages: vehicle stable about the transverse axes for long periods of time; sensing gyros

and onboard computers not required

spinning body provides a built-in scan for sensors and provides a centrifugal bottoming for any

liquid propellants; thrust vector not require for ∆V maneuvers

despun platform provides pointing for antenna and instruments

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1. common attitude control system types: DUAL-SPIN SYSTEM

Disadvantages: despin drive assembly (motor, bearings, slip rings) is expensive and failure

prone

Nadir tracking not practical except at high altitudes, geosynchronous and above

solar-array efficiency is limited because a given cell is illuminated 32% of the time

complex nutation dynamics must be dealt with; For stability a dual spinner places constraints on

the inertial properties and damping in the spun and despun sections

energy dissipation of the spun section must be greater than that of the despun section–expensive

issue late in the development of Galileo

examples of dual-spin s/c are Galileo and INTELSAT VI

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1. common attitude control system types: THREE-AXIS STABILIZED SYSTEM

Description: a three-axis stabilized system actively maintains the vehicle axis aligned with a

reference system, usually inertial reference or nadir reference.

typical system uses gyros as inertial reference and updates the gyros periodically using star

scanning or horizon scanning.

attitude errors are removed by torquing reaction wheels, which are periodically unloaded using

thrusters

thruster layout provides pure torque about all three axes and positive or negative translation

along each axis

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Advantages:

unlimited pointing capability in any direction-nadir, inertial, sun, scanning

provides the best pointing accuracy, limited only by sensor accuracy

pointing accuracy of greater than 0.001 degrees can be achieved

solar panels can make full use of available solar energy; solar panel size is not restricted; most

adaptable to changing requirements.

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Disadvantages:

ACS hardware (gyros, reaction wheels, star scanners, computers) are complex, heavy,

power-consumers, failure sources and expensive

active thrust vector control is required for ∆V burns; propellant tanks require 0-g propellant

control devices

mechanical gimbals required for scanning instruments Examples of three-axis controlled s/c are:

Magellan, INTELSAT VIII, Hubble Telescope and GPS

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1. common attitude control system types: GRAVITY-GRADIENT SYSTEMDescription: takes advantage of the tendency of a s/c to align its long axis with the gravity vector

for this to work, it is necessary that the gravity-gradient torques are greater than any disturbance

torque;

this can be met in orbits lower than 1000 km

necessary for the moment of inertia about x and y axis to be much greater than the moment of

inertia about the z-axis

deployed booms have been used on the long axis to improve inertial properties

gravity gradient stabilizes the pitch and roll axes and not the yaw axes

common practice to use a momentum wheel with its axis perpendicular to the orbit plane to

provide stiffness in yaw

Gravity-gradient torques are small and active damping might be required to prevent slow

oscillations of as much as 10 degrees.

useful when long life and high reliability are required and the pointing requirements are modest

Examples of s/c that used gravity-gradient stabilization: ATS-5, GEOSTAT and ORBCOM

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1. common attitude control system types: MOMENTUM-BIAS SYSTEM

Description: uses a momentum wheel to provide inertial stiffness in two axes and control of

wheel speed provides control in the third axis

particularly useful for a nadir pointing s/c using wheel speed to hold z-axis on nadir

relatively simple and good for long-life missions

cheaper than a three-axis system

good pointing in one axis (usually pitch) and poor accuracy in the wheel axes (usually roll/yaw)

momentum bias cannot achieve the pointing accuracy of three-axis control.

maneuvering capability very restricted

does not provide adequate torque authority for thrust vector control

Examples: Seasat and INTELSAT VIII used this technique

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2. disturbance torques

A s/c released into Earth orbit w/o attitude control would tumble in response to 5 different kinds of

environmental torques:

1. drag torque - orbits below 500km

2. gravity-gradient torque - orbits 500 to 35,000km

3. magnetic torque - orbits 500 to 35,000km

4. solar torque - dominant geosynchronous and above

5. spacecraft-generated torques

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2. disturbance torques: DRAG TORQUEAerodynamic drag is a source of torque as well as velocity reduction for s/c in low Earth orbits.The drag force is

D =12

ρV 2 Cd A

where:

• D = drag force - aligned with the velocity vector and opposite in sign

• ρ = atmospheric density, kg/m3

• V = s/c velocity, m/s

• Cd = drag coefficient-depends on shape, usually about 2.5

• A = area normal to velocity vector, m2

greatest uncertainty in s/c drag analysis is in atmospheric density (altitude, temperature, time ofday, intensity of solar radiation← 11-year cycle).

Drag torque is TD = DL where L is the distance between the center of pressure and the center ofgravity

Example: Consider a s/c in a 400-km circular Earth orbit. What is the drag force on a solar panel

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2. disturbance torques: DRAG TORQUE

with 9m2 of surface area normal to the velocity vector?

The velocity of a s/c in a 400-km altitude Earth orbit is 7.669km/s. Assuming the atmospheric

density at 400km is 1.2×10−11 kg/m3, under average conditions, the drag force is

D =12(1.2×10−11 kg/m3)(7669km/s)2 (2.5)(9m2) = 7.9×10−3 N

Using the same s/c as in the solar torque example further down, assume that the body and solar

arrays are each uniform such that their center of pressures are at the centroid. The torque on the

main body would be zero because the center of gravity is at the centroid. The drag torque caused

by the solar array is

T = (7.9×10−3 N)(2.25m) = 1.78×10−2 N m

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2. disturbance torques: GRAVITY-GRADIENT TORQUE

For long slender s/c (dumbell-shaped) the lower extremities of the s/c are subjected to

exponentially higher gravity forces than the upper extremities. The effect acts to align the long

axis with the Earth radius vector. The gravitational acceleration on the lower mass is g = GM⊕r21

and on the upper mass g = GM⊕r22

.

Because r2 is greater than r1, the gravitational force is greater on the lower mass than the upper

mass, and the net force tends to hold the s/c upright.

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The resulting torque is

Tg =3µr3 |Iz− Iy|θ

where

• Tg = gravity-gradient torque, N-m

• µ = gravitational parameter, 398,600.4km3/s2 = GM⊕

• r = radius from s/c center of mass to central body center of mass, km

• Iz = moment of inertia about z axis

• Iy = moment of inertia about the y axis

• θ = angle between s/c z axis and nadir vector (orbit normal), rad

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2. disturbance torques: GRAVITY-GRADIENT TORQUEExample: The Skylab was the first space station launched by the United States and the largest

U.S. s/c launched to that time (1973). Estimate the gravity-gradient torque on Skylab given the

following:

Vehicle properties:

• Mass = 90,505 kg

• Height = 35m

• Diameter = 5.4 m

• Radius = 2.7m

Orbit:

• Altitude = 442 km circular

• Radius - 5820 km

Attitude error:

• 5 degrees or 0.087266 radians

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Assume a uniform density, calculate moments of inertia

Iz =mr2

2=

(90,505kg)(2.7m)3

2= 329,890.7kgm2

Ix,y =m12

(3r2 +h2) =90,505kg

12(3(2.7m)2 +(35m)2)= 9,403,997.5kgm2

Then

Tg =3(398,600km3/s2)

(6830km)3

(9,403,997.5kgm2−329,890.7kgm2)(0.087266rad)

= 2.9851N m

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2. disturbance torques: MAGNETIC TORQUEThe earth and several other planets have a magnetic field that produces torque on s/c. Thetorque of any magnetic field on a current-carrying coil is

T = N I AB sin(θ)

where

• T = magnetic torque, N-m

• N = number of loops in the coil

• I = current in the coil, amperes

• B = Earth’s magnetic field, tesla

• θ = angle between magnetic field lines and perpendicular to the coil

the residual magnetic field of a s/c is the result of current loops and residual magnetism in themetal parts, and given by

M = N I A, and T = M B sin(θ)

Earth’s magnetic field is tilted 11 degrees wrt the Earth’s rotational axis, centered about 400kmfrom the Earth’s geometric center; hence, at a given altitude the field is stronger over the Pacific

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2. disturbance torques: MAGNETIC TORQUEthan the Atlantic. The magnetic field varies as one over the radius from the Earth’s center cubed.

the higher the orbit, the less disturbance

The field strength also varies by a factor of 2 depending on latitude with the highest value at thepoles:

B =B0r3

0r3

√(2sin2(L)+1)

where

• B = Earth’s magnetic field strength at any altitude or latitude

• B0 = Earth sea-level magnetic field strength, ≈ 3×10−5 tesla

• r = s/c orbital radius, m

• r0 = Earth’s surface radius 6,378,000 m

• L = latitude in magnetosphere, degrees

Using the above formula, the Earth’s magnetic field strength at the poles is twice the equatorialstrength

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2. disturbance torques: MAGNETIC TORQUE

Example: Consider a s/c with a residual dipole of 2Am2 in a circular equatorial orbit at an

altitude of 400km. What is the magnitude of magnetic moment on the s/c?

We first calculate the orbit radius r = (400+6478)×103 m = 6,778,000m. The Earth’s

magnetic field in a 400-km equatorial is

B =

(6,378,0006,778,000

)3

3.1×10−5 tesla(3sin0+1)2 = 2.5×10−5 tesla

Then T = (2.5×10−5 tesla)(2Am2) = 5×10−5 N m

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2. disturbance torques: SOLAR TORQUE

• solar photon strikes a s/c surface

• small momentum exchange

• force exerted on surface

• pressure produced is proportional to the projection of surface area perpendicular to the sun

and solar intensity, which is inversely proportional to the square of the distance from the sun

• pressure depends on whether photon is

– absorbed,

– specularly deflected or

– diffusely reflected

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Absorption: if solar radiation impinging on a surface is totally absorbed, then the force on the

surface will be aligned with the sun vector, and will have magnitude

F = PsAcos(α)

where

• Ps =Isc = 1376W/m2

2.998×108 m/s = 4.59×10−6,N/m2, (near Earth)

• Is = incident solar radiation, W/M2

• c = speed of light, m/s

• Ps = solar pressure, N/m2

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2. disturbance torques: SOLAR TORQUESpecular reflection: The force resulting from impingement on a specularly reflective surface isnormal to the surface regardless of sun line and is an elastic collision with twice the magnitude ofthat of an absorbing surface

F = 2PsAcos(α)

Diffuse reflection: A diffusely reflective surface can be considered to be an absorption and areradiation uniformly distributed over a hemisphere. The absorption component is aligned withthe sun vector with magnitude given by the one above. The net force resulting from the reflectedcomponent is normal to the surface; all tangential components cancel.

Fs =23

PsAcos(α)

The solar torque on the s/c is the sum of all forces on all elemental surfaces times the radius fromthe centroid of the surface to the spacecraft center of mass. Total torque:

Ts = PAL(1+q)

where

• Ts = total torque on s/c caused by a surface A, N m27


• A = area of surface projected to sun line normal, m2

• L = distance from the centroid of the surface to the center of mass of the s/c, m

• q = reflectance factor, 0≤ q≤ 1. S/c bodies tend to be reflectors; a q of 0.5 is

representative; solar panels tend to be absorbers, a q of 0.3 is representative

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Example: What is the solar force on a 9m2 solar panel inclined at 20 degrees to the sun with a

reflectance factor q of 0.3 if the vehicle is in Earth orbit?

Using Fs = PA(1+q)cos(α) we obtain

Fs = (4.59×10−6 N/m2)× (9m2)× (1+0.3) cos(20o) = 4.0×10−5 N

Now, what is the resultant torque for a s/c with a single square solar panel of this size with a 1-m

body with the c.g. in the center of the body and a 0.25m boom to attach the panel?

T = (4×10−5 N)(2.25m) = 9.0×10−5 N−m

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2. disturbance torques: SPACECRAFT-GENERATED TORQUE

In addition to environmental torques, there are a variety of s/c generated torques. These are

generally much smaller than the external torques but must be accounted for, especially for a

high-precision pointing system.

Common causes of internal torques are:

• pointing rotation of solar arrays, antennas, or cameras

• deployment of antennas, solar arrays, instruments, booms

• parts jettison, which means that the s/c will react to jettison of parts such as covers, doors,

and solid-rocket-motor cases

• propellant slosh, which can cause motion of the vehicle and center of gravity-slosh is

attenuated by bladders and diaphragms

• flexible appendages can cause motion by thermal distortion or by dynamic interaction with

the attitude control system

• reaction wheel imbalance, which is caused by small misalignments in the reaction wheels

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2. disturbance torques: Torques due to air leaks

Common causes of internal torques are:

• Air leak in the pressurized module

• Depressurization inside the cabin

• Leaking hole will act like a thruster because of the air leaving the station produces a reaction

force

• Attitude change occurs due to reaction torque

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2. disturbance torques: Torques due to air leaks

Figure 1: Thruster-Like leak hole

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2. disturbance torques: SYSTEM SIZINGSystem sizing Once all disturbance torques have been identified and quantified, the actuatorsizing can be determined. First, the magnitude of the torques must be found. The actuator musthave sufficient torque authority to counteract the disturbance torques

The difference in the magnitude of the disturbance torque and the actuator torque capacity is ameasure of the control authority.

The control authority is expressed as a percentage such that an actuator with twice the capabilityof the disturbance torques would have a 100% control authority margin

After the actuator with sufficient control authority is chosen, then the system resources over timemust be considered; in the case of a three-axis stabilized s/c with reaction wheels, the storagetime of the reaction wheels must be considered. Reaction wheels store momentum until theyreach their maximum specified speed, at which point they are saturated and must be desaturatedby another torque.

In LEO, magnetic torquers typically used for wheel desaturation; For higher orbits orinterplanetary s/c, reaction control system or thrusters are used.

Magnetic torquers require electric power, but avoid use of consumable propellant.

If thruster control is selected, the disturbances caused by the thruster firings and the amount of33

2. disturbance torques: SYSTEM SIZING

propellant consumed must be considered

Example on reaction wheel sizing: Consider the s/c from the solar torque and drag force

examples and determine the size, that is, the torque capability and momentum storage capability

of a reaction wheel required to maintain position and require desaturation once per 98-minute

orbit

Solar torque and drag force are acting in the same direction, therefore

T = solar torque+drag torque = 9.0×10−5 +1.78×10−2 = 1.789×10−2 N m

reaction wheel torque capability, at least 1.85×10−2 N m. Momentum buildup over 1 orbit:

M = T t = 1.85×10−2 (98)(60) = 108.78N ms

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3. attitude determination

Determined by the following

1. gather data from onboard sensors; these data corrected for errors and biases, then analyzed

mathematically to determine attitude estimate

2. body frame axes or spin axis location determined form sensor data

3. instantaneous attitude, or state vector, is expressed wrt a reference frame, usually inertial or

geocentric, as a set of Euler angles, a direction cosine matrix, or a quaternion

4. attitude estimate is the basis for correcting the attitude

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3. attitude determination: DCM

relationship between reference frame and s/c frame is defined by the three rotation angles (Euler

angles)

Euler angles are a set of three angles and a sequence of rotation such that one coordinate

system can be rotated into another

both the magnitude of the angles and the sequence of rotation are important; there are 12

different Euler sets that describe the same relative position

A direction cosine matrix (DCM) is defined as the product of the three Euler rotations;

the Euler angles can be extracted from the DCM; for example, using the specific expression (§9)

for Rib, the Euler angles are as follows:

ψ1 = tan−1(

r1,2

r1,1

), ψ2 = tan−1

−r1,3√1− r2

1,3

, ψ3 = tan−1(

r2,3

r3,3

)

where ri, j denotes the element in the ith row and jth column of Rib

when attitude determination involves very small angles, the small-angle approximation can be

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3. attitude determination: DCM

made and for the specific rotation matrix in (§9), we have

Rib ≈

1 ψ1 −ψ2

−ψ1 1 ψ3

ψ2 −ψ3 1

performing a rotation using a DCM, requires 27 multiplications, 12 additions/subtractions and 29

trigonometric evaluations⇒ require a large amount of memory and are computationally intensive

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3. attitude determination: QUATERNIONSan alternative to the DCM is the quaternion (a.k.a. Euler symmetric parameters), which has nosingularities and no trigonometric functions;

Quaternions make use of Euler’s theorem (any series of rotations of a rigid body can beexpressed as a single rotation about a fixed axis-can be shown that any attitude transformation inspace by consecutive rotations about the three orthogonal unit vectors of the coordinate systemcan be achieved by a single rotation about the eigenvector with unity eigenvalue)

orientation of a body can be defined by a vector giving the direction of a body axis and a scalarangle specifying a rotation about that axis; i.e. quaternions express the same information as aDCM: rotation from one frame to another, with four elements; three elements express the vectorof rotation and the fourth element is the angle of rotation Q = iq1 + jq2 + kq3 +q4 with i, j,ksatisfying i2 = j2 = k2 =−1 i j =− ji− k, jk =−k j = i, ki =−ik = j

the conjugate of Q is Q∗ =−iq1− jq2− kq3 +q4 and the norm (magnitude) of the quaternion is

a scalar |Q|=√

q21 +q2

2 +q23 +q2

4

can relate the DCMs and quaternions

may relate a frame A to frame B using quaternions; this computation requires 15 multiplicationsand 12 additions/subtractions

38

3. attitude determination: QUATERNIONS

to relate the Quaternions to the Direction Cosine Matrix, first denote q = (q1,q2,q3) which

implies Q = (q4, q), then

Rib = (q24−qT q)I +2qqT −2q4ΩQ, ΩQ =

0 −q3 q2

q3 0 −q1

−q2 q1 0

may use Quaternions to parameterize the attitude error

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3. attitude determination: STATE ESTIMATION

may also use State Estimation Methods: successively correct estimates of the attitude

• sequential estimator (recursive estimator): obtains a new state estimate after each

observation

• batch estimator processes all observations concurrently to produce a new estimate of state

vector

two types of estimators:

• least squares estimator: determines the state vector, which minimizes the square of the

difference between observed data and computed data from a dynamics model; error

assumed to have Gaussian distribution

• Kalman filter: makes a sequential minimum variance estimation

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3. attitude control systems

An attitude control system is composed of three major parts

1. attitude sensors, which provide direct measurements of s/c attitude

2. a feedback control system, which corrects measured attitude to desired attitude

3. actuators (a.k.a. effectors or torquers), that provide the desired control torques

41


brief description of feedback control system:

let θa be the angle between the s/c axis and the reference coordinate, and let θr be the desired

angle

define the error signal θ = θr−θa; the error signal is used by the control law to calculate the

necessary control torque Tc; the sum of all torques creates vehicle rotation θa in accordance with

the relation

Ta = Ivθa

• Ta = actual torque on the vehicle about a given axis

• Iv = moment of inertia of the vehicle about the axis of rotation

• θa = actual rotational acceleration of the vehicle about the given axis

42


some typical Control laws:

1. Proportional control Tc =−Kθ

• Tc = control torque

• K = system gain

• θ = error signal

proportional control is seldom used because it allows large angular excursions

2. Bang-bang control, a type of proportional control, sometimes used with thruster control,

Tc = Tp sign(θ); when a dead band is added, the performance of the bang-bang controller is

improved; in this case the error signal is compared to a limit and a pulse is fired only if the

error exceeds the limit

43


some typical Control laws:

3. Position-plus-rate controller: Tc =−k1θ− k2θ, also known as PD-controller; the rate term

provides damping and reduces the angular excursions

4. linear state feedback controller, nonlinear controller; include adaptation, robust modifications

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4. attitude control hardware

describe the specialized equipment used in an ACS; requires three types of specialized

equipment

1. sensors used to measure attitude of s/c wrt known quantities such as the sun, starts, or Earth

2. actuators are used to provide a torque to s/c to correct measured attitude to desired attitude

3. computers are used to perform the sensor processing, attitude determination, control law,

attitude, and maneuver calculations, on-line learning (neural networks, fuzzy learning)

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4. attitude control hardware-SENSORS

sensors provide “sensed” data about the position of the s/c relative to known quantities; A s/c

uses sensors to:

1. detect and measure rotation about three axes

2. locate the spacecraft-sun vector

3. measure rotational and linear acceleration

4. detect or track stars

46

4. attitude control hardware-RATE SENSORSGyros are precision instruments that detect small rotations wrt inertial space; have small angularrange and high accuracy as opposed to aircraft instrument gyros, which have a wide range andlow accuracy

operate on the principle that when a torque is applied to a spinning wheel the wheel precesses.

the axes that describe precession are the spin axis, the torque axis and the precession axis

angular velocity vector and momentum vector are aligned with spin axis

vector direction determined by RH rule

precession and angular acceleration in the direction of torque

for single axis gyro, the torque axis is called the input axis and the precession axis the output axis

angular rate of precession ωp is directly proportional to the input torque and inverselyproportional to the momentum of the gyro ωp =

TinIwωw

Inertial systems: Gyros used in two major ways to effect attitude control

1. Gyros and accelerometers mounted on a servo-driven stable platform; gyro output is used tokeep platform inertially fixed; vehicle control information obtained in inertial coordinates bycomparison with the stable platform position

47

4. attitude control hardware-RATE SENSORS

2. more popular method uses strap-down gyros which are fixed to the s/c body; gyros read

disturbance in body-fixed coordinates and the ACS computer is used to relate body-fixed

output to inertial reference frame; offers hardware simplicity, less power and weight at a cost

of computational complexity

48


Figure 2: Gyroscope

49

4. attitude control hardware-RATE SENSORSGyro errors or drift: result from imperfections in gyro; some forms of drift are proportional toacceleration or acceleration squared; some repeatable forms of drift can be measured andremoved by calibration corrections.

Description of various gyros and other sensors

1. one-degree-of-freedom gyros: single gimbal, free to rotate about output axis and is otherwisefixed; reference axis is body fixed and coincident with gyro spin axis at null; gyro input axis isalso body fixed and perpendicular to reference axis and output axis; gyro input is a rotation ofthe case about input axis; rotation is transmitted to wheel and axle through the gimbalbearings and constitutes a forced precession of the gyro, causes a rotation θ about outputaxis. Instrument measures the error angle, which can then be used to correct error.Depending on the way disturbing torque error is handled, the gyro is an integrating gyro, anundamped gyro, or a rate gyro

θout =HC

∫ t

0θin dt, or θout =

HC

θin

where:

• θin = angular input error caused by s/c motion

50

4. attitude control hardware-RATE SENSORS• θout = sensor output angle

• H = momentum of gyro rotor

• C = viscous damping around output axis

• H/C = gyro gain

2. two-degree-of-freedom gyros: Gyro wheel is set on bearings in the inner gimbal; the inner

gimbal is set in bearings in the outer gimbal, which in turn is set in bearings in the gyro case;

the gimbal arrangement allows the case rotational freedom wrt the inner gimbal; motion of

the inner gimbal is measured in 2 sensitive axes wrt the case; any small motion about the

sensitive axes is measured and used to correct disturbing torques.

A variety of designs are used to reduce friction:

• electrostatic gyro; spherical rotor is supported electromagnetically in cavity

• gas-bearing gyro; spherical rotor supported in cavity by a thin layer of gas under pressure

3. ring-laser gyro: few moving parts since spinning light instead of spinning mass is used; gyro

detects and measures angular rates by measuring the frequency difference between two

contrarotating laser beams

51


4. hemispherical resonator gyro; small volume and mass along with simple operation and no

wearout components; a hemispherical resonator is driven at its resonant frequency;

disturbance torques produce measurable changes in the resonance pattern of the

hemisphere, which is detected by a collar surrounding the resonator

5. accelerometers: simple instrument that measures force on a known mass

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4. attitude control hardware-INERTIAL SENSORS1. star scanners: rotated past the calculated position of a guide star; difference between the

calculated position and the measured position of the guide star is used to calculate anattitude update

2. star tracker: camera-like using a charge-coupled device (CCD) array; provides a horizontaland vertical position (in tracker coordinates) which is then converted to a position error;provides continuous position updates as the star moves through the instruments field of view

3. star cameras: use CCD combined with image processing performed in the onboardcomputer; observes a segment of sky and deduces position by pattern matching

4. sun sensor: wide-angle measurement used primarily to point solar panels or in attitudeinitialization; much smaller, more rugged instrument than star scanners; weigh about 0.3kgand consume about 0.5 W continuously

5. horizon sensors: useful for finding the nadir vector; are an infrared (IR) sensing instrument;location of the horizon is sensed by the dramatic difference in IR emission of the Earth diskand cold deep space; suitable for spinning s/c. It used on a three-axis s/c, the instrumentmust have a scanning head. Used in pairs they can provide nadir within about 0.1 degrees;weigh about 2-7kg and require 5-10 W.

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4. attitude control hardware-INERTIAL SENSORS

6. global positioning system receiver: small, light, very accurate instrument for determining

position (navigation)

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4. attitude control hardware-ACTUATORS1. wheels

• control moment gyros (CMG): gimbaled wheels spinning at a constant rate (§10);commanded force on the input axis of the gyro causes a control torque to the s/c on theoutput axis; larger and heavier than reaction wheels and consume more power

• momentum wheels: are flywheels designed to operate at a biased nonzero speed (§10);momentum is exchanged at the wheel by changing wheel speed; usually body fixed.Momentum wheels and reaction wheels differ only in speed bias

• reaction wheels; small flywheels powered by dc motor, which exchanges momentum withthe s/c by changing wheel speed.

• torque rods; take advantage of Earth’s magnetic field to generate a correcting force on as/c; it is simply a wire coil wrapped around a rod, usually a few centimeters in diameterand about a meter in length; when current is sent through the coil a torque is generatedby the interaction of the current and Earth’s magnetic field

T = NBAI sin(θ)

where

– T = torque, N-m55

4. attitude control hardware-ACTUATORS

– N = number of loops in coil

– B = magnetic field of central body, tesla

– A = area of coil, m2

– I = current, amperes

– θ = angle between Earth’s magnetic field lines and coil centerline

2. thrusters provide momentum to s/c by ejecting mass overboard in the form of high velocity

exhaust gas; three types:

• cold gas; simplest, used for small s/c with impulse requirements of a few hundreds

newtons per second

• monopropellant hydrazine; dominant choice, gives mid-range specific impulse with a

simple system; requires 12 thrusters to provide pure moments about three axes

• bipropellant; most expensive and complex; used for trajectory control and infrequently for

attitude control

Thrusters can be used directly to control the s/c attitude or used as momentum desaturation

actuators for the reaction wheel, (§10)

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4. attitude control hardware-COMPUTERS

used for attitude control system and data handling; considerations for central computer for both

control and data handling and attitude control vs individual computers for each subsystem:

• central computer is lighter and cheaper

• central computer is a simpler system from the hardware standpoint; however, the software

system may be more complex

• dominant requirements for the two systems are different; attitude control system needs a

very fast computer; data system needs large memory and file handling features; specialized

computers offer better performance; central computer is a performance compromise

• two different computers make a more comprehensive fault protection system possible; the

ACS can monitor the C&DA computer and vice versa; to take full advantage of cross

monitoring requires redundant computers of each type so that a failed computer can be

taken off line; such a system requires substantially more complicated software

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Documents

AE4713F15LectureonACS.pdf