Active Pointing, on a Budget
The Sun Devil Satellite 1 (SDS-1), and
The Flare Initiation Doppler Imager (FIDI)
The FIDI Instrument
http://sdsl.club.asu.edu/
Authors
The Sun has been imaged in great detail in a multitude of wavelengths, however high time
resolution data of solar flares is still somewhat lacking. The Flare Initiation Doppler Imager, as its
name implies, aims to obtain doppler images of the Sun during increased solar activity, at a time
resolution of 1s.
Aaron M. Goldstein
Christopher T. Kady
Abstract
The FIDI instrument consists of two co-aligned EUV telescopes that form two images side-by-side
on the same focal plane array. The two telescopes image the solar disk in two bandpasses,
centered to the red and blue sides of Fe XVI 335 Å. The difference of the two images provides a
measure of the Fe XVI 335 Å Doppler shift with a sensitivity to shifts of 25 km/s and greater. The
two images will be formed side-by-side and captured by the same focal plane array, a thinned
back-illuminated CMOS sensor. To achieve consistent and clean capture of the Sun, the FIDI will
have to be pointed with an accuracy of +/- 0.2º, at less than 0.1º/s.
Interplanetary travel, much like early earth exploration, is an advent
that produces not only tremendous public interest but ground breaking
technology as well. The capability of active pointing on a CubeSat is an
essential
part of
an interplanetary
mission,
costis and
design
Interplanetary
travel,
much like early
earth however
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work
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with
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Using
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to implement
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we present momentum
a 3u CubeSat
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the
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torque
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sensorybore-sight,
and actuator
system
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is
expected
around $100,000,
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implementing
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a similar
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the
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incurred inwhich
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is considerably
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(ACS)
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related
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Using
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pointing
system,
interplanetary
CubeSatthistravel
made
more
simplified,
accessible. and easily repeated. Through the development of an
accurate and inexpensive active pointing system, interplanetary
CubeSat travel is made more accessible.
Abstract
The SDS-1 CubeSat
The SDS-1 is the CubeSat platform that will support the FIDI instrument. Mounted within the SDS-1
structure, the FIDI will occupy the front half of the satellite, and will point in a parallel direction
with two deployable solar panels. To properly obtain the data rate necessary, the SDS-1 will
downlink twice a day using a 2.4GHz patch antenna. To achieve these critical mission
requirements, the SDS-1 places significant emphasis on its 3-axis attitude control subsystem.
Actuators
Modeling Overview
Sensors
Reaction Wheels
Sinclair Interplanetary – RW-0.01-4
Fine Sun Sensor
Sinclair Interplanetary – SS-411
Specs:
Accuracy:
Specs:
Nominal Torque:
1 mNm
Momentum Storage:
+- 0.1 deg
Field of View:
+- 70 deg
10 mNm-sec @ 3410 RPM
Inertial Measurement Unit
Micro Aero Solutions – MASIMU-02
Torque Rods
Satellite Services Ltd.
Specs:
Rate Gyro
Specs:
Nominal Dipole:
0.2 Am2
Accuracy: 0.02 deg
Drift: <= 0.2 deg/min
Range: +- 150 deg/s
Model Details
Torque Determination
(Hardware Response)
Control Mode (Control Mode Select)
The SDS-1 enters 1 of 2 control modes, every clock cycle,
depending on the reaction wheel momentum status:
The simulation conducted was developed
in MATLAB Simulink. It follows a typical 3
input, 3 output, feedback control loop
format. The control law selection and
determination blocks, or the Control
Mode Selector, and Hardware Response
blocks, feed into a plant model, or the
Rigid Body Dynamics block, which
determines the SDS-1's current euler
angles. These angles are fed back through
a sensor distoration, or Sensor Dynamics
and Kalman Filter block,
An ideal torque desired (1.) is determine from
the controller gains selected. This desired
torque is fed intro the Hardware Response
block where it is subtracted from the torque
rod torque (2.), depending on the Control
Mode, and the rest of the torque is applied
through the reaction wheels (3.).
Mode 1: Utilize the torque rods, applying a moment in the
reverse direction of the current reaction wheel stored
momentum to desaturate the reaction wheels.
Mode 2: Turn torque rods off, allowing reaction wheels to
maintain full attitude control.
Torque
RW
momentum
Mode 2
Mode 1
Mode 2
Modeling the reaction wheels is accomplished through
specifying a maximum and minimum torque value (+/
- 1 mNm), as well as a maximum and minimum stored
momentum value (+/- 1 mNm-sec). When the limiting
torque value is reached, the model simply uses the
corresponding limiting torque value. However, when
the limiting momentum value is reached, the model
drives the available torque to 0 mNm.
Euler
Angles
-0.01
0
1000
2000
3000
4000
5000
Time [s]
6000
7000
8000
9000
10000
+
Euler
Angles
d
dt
Body Rates
Transformation
Uniform
Linear Error
To
Coupled
& 1D
Kalman
NOAA World
Magnetic
Model [1]
Conversion to
Discrete Voltage
+
x 10
X-dir
Y-dir
Z-dir
X-dir
Y-dir
Z-dir
3
2
0.5
0
-0.5
-1
0
1000
2000
3000
4000
5000
Time [s]
6000
7000
8000
9000
10000
1
0
-1
-2
-3
-3
12
Euler Angles [rad]
8
6
4
2
0
0
1000
2000
3000
4000
5000
Time [s]
6000
7000
8000
9000
10000
Reaction Wheel Momentum [N-m-s]
z
10
6
x 10
-4
X-dir
Y-dir
Z-dir
4
2
0
-2
-4
-6
-8
0
1000
2000
3000
4000
5000
Time [s]
6000
7000
8000
9000
10000
0
1000
2000
3000
4000
5000
Time [s]
6000
7000
8000
9000
10000
Above shows the sum total
disturbance torque applied
throughout the mission day.
-5
6
The hardware response of the actuators
over the full mission day are shown
above. Modes 1 and 2 can be observed
above, mode 1 occurs when torque rods
are generating an applied torque.
x 10
X-dir
Y-dir
Z-dir
4
2
Magnetic Field [nT]
The plots above depict the attitude of
the satellite over approximately 16
orbits, or 1 full mission day. The
attitude is shown in the x and y planes
to be holding a constant reference, and
in the z plane to follow a moving
reference.
0
-2
-4
-6
0
1000
2000
3000
4000
5000
Time [s]
6000
7000
Right Ascension [deg]
Using Keplerian orbital mechanics, 1 full day of the mission of
SDS-1 was simulated, consisting of approximately 16 orbits.
This data was used to generate the environmental
disturbance predictions, predict the magnetic environment,
and was largely an input to the attitude control simulator.
Aerodynamic Drag
The most significant component of the disturbance
environment was the aerodynamic drag and torque, since
the orbital altitude is approximately 350 [km]. The 1976
Standard Atmosphere Model [2] was used to determine the
mean atmospheric density at this altitude. In order to
determine the aerodynamic torque, it was necessary to
determine the moment arm between the center of pressure
and center of mass. This was determined by considering the
silhouette of the satellite was a flat plate. The angles at
which the silhouette was oriented was determined to be
proportional to the angles between the sun vector and wind
velocity vector.
8000
9000
1D Kalman
The magnetometer data, and the z axis
body rate were cfiltered using 1D Kalman
filter methods.
Coupled Kalman
The body rates in the x and y axes were
filtered with x and y angles in a coupled
kalman filter.
Conclusion
Environment
-6
4
+
To 1D
Kalman
Kalman Filtering
The IMU was modeled by transforming the Euler angles
from the rigid body dynamics to body rates. Then, error
was included by considering the resolution and drift
present in the device.
x 10
+
+
For a particular orbital position, MATLAB’s
‘wrldmagm’ function was utilized to lookup a
predicted value of magnetic field. To mimic a
reading, noise and error was added according to
the HMC 1043 specification.
To
Coupled
Kalman
+
Conversion to
Discrete Voltage
Gaussian
Noise
Drift
Error
1
-1.5
Magnetometer
Inertial Measurement Unit
Disturbance Torque [N-m]
-0.005
Torque Rod Torque [N-m]
Euler Angles [rad]
0
+
Hardware Response
-5
y
0.005
time
The sun sensor was modeled by defining the line of
sight of the sun sensor, and then by reading in the
Euler angles. These readings were discretized, and
uniform noise representing random error was added
to the signal.
The moment required from the torque rods is simply
limited by a maximum and minimum dipole
contribution of +/- 0.2 Am2 from each torque rod. In
simulation a desired torque rod moment direction is
found first, then utilizing magnetometer readings, a
possible dipole vector is found, which is then used to
determine an available torque rod moment.
Simulation Results
Conversion to
Discrete Voltage
Uniform
Error
Torque Rods
x
Environment Modeling
Total Desire Torque
Fine Sun Sensor
Reaction Wheels
1.5
120 ugauss
Sensor Modeling
Actuator Modeling
0.01
Resolution:
Torque Rod
Lower Momentum Limit
Attitude Response
1.56% Applied Field
3. Reaction Wheel Torque
1. Total Desired Torque
2. Torque Rod Torque
Upper Momentum Limit
time
Specs:
Total Error:
Declination [deg]
Introduction
Magnetometer
Honeywell – HMC1043
10000
Shown above is the simulated
magnetic field present.
At a final estimated hardware cost of
~$100,000 is considerably less than those of
similar accuracy specifications. This is largely
due to the use of ‘off the shelf’ hardware, and
implementing
computational
design
techniques.
Through the use of the
MATLAB/Simulink suite, the design of an active
pointing system can be accomplished with
relative ease. Future work may include the
implementation of a MATLAB GUI to assist in the
modeling and design process.
The ACS system was designed such that it
could be scaled up or down, depending on the
need. For instance, replacing torque rods which
depend on the Earth’s magnetic field with cold
gas thrusters could be simply implemented in
the ACS simulator model.
Other Disturbances
There are numerous other disturbances to consider, but
many were much smaller in magnitude than the
Aerodynamic drag. For instance, since the satellite is always
sun pointed, the solar pressure will produce very little or no
torque due to an extremely small moment arm between the
solar center of pressure and the center of mass. The gravity
gradient is also a torque commonly considered, but due to
the relative symmetry present in the inertia tensor, the
gravity gradient is very small compared to the aerodynamic
disturbance.
References
[1] NGA, , NGDC, and BGS. "World Magnetic Model." Provided By, NGDC & NOAA WMM.
[2]
(2005): n.pag. Web. 28 May 2012. <http://www.ngdc.noaa.gov/seg/WMM/
DoDWMM.shtml >.
NOAA, NASA, USAF. U.S. Standard Atmosphere, 1976. Washington, D.C.: 1976. Print.
<http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/ 19770009539_1977009539.pdf>.