Attitude and Orbit Control

Attitude & Orbit Control
System (AOCS)
Introduction
Unit II
Prepared By
P.Raja Pirian
Outline
1. Attitude/Orbit equations of motion
2. AOCS hardware
3. Attitude determination
4. Attitude control
5. AOCS design
Attitude/Orbit equations of
motion
Orbit (translation):
Simple model: Kepler time equation
Complicated model:
Lagrange planetary equation
Newton 2nd law of motion
Attitude (rotation):
Kinematic eq.
Dynamic eq.: Euler rotational eq. of
motion
Orbital dynamics: two-body
problem
Two-body problem: (point masses)
Conservation of energy (dot product with .)
Conservation of angular momentum (cross
product with )
Keplers 1st law: the orbit of each planet around
the sun is an ellipse, with the sun at one focus.
Keplers 2nd law: the radius vector from the sun to
a planet sweeps out equal areas in equal time
intervals.
Keplers 3rd law: the square of the orbital period of
a planet is proportional to the cube of the semi-major
axis of the ellipse.
Orbital dynamics: three-body
problem
Circular restricted three-body
problem: the motion of the two primary bodies
is constrained to circular orbits about their
barycenter.
Sun-Earth-Moon
Lagrangian (or libration) points
Halo orbit (closed Lissajous trajectory: quasi-periodic
orbit)
Elliptic restricted three-body problem

Earth-Moon-Satellite
Orbital dynamics: Keplers
time eq.
Keplers time eq.:
find the position in
an orbit as a
function of time or
vice versa.
Applicable not only
to elliptic orbits, but
all conic section
families (parabola,
hyperbola)
M: mean anomaly, E: eccentric anomaly

e: eccentricity, a: semimajor axis
Orbital dynamics: orbital
elements
At a given time, we
need 6 variables to
describe the state in
3D translational
motion
(position+velocity)
6 orbital elements:
Semimajor-axis, a
Eccentricity, e
Inclination, i
Right ascension of
ascending node,
Argument of perigee,
Mean anomaly, M
Orbital dynamics: environmental
perturbations
Conservative forces:
Asphericity of the Earth: zonal/tesseral
harmonics
Third body gravitational field: Sun/Moon
Non-conservative forces:
Aerodrag: area-to-mass ratio
Solar wind
Attitude dynamics:
constant body-fixed torque (M=const.)
Spinning axisymmetric body
Possesses a gyrostatic stiffness to external
disturbances (e.g., football)
The path of the tip of the axis of symmetry in
space is an epicycloid.
Asymmetric rigid body
About major or minor axis
About intermediate axis
Gravitational Orbit-Attitude Coupling
Why coupling? Because the rigid body is

not a point mass.
Derivation: expand the Earth gravitational
force in terms of Legendre polynomial,
then the corresponding torque appears in
higher order terms of the moment of
inertia dyadic.
Significant when the characteristic size of
the satellite is larger than 22 km.
Conclusion: dont worry about this effect
now.
Solve Attitude/Orbit dynamics
numerically
Orbit: Newtons 2nd law of motion
Cowells formulation
(Enckes method)
Attitude a): kinematic equation
Attitude b): dynamic equation

AOCS hardware
Sensors:
Sun sensor
Magnetometer (MAG)
Star tracker
Gyro
GPS receiver
Actuators:
Magnetorquer (torque rod) (MTQ)
Reaction wheel (RW)
Thruster
AOCS hardware: gyro
Rate Gyros (Gyroscopes)
Measure the angular rate of a spacecraft
relative to inertial space
Need at least three. Usually use more for
redundancy.
Can integrate to get angle. However,
DC bias errors in electronics will cause the output of
the integrator to ramp and eventually saturate (drift)
Thus, need inertial update
Mechanical gyros (accurate, heavy); Fiber
Optic Gyro (FOG); MEMS-gyros
AOCS hardware: MAG &
MTQ
Sensor: magnetometer (MAG)
Sensitive to field from spacecraft (electronics),
mounted on boom
Get attitude information by comparing measured B to
modeled B
Tilted dipole model of earths field
Actuator: torque rod (MTQ)
Often used for Low Earth Orbit (LEO) satellites
Useful for initial acquisition maneuvers
Commonly use for momentum desaturation
(dumping) in reaction wheel systems
May cause harmful influence on star trackers
AOCS hardware: reaction
wheel
One creates torques on a spacecraft by creating
equal but opposite torques on Reaction Wheels
(flywheels on motors).
For three-axes of torque, three wheels are
necessary. Usually use four wheels for
redundancy (use wheel speed biasing equation)
If external torques exist, wheels will angularly
accelerate to counteract these torques. They
will eventually reach an RPM limit (~3000-6000
RPM) at which time they must bedesaturated.
Static & dynamic imbalances can induce
vibrations (mount on isolators) jitter.
Usually operate around some nominal spin rate
to avoid stiction effects: avoid zero crossing.
AOCS hardware: thruster
Thrust can be used to control attitude but at
the cost of consuming fuel
Calculate required fuel using Rocket Equation
Advances in micro-propulsion make this
approach more feasible. Typically want Isp>
1000 sec
Use consumables such as Cold Gas (Freon, N2) or
Hydrazine (N2H4)
Must be ON/OFF operated; proportional control
usually not feasible: pulse width modulation (PWM)
Redundancy usually required, makes the system
more complex and expensive
Fast, powerful
Often introduces attitude/translation coupling
Standard equipment on manned spacecraft
May be used to unloadaccumulated angular
momentum on reaction-wheel controlled spacecraft.
Attitude Determination
IMU (Inertial Measurement unit): gyro +

accelerometer
IRU (Inertial Reference Unit): gyro
Gyro-stellar system: gyro + star tracker
Gyro: rate output, but has bias need to
estimate gyro drift: Kalman filter or a low
pass filter; integrate to obtain angle.
Star tracker: angle output differentiate to
obtain rate (will induce noise)
Orbit Determination
GPS receiver: obtain measurements
Extended Kalman Filter:
1. State propagation (or prediction) (Cowells
formulation: nonlinear)
2. State residual covariance matrix propagation
(linearized state transition matrix)
3. Kalman gain computation: steady-state gain can be
solved from Riccati equation.
4. State update (or correction)
5. State residual covariance matrix update (or
correction): use Joseph form to maintain symmetry.
Attitude control: some
definitions
Attitude Control
The environmental effects
Spin stabilization
Dual-spin stabilization
Three-axis active control
Momentum exchange systems
Passive gravity gradient stabilization
Attitude control:
environmental effects
Solar radiation pressure
Force
Torque: induced by CM & solar CP offset. Can
compensate with differential reflectivity or reaction
wheels.
Gravity gradient torque
Geo-Magnetic (near field) torque: model
spacecraft as a magnetic dipole
Aerodynamic torque: drag coeeficient CD=2.2 for a
spherical shape satellite; CD=3 for a cylinder. Only a factor
for LEO.
Attitude control:
spin/dual-spin stabilization
Spin stabilization:
Requires stable inertia ratio: Iz>Ix=Iy
Requires nutation damper: ball-in-tube, viscous ring,
active damping
Requires torquers to control precession (spin axis drift)
magnetically or with jets
Inertially oriented
Dual-spin stabilization
Two bodies rotating at different rates about a common
axis
Behave like simple spinners, but part is despun
(antenna, sensor)
Requires torquers for momentum control and nutation
dampers for stability
Allows relaxation of majar axis rule
Attitude control:
three-axis active control
Reaction wheels most common actuators
Fast; continuous feedback control
Moving parts
Internal torque only; external still need
momentum dumping (off-loading)
Relatively high power, weight, cost
Control logic simple for independent axes
Attitude control:
gravity gradient stabilization
courtesy from Oliver L. de Weck: 16.684 Space System Product Development, Spring 2001
Department of Aeronautics & Astronautics, Massachusetts Institute of Technology
Requires stable inertias: Iz<<Ix, Iy

Requires libration dampers: hysteresis rods
Requires no torquers
Earth oriented
Attitude control:
momentum exchange
Reaction wheel (RW) systems
Momentum bias systems: a single RW is aligned
along the pitch axis of the spacecraft which is oriented
along the normal to the orbital plane.
Control moment gyro (CMG) systems
Single gimbal CMG
Double gimbal CMG
RW has smaller output than CMG; CMG has
singularity in momentum envelope.
AOCS Design: spin
stabilization
Suppose there is no thurster on the spacecraft.
Maintain current and accurate properties of the spacecraft

and alternate configurations.
Determine the mass and balance of the spacecraft.
Provide adequate gyroscopic stiffness to prevent
significant disturbance of the angular momentum vector.
Approximate rule of thumb: 1.05<Ispin/Itrans<0.95
Keep track of inertia ratios and the location of the center of
mass.
Consider nutation, spin-axis orientation, spin rate, and
attitude perturbation.
AOCS Design: dual-spin
stabilization
1. Energy dissipation of the spacecraft should be managed.
2. The center of mass of the spinner should be as close to the
bearing axis as possible.
3. The bearing axis should be the principal axis of the
spinning part to prevent forced oscillations and nutation
due to center of mass offset and cross products of inertia
of the spinner.
4. The spinner should be dynamically symmetric (equal
transverse moments of inertia) or the stability of spin
about the minor principal axis of the spacecraft must be
reevaluated by numerical simulation.
5. For the general case when the despun body has significant
cross products of inertia or if its center of mass is not on
the bearing axis, simulation of the system equations is
recommended.
AOCS Design: three-axis active
control
1. Ensure that all closed loop control systems exhibit
acceptable transient response.
2. Control system torque capability must be sufficiently
large to correct initial condition errors and maintain
attitude limits within specified values in the presence
of the maximum environmental disturbances.
3. The control logic must be consistent with the minimum
impulse size and lifetime specification of the thrusters.
4. Evaluate system performance incorporating as many
hardware elements in a simulation as possible,
5. Combine the normal tolerances statistically with the
beginning and end-of-life center of mass location and
moment of inertia characteristics.

Attitude and Orbit Control

Uploaded by

Copyright:

Available Formats

Attitude and Orbit Control

Uploaded by

Document Information

Original Description:

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Attitude and Orbit Control

Uploaded by

Copyright:

Available Formats

Attitude & Orbit Control

Elliptic restricted three-body problem

M: mean anomaly, E: eccentric anomaly

Why coupling? Because the rigid body is

Attitude b): dynamic equation

IMU (Inertial Measurement unit): gyro +

Requires stable inertias: Iz<<Ix, Iy

Maintain current and accurate properties of the spacecraft

You might also like