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Attitude Control System of a Cube Satellite with Small Solar Sail

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Attitude Control System of a Cube Satellite with Small Solar Sail

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This paper describes attitude control scheme and carries out numerical simulations for a cube satellite that is equipped with a small solar sail. The satellite must perform Sun pointing maneuver for testing effects of the solar sail in a circular orbit of 700km altitude. For the purpose of Sun pointing operation, the modified B-dot control scheme and PD-like control scheme are implemented. To verify the feasibility and performance of the proposed controller, the simulations consider aerodynamic, solar radiation pressure and gravity gradient disturbances. The simulations show that the satellite can be detumbled within 5 hour from tip-off rate due to ejection from the P-POD.
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Attitude Control System of a Cube Satellite with
Small Solar Sail
Yeona Yoo, Soyeon Koo, Gyeonghun Kim, Seungkeun Kim§, and Jinyoung Suk
Chungnam National University, Daejeon, 305-764, Republic of Korea
Jongrae Kimk
University of Glasgow, Glasgow, G12 8QQ, UK
This paper describes attitude control scheme and carries out numerical simulations for
a cube satellite that is equipped with a small solar sail. The satellite must perform Sun
pointing maneuver for testing effects of the solar sail in a circular orbit of 700km altitude.
For the purpose of Sun pointing operation, the modified B-dot control scheme and PD-
like control scheme are implemented. To verify the feasibility and performance of the
proposed controller, the simulations consider aerodynamic, solar radiation pressure and
gravity gradient disturbances. The simulations show that the satellite can be detumbled
within 5 hour from tip-off rate due to ejection from the P-POD.
I. Introduction
The objective of CNUSAIL-1 project is to develop and operate a 3U-sized cube satellite. The purpose
of the mission is to successfully deploy the solar sail in a low earth orbit. The satellite is in circular
sun-synchronous orbit of 700km altitude and 98.1913 inclination. To test various effects of the solar sail,
Sun-pointing maneuver will be performed by satellite attitude control. This research project is supported
by the Korea Aerospace Research Institute in terms of finance, environmental test, and arrangement for
possible launch in late 2015. If successful in the operation, the CNUSAIL-1 will be the first cube satellite
with solar sail in Korea.
This paper aims to design and verify the attitude controller for spin stabilization and Sun pointing. To
verify the controller performance, numerical simulations are done for the cases with and without solar sail
deployment. Attitude determination is based on Extended Kalman Filter using sun sensors, magnetometers,
and gyroscopes. As control laws, modified B-dot and three-dimensional PD-like feedback controller are
applied to spin-stabilization and sun-pointing, respectively. The next section presents description of attitude
determination and control system, followed by a representation of the external disturbance with considering
solar sail area and angle, control modes, and control law. Figure 1 shows (a) the conceptual drawing of
CNUSAIL-1, and (b) the design of an operational orbit.
Graduate Student, Department of Aerospace Engineering, Daejeon, South Korea, yandoll2@gmail.com
Graduate Student, Department of Aerospace Engineering, Daejeon, South Korea, esther91127@hanmail.net
Graduate Student, Department of Aerospace Engineering, Daejeon, South Korea, nuber007z@naver.com
§Assistant Professor, Department of Aerospace Engineering, Daejeon, South Korea, skim78@cnu.ac.kr, AIAA member.
Professor, Department of Aerospace Engineering, Daejeon, South Korea, jsuk@cnu.ac.kr, AIAA member.
kLecturer, Department of Aerospace Engineering, University of Glasgow, Glasgow, G12 8QQ, UK, jkim@aero.gla.ac.uk
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(a) Solar sail deployment (b) Operational orbit
Figure 1. A conceptual design and the operational orbit of the CNUSAIL-1
II. Attitude determination and control system
Attitude determination and control system (ADCS) of the CNUSAIL-1 assists a solar sail mission by
controlling the orientation of the satellite into the desired attitude. The systems consist of Sun sensors, an
IMU, a 3-axis magnetometer and three magnetic torquers. The requirement of the ADCS are to maintain
Sun pointing accuracy under 10 degrees. In addition, the satellite must be slowly spinned about Z-axis.
Figure 2 shows the feedback loop of attitude determination and control system.
Figure 2. Attitude control block diagram
III. System dynamics and disturbacne
A. Coordinate frame
The attitude control simulations and equation of motions are calculated in the body-fixed frame. The
Earth-centered-inertial frame has an origin at the Earth center. The Z-axis is the perpendicular to Earth’s
equatorial plane. X-axis points towards the vernal equinox direction, Y-axis follows the right hand rule.
LVLH(Local vertical local horizontal) frame has an origin at the center of gravity of the satellite and follows
the orbit trajectory. The Z-axis points towards Earth center. Y-axis is perpendicular to the orbital plane,
which is parallel to the orbital angular momentum direction. X-axis follows the right hand rule. The body-
fixed frame has origin at the center of mass of satellite. It is fixed on the satellite and coincided with the
satellite axes of moments of inertia. Figure 3 shows the coordinate frames used in this study.
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(a) Earth-centered inertial frame (b) LVLH frame (c) Body-fixed frme
Figure 3. Coordinate Frames
B. Dynamics and kinematics
The attitude dynamics of rigid satellite is as follows1
I ˙ω=Tdis +Tmag ω×Iω (1)
where Iis the inertia matrix, ωis the angular velocity of the body frame, Tmag denotes the magnetic control
torque and Tdis denotes the disturbance torques which include aerodynamic torque, solar radiation pressure
torque, and gravity-gradient torque. The attitude kinematics in terms of quaternion are2
˙=1
2η1 + ×ω(2)
˙η=1
2Tω(3)
where is the vector part of the quaternion, ηis the scalar part of the quaternion and
×=
032
301
210
.(4)
Magnetic control torque law is
Tmag =M×B.(5)
This magnetic torque effects the satellite perpendicularly to the Earth magnetic field by magnetic torquers.
Magnetic coils have saturation on the maximum magnetic moment and coil current. The maximum current
is restricted to 0.1A, and the maximum magnetic moment is 0.2Am2.
C. Disturbance
The gravity gradient torques result from the Earth’s gravitational force which is not constant with the
distance and position from the Earth’s center. The gravity gradient torques of the body frame are expressed
as1:
Tgg =3µ
r3
o
ue×Iue(6)
where µ= 3.986 ×1014m3/s2is the earth’s gravity constant, rois the distance from the earth’s center, ueis
the unit vector towards the nadir direction of body frame and I is the inertia matrix.
In low earth orbits, there will be residual earth’s atmosphere, and this causes a drag force on the satellite.
The aerodynamic force acting on solar sail of satellite is
Faero=1
2CdρV 2As(7)
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where Faero is the aerodynamic force, Cdis the drag coefficient, ρis the atmosphere density, Vis the satellite
velocity, Ais the projected srea, and sis the direction unit vector. The aerodynamic torque occurs because
of offset between the center of pressure and center of mass rcp. It can be expressed as :
Taero =rcp ×Faero (8)
The SRP (solar radiation pressure) force occurs due to photons acting on a satellite and sail surface in
space. The SRP force acting on a flat sail surface with optical properties of sail material is as3:
Fsrp =P Acos α(1 + rs) cos α+Bfr(1 s) + efbfebBb
ef+eb
(1 r)n+ ((1 rs) sin α)t(9)
where Fsrp is the SRP force, P= 4.563 ×106N/m2is the nominal solar radiation pressure constant at 1AU
from the sun, ris the reflectivity of surface, sis the specular reflection coefficient, αis the sun angle, ef&
ebis front and back surface emission coefficients and Bf&Bbis non-Lambertian coefficients for front and
back surfaces. The solar radiation pressure torque gives similar to the aerodynamics torque as :
Tsrp =rcp ×Fsrp (10)
Figure 4. Disturbacne as an altitude
Figure 4 shows maximum torques with respect to altitude change. The solar radiation pressure torque,
and the aerodynamic torque get maximum when the solar sail is the perpendicular to each force vector.
Figure 5 shows the disturbance torques in the Sun pointing mode operation. Aerodynamic torque fluctuates
according to the variation of angle between the sail and velocity vector.
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0 5000 10000 15000
−5
0
5x 10−6
Time(Period)
Torque(N/m
Disturbance
Gravity Gradient
SRP
Aero Drag
0 5000 10000 15000
−2
0
2
x 10−6
Time(Period)
Torque(N/m
Gravity Gradient
SRP
Aero Drag
0 5000 10000 15000
−1
−0.5
0
0.5
1x 10−5
Time(Period)
Torque(N/m
Gravity Gradient
SRP
Aero Drag
Figure 5. Disturbance in the Sun pointing mode
IV. Control law
The CNUSAIL-1 has two control modes. First control mode, detumbling mode, will use a ‘modified
B-dot controller’ to damp out the initial tip-off rate and establish a desired spin rate about Z-axis using
magnetic torquers. The control law is given as4:
M=K( ˙
B+ωd×B) (11)
where K is a positive gain, B is the magnetic field in the body frame, ˙
Bis the derivative of magnetic field,
ωdis the desired spin rates, and M is magnetic dipole.
Second control mode, Sun pointing mode, will maintain the Sun pointing orientation within 10 degrees
which faces normal to the solar sail in order to investigate solar radiation pressure effect. The control torque
is designed as the PD-like control law2:
Tdes=kpekdωe(12)
where kdis the positive derivative gain, kpis the positive proportional gain, eis the attitude error by
quaternion, and ωeis a rate error. The required magnetic moment is calculated as :
M=Tdes ×B
|B|2.(13)
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V. Simulation
The numerical simulations are done with considering aerodynamic, solar radiation pressure, and gravity
gradient disturbances in a MATLAB Simulink environment to verify the feasibility and performance of the
proposed controller. The satellite is assumed to be rigid. The optical properties of metalized mylar is
considered for solar sail material. Assumptions and initial conditions are given as follow.
Table 1. Simulation parameters
parameter value
Satellite mass 4 kg
Sail un-deployed inertias Ixx=0.0506, Iyy=0.0506, Iz z=0.010
Sail deployed inertias Ixx=0.6, Iyy=0.6, Iz z=1.2
Orbit 700km, Sun Synchronous Orbit
Initial attitude quaternion [0 0 0 1]T
Initial body rate [10 10 10]Tdeg/sec
A. Modified B-dot contol scheme simulation
Figure 6. Detumbling mode; body rates are damped out from initial rotational velocity within 3 orbits.
The simulations are carried out with the modified B-dot control scheme. Desired spin rates ωdare [0 0
5]Tdeg/sec. Figure 6 shows that body rates are damped by magnetic torquers in about 3 period(5 hours).
Also, Z-axis body rate converges to the desired spin rate. Figure 7 shows that body rates are not damped
out by torquers in about 3 orbit periods and Z-axis spin rate diverges. Once the solar sail of satellite is
deployed, inertia matrix is large so that body rates cant be damped out by the magnetic torquer only. For
the purpose of the Sun pointing mode operation, spin rate must be damped out. Thus, more control torque
will be required by using reaction wheels.
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Figure 7. Sail deployed. The body rates are not damped out from initial rotational velocity.
B. PD-like control scheme simulation
Figure 8. PD-like control scheme. The initial pointing error is 90 degree.
Figure 8 shows the result of Sun pointing simulation using the PD-like control scheme with allowable
torques are unlimited. The Sun pointing error is conversed to the zero. More results and detailed analysis
using the PD-like control scheme will be updated in the final manuscript.
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VI. Conclusions
This paper presented the attitude control system for a cube satellite with solar sail. The two modes
were designed to stabilize the satellite and maintain Sun pointing orientation. External disturbances were
calculated and compared with the worst case. In the Sun pointing mode operation, the solar radiation
pressure torque was maintained constantly, but aerodynamic torque was changed according to the angle
between tangential vector of sail and velocity vector. The modified B-dot control scheme damped out body
rates from initial tip-off rate when the sail was not deployed. However, it can’t stabilize body rates when
the sail was deployed. The simulation of PD-like control scheme was performed for the situations when the
sail is deployed and undeployed. The PD-like control scheme simulation results and detailed analysis will be
updated in the final manuscript.
Acknowledgments
This research was supported by Cubesat Contest and Developing Program through the National Research
Foundation of Korea (NRF) and the Korea Aerospace Research Institute (KARI) funded by the Korea
government (Ministry of Science, ICT and Future Planning)(No. NRF-2013M1A3A4A01075962).
References
1Wertz, J.R, Spacecraft attitude determination and control, D. Reidel publishing Company, 1986.
2Anton H. de Ruiter, Christopher Damaren, James R. Forbes , Spacecraft Dynamics and Control: An Introduction, Wiley,
2013.
3Bong Wie, “Solar Sail Attitude Control and Dynamics, Part 1,” Journal of guidance, control, and dynamics, Vol. 27,
No. 4, 2004, pp. 526–535.
4Glenn Creamer, “The HESSI magnetic attitude control system,” AIAA Guidance, Navigation, and Control Conference ,
1999.
5Julie Thienel, Robert Bruninga, Robert Stevens, Cory Ridge, and Chad Healy, “The Magnetic Attitude Control System
for the Parkinson Satellite (PSAT) A US Naval Academy Designed CubeSat,” AIAA Guidance, Navigation, and Control
Conference, 2009.
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... In the aerospace industry, there has been increasing interest in low-budget space missions involving CubeSats. [1][2][3][4][5] Assembly of multiple CubeSats in space into large structures such as a space telescope or solar panels could be tremendously beneficial for the science and engineering communities. Several research groups [6][7][8][9] are currently tackling the challenges associated with autonomous rendezvous and docking of small scaled spacecraft on orbit. ...
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