Download Design of FIU FUNSAT System: Attitude Control for the 3U CubeSat

Design of FIU FUNSAT System: Attitude Control
for the 3U CubeSat
Pradeep Shinde, Elijah Newman, Ibrahim Tansel, Sabri Tosunoglu
Department of Mechanical and Materials Engineering
Florida International University,
10555 West Flagler Street
Miami, Florida 33174
[email protected], [email protected], [email protected], [email protected]
ABSTRACT
CubeSats are inexpensive, versatile, light in weight and
make for a very good resource when desired an inexpensive
way to collect data in space. One of the subsystems of the
CubeSat, which is very important and often times
determines whether a mission will fail or not, is the attitude
control system. Standard size of 3U CubeSat is 10 cm x 10
cm x 30 cm. Given such small dimensions, traditional ways
of control are not feasible and thus the necessity for smaller
components and parts arise. With this in mind, magnetic
torque bars are a relatively new invention that, when
mounted on the satellite’s frame has the ability to create
torques. They consist of a metal rod usually wrapped in
copper wire to create an electromagnet. The magnetic field
created by the electromagnet will try to align itself with the
earth’s magnetic field which creates the torques. This paper
presents a simple design for a torque rod developed
intended to be implemented on Florida International
Universities’ RoarSAT.
Keywords
Attitude control, Attitude determination, CubeSat, 3U, FUNSAT
1. NOMENCLATURE
µ
τ
V
M
B
Core Radius, m
Core length, m
Permeability of Free Space, H/m
Relative Permeability of Core, H/m
Torque, Nm
Voltage, V
Current, A
Wire Resistivity, /
Solenoid Resistance,
Wire Length, m
Core Length, m
Demagnetizing Factor
Coil Turns
Total Moment, Nm
Magnetic Field, T
p
m
P
F
f
Momentum,
Mass,
Power, W
Force, N
Frequency, Hz
/
2. INTRODUCTION
CubeSat’s have grown in popularity in recent years. This is
due to their small size, light weight, low cost and their
ability to transport a variety of payloads. Because of this, it
is necessary to miniaturize components, which includes the
attitude control system (ACS). Full-scale satellite attitude
control systems, in general are too large or too expensive to
be installed in the CubeSat’s [1]. In recent years, the use of
magnetic torque bars (aka magnetorquers) and small sized
reaction wheels, have been explored in the application of
controlling these small space vessels [2, 3, 4]. The work of
A magnetic torque bar as referred to in this paper, is a
current carrying solenoid with a magnetic-material core,
which, when a current is passed through, it produces a
resulting torque. While this is the type of torquer that will
be elaborated on, there are two other primary ones; the air
coil torquer and the permanent magnet. The air coil is a
planar enclosed current carrying coil; similar to the first
torquer it creates a moment when a current is sent through
it. The third is the permanent magnet, which by interaction
with earth’s magnetic field creates a magnetic moment;
however, there is no simple way of controlling its
magnitude and direction. With this in mind, the
electromagnetic torquer remains the most feasible given
that they require the least amount of power and have the
ability to be adjusted based on requirements. While the
produced torque is small, the satellite will be operating at
LEO, and the necessary minimal torque is therefore
justified.
This paper has organized as follows: Section 3 summarizes
the architecture od the attitude control system, its mission
goals in respect with RoarSAT, theoretical calculation
Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016.
266
procedures, orbital parameters, design specifications and
proposed design. The equations used for the theoretical
calculations are from the work of Bauer, W., and Gary D.
[5] and Mehrjardi, Mohamad Fakhari, and Mehran
Mirshams [6]. Section 4 discusses the proposed attitude
control system with the cost and weight budget of the
proposed system. In section 5 conclusions are made and
future considerations are proposed. Followed by the
acknowledgement and references in sections 6 and 7
respectively.
and z directions). This component will be controlled by an
ATmega328 single chip host controller. The responsibility
of the sun sensor is to keep track and measure the position
of the sun with respect to the satellite. It works by letting
light into the chamber of the sensor which strikes lightsensitive cells. With a reference centerline, a refraction
angle can be measure using the chamber height. Because
3. ATTITUDE CONTROL SYSTEM
An attitude control system can be divided and distinguished
as individual counterparts, i.e. attitude determination (AD)
and the actual attitude control (AC). These counterparts
each have their own components and specifications, and in
combination they form a complete attitude control system.
Upon initial launch and release into orbit, the satellite will
be tumbling about all axes in an uncontrolled manner. It is
the responsibility of the ACS to correct this and then orient
the satellite in a specific direction based on the
predetermined requirements. Accounting for the fact that
there has been a plethora of research in the field
encompassing concepts, manufacturing and testing of such
systems, this paper presents a basic but highly effective
design to be implemented on Florida International
University’s RoarSAT.
An AD system can be made using a variety of sensors. The
idea is to measure variables that allow the onboard
computer to develop a matrix which describes the motion
about all axes of the satellite at a specific moment. The
computer then uses this to generate a correction matrix to
be implemented by the AC. A correction matrix after
launch will be generated instantly by the satellite, however
all other maneuvers that are mission specific will be sent
from earth for the satellite to keep its path. The next step is
to implement the AC.
Like AD, there are numerous ways to make and implement
attitude control. Typically, larger space vessels and
satellites use thrusters, however, given the constraints,
magnetic torque bars will be employed on each principal
axis. Each torque bar will have the ability to produce a
torque which in turn acts on the satellite to change its
direction. However, the produced force is limited and
remains a function of the electromagnetic core and the
specifications of the coil.
3.1 Attitude Determination
The purpose of the AD system is to establish the satellites
orientation and position at a given moment. To do this, the
LSM9DS0 sensor board (Figure 1) will be used in
conjunction with a sun sensor (Figure 2) to determine the
acceleration, orientation, magnetic field and position with
respect to the sun. This sensor board is a SIP containing a
3D accelerometer, 3D gyroscope and a 3D magnetometer
(3D in this case represents a sensor measurement in the x, y
Figure 1. LSM9DS0-9DOF Sensor
the light cells operate on the photoelectric effect, the
photons are converted into electrons and then into a digital
signal to be read by the host controller.
In different AD systems implemented on other satellites,
sensor selection can be different. This is usually dependent
on mission objective and any constraints presented during
the design, construction and fabrication process for the
vessel. One application that has been explored during the
process of developing this proposal is the observation of
earth through a long optical lens. The payload would also
include a thermal camera and the main purpose would be to
gather weather data and thermal images that can help
predict cloud height amongst other things. With this
endeavor, it is not necessary to keep and maintain very
accurate pointing coordinates, and it would be a waste of
power if that were attempted. This means that there is a
tolerance that is acceptable; a reasonable degree of
inaccuracy to which the satellite can point without
compromising the mission objective. However, if a high
degree of accuracy was desired, using reaction wheels and
or control moment gyros in combination with the
magnetorquors would allow for a much better degree of
accuracy. The reaction wheels and or the gyros would act
as the main source for attitude control, the torquers would
then be a secondary means-useful for desaturation and
despinning the satellite after launch into orbit. However, it
is important to note that the addition of these components
add to the total weight resulting in increased costs.
Figure 2. Sun Sensor
Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016.
267
3.2 Attitude Control
Magnetic torquers work through interaction of the
satellite’s magnetic field with earth’s magnetic field. With
each coil, when current flows through the loop it creates an
electromagnet. With each of the torque bars placed and
oriented along different axes, the corresponding directions
of the magnetic fields will be different. By determining a
value for the current flowing through the loops based on
voltage and resistance, a magnetic field for each torque bar
can easily be calculated. The magnitude and direction of
earth’s magnetic field will also vary, and maintaining that
the satellite is in a LEO, the earth’s magnetic field is still
strong enough to create a torque on the satellite thus
changing its direction.
3.3 Velocity Calculations
Given a maximum force that each torquer is required to
produce, the equations below outline the requisite steps
needed to obtain a final design.
First, a period must be defined. When launched into space,
depending on the altitude of the orbit the satellite will take,
the period will vary and therefore this must be the first
parameter defined as this affects all further calculations.
The frequency ‘ ’ is calculated using (1) where ‘T’ is the
period.
1
(1)
The angular velocity is then calculated using (2) and
velocity using (3) where ‘c’ is defined as the radius of orbit.
2
(2)
(3)
Momentum equations relate the mass and velocity of an
object. With this, the required force needed to shift the
satellite can be calculated.
(4)
A velocity vector relationship (Figure 3) can then be
developed to calculate the velocity difference needed to
shift the satellite θ degree in pre-specified time frame,
which would then be resubstituted into (4) to obtain the
design force that each torquer would need to produce.
vi
θ
vdifference
summarizes the orbital information operating at 600km
above the surface of the earth.
Table 1. Orbital Parameters
Orbital Radius
6971 km
Orbital Time
1 h, 36 m, 41 s
Period
5801 s
1.723841
Frequency
1.083121
Angular Velocity
Velocity
10
Hz
rad/s
7.55 km/s
Momentum
30200 kg-m/s
In the design of the attitude control system for RoarSAT
mission, a standard scenario was considered. Change in
momentum required for one-degree change in angular
rotation in one particular direction was determined. Table 2
summarizes the parameters obtained to be used in the
design of the torquers.
Table 2. Design Parameters
1 Degree Rotation
Initial Momentum
30200 kgm/s
Required Change in Velocity
131.78 m/s
Required Change in Momentum
527.14 kgm/s
3.4 Torquer Calculations
Torquer system is designed in the following sequence to
generate desired control on attitude of the satellite. First, as
designed parameters, a wire length and core radius will be
defined from which the number of loops is calculated using
equation (6).
(6)
2
It is then necessary to obtain a value for the total resistance
of the wire. Equation (7) shows the resistance calculation
and finally a current is obtained using (8).
(7)
(8)
It is necessary to calculate a demagnetization factor which
accounts for the stray field produced by the magnetization
of the cylindrical core. This is given by (9).
4 ln
vf
10
1
(9)
4ln
Figure 3. Velocity Vector
tan θ
(5)
RoarSAT’s mission focusses on Earth’s ground
surveillance from 600km above the Earth’s surface. Table 1
Finally, a magnetic field and moment for the satellite can
be calculated using (10) and (11) respectively.
1
Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016.
(10)
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1
(11)
1
1
With the calculated moment and magnetic field, the torque
produced is given by (12).
1
(12)
Applying these equations for a torquer core of perm alloy
and a copper solenoid, the values obtained are as follows.
Table 3. Torquer Specifications
Core Length
0.09 m
Core Radius
0.002 m
Demagnetization Factor
0.005586028
Wire Resistivity
1.68E-08
Relative permeability
75000
Wire Length
100,m
Number of Turns
7957
Wire Resistance
3.44 Ω/m
Wire Gauge
40
Coil Layers
6.96
Magnetic Field
0.2311258 T
Magnetic Moment
0.208828 N-m
Torque
0.048265 N-m
Force
24.133 N
Table 3, above shows the torquer specifications of the
proposed design. For the proposed torquer design, the
generated force at the end of the torque bar can be found
around 24 N. With this generated force and change in
momentum required for one-degree change in angular
rotation of the RoarSAT, total time required can be found
using the equation (13) below. For the current design total
time of around 21.84 seconds was found to change the
attitude of the RoarSAT by one-degree change in angular
rotation.
(13)
∆
∆
Alternatively, a power and voltage can be defined as
designed parameters, from which the total circuit resistance
and wire length can be calculated. This is given by (14) and
(15) respectively.
permalloy core with 4 mm diameter and 9 cm length and
40-gauge copper coil with 100 m in length was proposed.
With the design presented, the force produced by the
attitude control system was ~24 N, and the time required to
change the RoarSAT’s attitude by one-degree change in
angular rotation is ~22 seconds assuming there are no
external forces that act on the satellite and no interruptions
in its flight path. The power consumption of the proposed
design is found to be 0.0465 W, based on the 4 V supply
from the on-board power system. Total cost and weight
estimate of the attitude control system is another primary
aspect in terms of determining the feasibility of the system
for the required mission. Total cost of the proposed system
is $2135 whereas the weight of the system is around 41 g,
as can be seen from Table 4, below.
Table 4. Cost and Weight Estimate
Component
Cost
Weight
LSM9DS0
$40
4g
Sun Sensor
$2000
5g
Perm alloy Rod x3
$70
30 g
40ga Copper Wire (300m)
$25
1.5 g
Total
$2135
40.5 g
It is to be noted that there is only one sun sensor used in the
proposed design due to the high cost of the sensor. Ideally,
six of these sensors should be used on each face of the
structure. However, using only one sun sensor RoarSAT
team is proposing the cost efficient system. Use of only one
sun sensor will require initial alignment of the sun sensor in
the direction of the sun. Initial alignment will be conducted
by continuously changing the attitude of the RoarSAT in
search of the sun in all three directions, by receiving the
output from the sun sensor. This will consume more time
during the initial alignment, however it will save $10,000
on the additional five sensors cost.
5. CONCLUSION
4. DISCUSSION
Light weight, low power and cost effective RoarSAT
attitude control system has been conceptually designed for
complicate mission demands. The design presented makes
use of a perm alloy rod, 9cm in length and having a
diameter of 4mm. It is wrapped in 40-gauge copper wire
forming approximately 7 copper layers of coil with a
combined total of 7957 turns. The proposed design
precisely shows around 22 seconds required to change onedegree angular rotation of RoarSAT. The proposed system
weighs around 41 g, consumes around 0.0465 W and costs
$2135.
The paper presents two alternative methods of designing
the attitude control system in the earlier section. The first
one with wire and core as design parameters where as the
second one is the voltage and power available as the design
parameters. First method of design was elaborated in the
paper. For the RoarSAT’s attitude control system
The proposed design is only left to be tested. For further
development, the present design can be optimized with the
trade off between the weight, power consumption and
attitude control time. Another improvement can be done by
reducing the components cost, specifically the cost of the
sun sensor, by replacing the sun sensor with light sensor for
(14)
(15)
Following this, the procedure highlighted above would then
be applied and carried through the same way to ultimately
obtain a design force and time required for the precise
control of the RoarSAT’s attitude.
Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016.
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the required wavelength and use of more complex
programming.
6. ACKNOWLEDGMENTS
RoarSAT development is conducted as a part of the
FUNSAT 2015-2017 competition organized by NASA’s
Florida Space Grant Consortium (FSGC). Therefore, the
authors acknowledge the financial support and motivation
provided by FSGC. The authors also acknowledge the
support received from the Department of Mechanical and
Materials Engineering (MME) of Florida International
University (FIU). Authors extend their thanks to the
reviewers for many useful comments which helped to
greatly improve the paper. The authors finally wish to
thank the members of the Near Earth Explorers (NEE)
Student Club at FIU for the continuation of the present
work towards building and testing of the proposed attitude
control system.
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