904708

Research Article
Microsatellite Attitude Determination and Control Subsystem
Design and Implementation: Software-in-the-Loop Approach
Ho-Nien Shou
Department of Aviation & Communication Electronics, Air Force Institute of Technology, Kaohsiung 820, Taiwan
Correspondence should be addressed to Ho-Nien Shou; lon[email protected]
Received  February ; Accepted  March ; Published  May 
Academic Editor: Her-Terng Yau
Copyright ©  Ho-Nien Shou. is is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
e paper describes the development of a microsatellite attitude determination and control subsystem (ADCS) and verication of
its functionality by soware-in-the-loop (SIL) method. e role of ADCS is to provide attitude control functions, including the
de-tumbling and stabilizing the satellite angular velocity, and as well as estimating the orbit and attitude information during the
satellite operation. In Taiwan, Air Force Institute of Technology (AFIT), dedicating for students to design experimental low earth
orbit micro-satellite, called AFITsat. For AFITsat, the operation of the ADCS consists of three modes which are initialization mode,
detumbling mode, and normal mode, respectively. During the initialization mode, ADCS collects the early orbit measurement data
from various sensors so that the data can be downlinked to the ground station for further analysis. As particularly emphasized in
this paper, during the detumbling mode, ADCS implements the thrusters in plus-wide modulation control method to decrease the
satellite angular velocity. ADCS provides the attitude determination function for the estimation of the satellite state, during normal
mode. e three modes of microsatellite adopted Kalman lter algorithm estimate microsatellite attitude. is paper will discuss
using the SIL validation ADCS function and verify its feasibility.
1. Introduction
epurposeofthesatelliteprojectistoestablishindigenous
capability for spacecra development, including the design,
analysis, manufacturing, assembly, integration, tests, and in-
space validation. e paper is relevant to the design and
implement of the attitude determination and control sub-
system (ADCS) for a microsatellite simulation in soware.
e simulation of the system in soware, settle SIL, is the
aimofthepaper.Inasatellitemission,theADCSplaysan
important role as it provides the attitude information of the
satellite and stabilizes the satellite. e design of the ADCS is
typically divided into several phases, including simulation of
the system in soware, implementation into hardware, real-
ization and implementation of coding in hardware, and the
verication test of the system. SIL for research development
easy and do not have to spend too much hardware funding;
it is suitable for students in the lab as a topic of special
purpose.
Micro-satellite Attitude Determination and Control Sub-
system Design and Implementation: Soware-in-the-loop
Approach.
To support the satellite mission, the ADCS is required to
provide the in-orbit attitude control and determination func-
tions. e attitude control function includes the stabilization
and detumbling control of the satellite to the prerequisite
value, while the attitude determination function is to facilitate
the estimated attitude information. ADCS will also operate
and record the pertinent data aer the separation of satellite
from the launcher.
SIL is on a mathematical model, in theory, to com-
plete the preliminary microsatellite ADCS design. e SIL
platform contains a dynamic simulator and a real-time
microcontroller, as well as some interfacing circuitry. e
dynamic simulator is capable of performing simulation of the
space environment, orbit dynamics, attitude dynamics, and
sensor/actuator models. e controller/estimator of ADCS
is a realization of the embedded microcontroller for attitude
Hindawi Publishing Corporation
Mathematical Problems in Engineering
Volume 2014, Article ID 904708, 12 pages
http://dx.doi.org/10.1155/2014/904708

Mathematical Problems in Engineering
determination and control. In this paper, the requirements
of AFITsat ADCS will be briey reviewed. e design and
implementation of AFITsat ADCS will also be described [–
]. Furthermore, the design of the ADCS design can then be
veriedbytheSILtestandtheperformanceoftheADCScan
be observed from the simulation results.
In designing the ADCS, the satellite environment,
dynamics, control, and estimation functions are simulated
through a SIL simulation endeavor. SIL simulation is a
virtual platform which can provide the simulation of the
satellite working environment, satellite dynamics, and ADCS
instruments including attitude sensors and actuators. Besides
oering a exible working platform for the early design stage
of ADCS, SIL also eases the modication of the design by
modulized all the models. e attitude determination lter
andattitudecontrollawareveriedthroughthisSIL.Aer
the simulation of ADCS in soware, the ADCS algorithm has
to be implemented in the ADCS on board microcontroller.
To fully develop a veriable ADCS algorithm, a processor-
in-the-loop (PIL) test is developed. PIL test is a way to bridge
the gap between the simulation results and the nal system
construction. It increases the realism of the simulation and
provides access to hardware features that are currently not
available in the soware-only simulation. PIL enables the
testing of the actual control and estimation codes running on
the microcontroller in the verication environment.
is paper is organized into six sections, which are
introduction, ADCS design, ADCS verication, verication
results, and conclusions, respectively. In Section ,thesatel-
lite model and space environment are briey reviewed. e
dynamics and kinematics models of the satellite are derived.
Moreover, the design of attitude controller and lter are
described. e verication methods and platform setups are
addressed in Section .Sectionreviews nonlinear ∞
robust control law. Section is brief introduction of the
algorithmofunscentedKalmanlter(UKF)andattituderate
estimator is described. Aer that, the results from ADCS
simulation and verication test are provided and discussed in
Section . At last, the paper is concluded with the summary
and some remarks for the future research are depicted.
2. ADCS Design
2.1. Satellite Model. e dynamics of the spacecra in inertial
space are governed by Euler’s equations of motion [–]
J 𝜔+𝜔×J𝜔=𝜏𝑐+𝜏𝑑,()
where Jis the moment of inertia which is symmetric:
J=J0+JΔ=
𝑥𝑥 00
0
𝑦𝑦 0
00
𝑧𝑧
+ 𝑥𝑥 00
0
𝑦𝑦 0
00
𝑧𝑧
,()
with 𝑖𝑖 being the moment of inertia along the -axis and
moment of inertia uncertain elements are expanded around
the nominal point in th direction with uncertainty, 𝑖𝑖 +𝑖𝑖,
𝑖𝑖 the inertia moment decrease progressively in submodes
transition, 𝜔isthevectorofangularratesofthesatellitein
body frame, and 𝑖is the satellite angular rates in the th
axis, the moment acting on satellite which consists of control
torque applied to the satellite 𝜏𝑐and disturbance torques 𝜏𝑑,
𝜏𝑑including gravity gradient force, air resistance force, and
magnetic disturbed force various sources.
𝜔×=0−𝜔
𝑧𝜔𝑦
𝜔𝑧0−𝜔
𝑥
−𝜔𝑦𝜔𝑥0is a corresponding 𝜔opposing skew
matrix.
e kinematic update of the satellite is realized by using
the quaternion representation. e following vector set of
dierential equations is used:
=−𝜔×𝜔
−𝜔𝑇0q
4, ()
where qistheattitudequaternionvector=
q4𝑇,q=
123𝑇, for convenient. e derivative of quaternion in
() can also be arranged as
q=1
2𝜔()
with
=
4−32
34−1
−214
−1−2−3
.()
2.2. Environment Model. e space environment must be
considered in modeling and analyzing the motion of space-
cra. e space environment models including magnetic eld
model, Earth’s upper atmosphere model, and sun position
model are described in the following. In the magnetic
eld model, the International Geomagnetic Reference Field
(IGRF) is an attempt by the International Association of Geo-
magnetism and Aeronomy (IAGA) to provide a geomagnetic
eld mathematical model []. In the SIL design, the latest
IGRF model, IGRF , is adopted.
Models of the upper atmosphere are usually based on
either empirical or theoretical work. e main concern is
about the total atmospheric density in upper atmospheric,
which will aect the satellite attitude. e atmospheric
density is determined by a modied analytical expression of
the Jacchia-Roberts theory []. For microsatellite which is
planned to operate at the altitude of  km, the atmospheric
density is about 1.454×10−13 kgm−3.
By knowing the Sun’s orbit and position with respect
to the satellite, the eclipse/shadowing status of satellite can
be determined. e microsatellite ADCS is concerned with
the satellite solar eclipse because the sun sensor reading
is aected. To this end, the sun position model is also
incorporated.
Satellites are subject to many types of disturbances
which will aect the attitude of the satellite in space. e
dominant sources of attitude disturbance torques are the
gravity-gradient torque, aerodynamic torque, and magnetic
disturbance. e gravity gradient torque is one of the largest
sources of disturbance that would aect the low earth orbit

Mathematical Problems in Engineering 
satellite. In orbit, any object which is nonsymmetrical with
nite dimensions will be subjected to a gravitational torque
due to the variation in the Earth’s gravitational force over the
object. e gravity-gradient torque act on the satellite can be
expressed as follows:
𝜏𝑔𝑔 =3
r𝑠 3r𝑠×Ir𝑠, ()
where is the earth’s gravity constant and r𝑠is the location of
the satellite mass center relative to the earth center in body
frame [,]. For the microsatellite operation, the gravity-
gradient torque is computed. e magnitude is of the order
−7 Nm.
e interaction of the upper atmosphere with the surface
of satellite will produce a torque about the center of mass. e
aerodynamic torque is given by the following equation:
𝜏ad =6
𝑘=1
r𝑘×fad,𝑘 ()
with
fad,𝑘 =
1
2𝑑2𝑘n𝑘⋅
k k,n𝑘⋅ k>0
0, n𝑘⋅
k≤0. ()
In the above, as the microsatellite is of rectangular shape,
there are six surfaces that need to be considered. e location
of the th plate is denoted by r𝑘. e corresponding force due
to the impact of molecules on the surface is denoted by fad,𝑘.
is force component is a function of the drag coecient
𝑑, atmospheric density , magnitude of the translational
velocity of the satellite ,areaoftheplate𝑘,unitnormal
vector of the surface n𝑘,andtheunitvectorofthevelocity
vector  k. e magnitude of the aerodynamic torque acting on
the microsatellite is computed to be of the order −8 Nm.
Finally, magnetic disturbance torques result from the
interaction between the satellite’s residual magnetic eld and
the earth geomagnetic eld. e dominant source of the
residual magnetic eld is the spacecra magnetic moments.
is instantaneous magnetic disturbance torque due to the
spacecra eective magnetic moment and the geocentric
magnetic eld can be described as follows [–]:
𝜏mag =m×bbody,()
where mis the sum of the internal residual magnetic dipole
moment and bbody is the geomagnetic ux intensity in body
frame.
e magnetic eld of microsatellites in orbit coordinates
frameisasshowninFigure.
3. Attitude Control
Attitude control is the process of changing the orientation of
satellite. is process is vital because a satellite will always
experience internal and external disturbance torques. e
attitude control in microsatellite is mainly concerned about
theattitudestabilization.Approachesofattitudecontrolhave
been discussed in this.
Latitude (deg.)
80
60
40
20
0
−20
−40
−60
−80
−150 −100 −50 0 50 100 150
4
3
2
1
0
−1
−2
−3
−4
−5
(NTeslas)
Bz at alt =500km, year/month: 2011/12 ×104
Longitude (deg.)
F : e magnetic eld of microsatellites in orbit coordinates
frame.
x
z
y
F : Microsatellite geometric appearance.
3.1. Production of Satellite rust [14–16]. e satellite exer-
ciseframeisasinFigure. Four thrusters are put in -
plane, including angle, the jet moves toward − direction,
and lines to be a square distance .Fuelisputthejet-
plane distance, and +direction is toward satellite center, in
Figure .
e ,,and, respectively, represent the jet includ-
ing angle, jet relative distance, and the uncertainty of the fuel
gravity position.
e following is production 𝜏ufrom the thruster:
𝜏u=
𝑥
𝑦
𝑧
=
1×
1
2×
2
3×
3
4×
4
1
2
3
4
=
−1Δ −1Δ 1Δ 1Δ
−2Δ 2Δ −2Δ −2Δ
3Δ −3Δ −3Δ 3Δ 
1
2
3
4
=𝛽u,
()

Mathematical Problems in Engineering
12
3
4
d
d
x
y
F : e geometric arrangement of the thrusters.
where
1234
=−(+)
−(+)
−(+)−(+)
(+)
−(+)(+)
(+)
−(+)(+)
−(+)
−(+)
1=−sin (+)
sin (+)
−cos (+), 
2=−sin (+)
−sin (+)
−cos (+),
3=sin (+)
−sin (+)
−cos (+), 
4=sin (+)
sin (+)
−cos (+),
= 1
2,
1=+,
2=−, 3=
,
1=−(+)+(++),
2=−(+)−(++),
3=1
(++),
𝑖Δ =𝑖+𝑖,=1,2,3. ()
3.2. Pulse-Width Modulation Rules [17–22]. e controller
requires a continuum of positive and negative thrust values,
which are physically impossible with the four xed thrusters.
isrequirementcanbemetbypulse-widthmodulating
the thrusters. e four thrusters span the three-dimensional
control space when generating a positive thrust along the
satellite -axis. e thruster commands are all biased upwards
so that each thruster receives a positive thrust command.
Each thruster can be commanded on for a variable time
during each control system sample period, with a resolution
ofmsec.evariablethrustlevelfromthelinearcontrol
signal is realized by turning on each thruster for less than
the full sample period, such that the impulse of the thruster
matches the commanded impulse.
Controller
ruster
PWM
Disturbance
On-time bias
Satellite
dynamics
+
−
Ts/2
−Ts/2
𝜙ref
𝜃ref
𝜑ref
Ts
Mthruster Ts
Mthruster
F : Microsatellite attitude control pulse-width modulation
block diagram.
e procedure to convert the controller to pulse-width
modulation is as follows.
() e thruster commands u.
() Convert ()from variable thrusts for the xed total
sample period to xed thrusts for variable times: on
= (sample time/thrust magnitude) ×u.
() Limit on-times to ±halfthesampleperiod.
() Compute a bias term; add the bias to all on-times such
that at least one thruster is on for the complete sample
period.
According to the PWM duty rule, the duty period can
be divided into two modulations: o-modulation and on-
modulation. In this project, an on-modulation is adopted.
Microsatellite attitude control pulse-width modulation block
diagramisasshowninFigure.Figureshows PWM
processing; from the control ow chart of pulse-width on/o
modulationalgorithm,thereisatleastonethrusterthatworks
in the o-modulation, while there is at least one thruster
that does not work in the on-modulation. In Figures and
,thruster,𝑠represents the maximum amplitude of the
thruster, sampling time.
4. Nonlinear ∞Robust Control Law
e microsatellite kinematic equation is described by
q=1
2−𝜔×𝜔
−𝜔𝑇0
0=1
2
×+0
−𝑇
𝜔=1
2(q)𝜔,()
where
(q)1
2
×+0
−𝑇
.()
In the attitude control design, it is desired that the system
is stable and the excursions of the angular rate and control

Mathematical Problems in Engineering 
On-modulation
O-modulation
Mcommand
Ts/2
−Ts/2
Ts/2
Ts
Mthruster
→t
on,i
tmax =max
itmin =min
i
tbias =T
s/2 − tmax
ton,i =t
on,i +t bias
ton,i =t
on,i −tmin
Mthruster
Ts
−→ Mcommand
ton,iton,i
F : Pulse-width on/o modulation control ow chart.
input are minimized. is motivates the use of the following
penalty function to be minimized:
z=1𝜔𝑇Δ𝜔+220
3u, ()
where 1,2,and3are weighting coecients introduced for
the trade-o between performance and control eort. e
function (0)is dened as (0)=2cos−1|0|.
e attitude control problem can then be formulated as
x=(x)+(x)+1(x)+1(x)w
+2(x)+2(x)u()
z=
(x)
u=1(x),()
where x=
𝜔𝑇𝑇0𝑇is the state xand wis the
disturbance. e ,1,and2are uncertain smooth
vector elds and mappings. Denote  = −1−1,for
small perturbations; ,1,2,1,,1,and2can be
expressed as
(x)=
−−1×
(q)𝜔, 1(x)=−1
0,
2(x)=
−1
0,
1(x)=1𝑇+220,
(x)=
−−1×+−1×+−1×
0,
1(x)=
−
0, 2(x)=−1−(+)
0.
()
4.1. Nonlinear ∞Robust Control eory. Consider a non-
linear state-space system 0
=+,(a)
=,(b)
where is the state vector, is the exogenous disturbance to
be rejected, and is the penalized output signal. We assume
that (),(),and()are ∞functions and =0is the
equilibrium point of the system; that is, (0)=(0)=0.
Given a positive number >0,system(a)and(b)
has a nite 2—gain less than if, for all ∈2[0,]with
0≤<∞,
𝑇
0
()
2≤2𝑇
0
()
2. ()
Lemma 1. Assume that ()=0,1()=0,and
2()=0in ().If((),1())is zero-detectable and there
exists a positive-denite function ()such that the following
Hamilton-Jacobi partial dierential inequality holds [23–25]
𝛾=𝑇
𝑥+1
2𝑇
𝑥1
21𝑇
1−2𝑇 2𝑥+1
2𝑇
11<0()
then the system has a nite 2gain less than . Once ()is
found, the control signal ucan be synthesized as
u=−𝑇
2𝑥,()
where 𝑥=/1/2⋅⋅⋅ /𝑛𝑇.