Abstract

In this paper, an H gain scheduling algorithm is proposed to solve a nadir-pointing problem of a small satellite using magnetic torquer actuators only. The time-varying nature of the Earth's geomagnetic field is leveraged, and its measurements can be used to define the scheduling parameters for the synthesis of a linear parameter varying gain scheduling (LPVGS) controller and the design of linear parameter varying (LPV) attitude model of the satellite driven with magnetic torquers. The developed algorithm performs well under the time changing magnetic field and allows the stabilization of the closed-loop satellite system in the presence of external disturbances. Since the stability for the H LPV model is ensured by design, all the simulations presented in this paper are performed using the nonlinear equations of the satellite.

References

1.
Wu
,
Y.-H.
,
Han
,
F.
,
Zheng
,
M.-H.
,
Wang
,
F.
,
Hua
,
B.
,
Chen
,
Z.-M.
, and
Cheng
,
Y.-H.
,
2018
, “
Attitude Tracking Control for a Space Moving Target With High Dynamic Performance Using Hybrid Actuator
,”
Aerosp. Sci. Technol.
,
78
, pp.
102
117
.10.1016/j.ast.2018.03.041
2.
Eshghi
,
S.
, and
Varatharajoo
,
R.
,
2018
, “
Nonsingular Terminal Sliding Mode Control Technique for Attitude Tracking Problem of a Small Satellite With Combined Energy and Attitude Control System (CEACS)
,”
Aerosp. Sci. Technol.
,
76
, pp.
14
26
.10.1016/j.ast.2018.02.006
3.
Sadigh
,
S. M.
,
Kashaninia
,
A.
, and
Dehghan
,
S. M. M.
,
2023
, “
Adaptive Finite-Time Fault-Tolerant Control for Nano-Satellite Attitude Tracking Under Actuator Constraints
,”
Aerosp. Sci. Technol.
,
138
, p.
108337
.10.1016/j.ast.2023.108337
4.
Sadigh
,
S. M.
,
Kashaninia
,
A.
, and
Dehghan
,
S. M. M.
,
2023
, “
Adaptive Sliding Mode Fault-Tolerant Control for Satellite Attitude Tracking System
,”
Adv. Space Res.
,
71
(
3
), pp.
1784
1805
.10.1016/j.asr.2022.09.064
5.
He
,
Y.
,
Wang
,
Z.
,
Yang
,
S.
, and
He
,
W.
,
2023
, “
Sun-Pointing Safe Control for Atmospheric Environment Monitoring Satellite Using Magnetic Actuation
,”
Adv. Space Res.
,
72
(
5
), pp.
1528
1537
.10.1016/j.asr.2023.04.044
6.
Das
,
S.
,
Sinha
,
M.
,
Kumar
,
K. D.
, and
Misra
,
A.
,
2010
, “
Reconfigurable Magnetic Attitude Control of Earth-Pointing Satellites
,”
Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng.
,
224
(
12
), pp.
1309
1326
.10.1243/09544100JAERO681
7.
Ovchinnikov
,
M. Y.
, and
Roldugin
,
D. S.
,
2019
, “
A Survey on Active Magnetic Attitude Control Algorithms for Small Satellites
,”
Prog. Aerosp. Sci.
,
109
, p.
100546
.10.1016/j.paerosci.2019.05.006
8.
Hablani
,
H. B.
,
1995
, “
Comparative Stability Analysis and Performance of Magnetic Controllers for Bias Momentum Satellites
,”
J. Guid., Control, Dyn.
,
18
(
6
), pp.
1313
1320
.10.2514/3.21547
9.
Hervas
,
J. R.
,
Reyhanoglu
,
M.
, and
Drakunov
,
S. V.
,
2012
, “
Three-Axis Magnetic Attitude Control Algorithms for Small Satellites in the Presence of Noise
,”
Proceedings of the 12th International Conference on Control, Automation and Systems
, Jeju, Korea, Oct. 17–21, pp.
1342
1347
.https://ieeexplore.ieee.org/document/6393044/citations#citations
10.
Prabhat
,
H.
,
Mukherjee
,
B. K.
,
Giri
,
D. K.
, and
Sinha
,
M.
,
2022
, “
Fault-Tolerant Sliding Mode Satellite Attitude Stabilization Using Magneto-Coulombic Torquers
,”
Aerosp. Sci. Technol.
,
121
, p.
107316
.10.1016/j.ast.2021.107316
11.
Alger
,
M.
, and
de Ruiter
,
A.
,
2022
, “
Magnetic Spacecraft Attitude Stabilization With Two Torquers
,”
Acta Astronaut.
,
192
, pp.
157
167
.10.1016/j.actaastro.2021.09.047
12.
Wisniewski
,
R.
,
2000
, “
Linear Time-Varying Approach to Satellite Attitude Control Using Only Electromagnetic Actuation
,”
J. Guid., Control, Dyn.
,
23
(
4
), pp.
640
647
.10.2514/2.4609
13.
Pittelkau
,
M. E.
,
1993
, “
Optimal Periodic Control for Spacecraft Pointing and Attitude Determination
,”
J. Guid., Control, Dyn.
,
16
(
6
), pp.
1078
1084
.10.2514/3.21130
14.
Psiaki
,
M. L.
,
2001
, “
Magnetic Torquer Attitude Control Via Asymptotic Periodic Linear Quadratic Regulation
,”
J. Guid., Control, Dyn.
,
24
(
2
), pp.
386
394
.10.2514/2.4723
15.
Wang, P., Shtessel
,
Y.
, and Wang, Y-Q.,
1998
, “
Satellite Attitude Control Using Only Magnetorquers
,”
Proceedings of Thirtieth Southeastern Symposium on System Theory
, Morgantown, WV, Mar. 10--10, pp. 500--504.10.1109/SSST.1998.660124
16.
Nguyen
,
A.-T.
,
Chevrel
,
P.
, and
Claveau
,
F.
,
2018
, “
Gain-Scheduled Static Output Feedback Control for Saturated LPV Systems With Bounded Parameter Variations
,”
Automatica
,
89
, pp.
420
424
.10.1016/j.automatica.2017.12.027
17.
Sadeghzadeh
,
A.
,
2017
, “
Gain-Scheduled Static Output Feedback Controller Synthesis for Discrete-Time LPV Systems
,”
Int. J. Syst. Sci.
,
48
(
14
), pp.
2936
2947
.10.1080/00207721.2017.1365967
18.
Preda
,
V.
,
Cieslak
,
J.
,
Henry
,
D.
,
Bennani
,
S.
, and
Falcoz
,
A.
,
2015
, “
LPV Control for Multi-Harmonic Microvibration Attenuation: Application to High Stability Space Missions
,”
IFAC-PapersOnLine
,
48
(
26
), pp.
127
132
.10.1016/j.ifacol.2015.11.125
19.
Boyd
,
S.
, and
Vandenberghe
,
L.
,
2004
,
Convex Optimization
,
Cambridge University Press
, Cambridge, UK.
20.
Duan
,
G.
, and
Yu
,
H.
,
2013
,
LMIs in Control Systems Analysis, Design, and Applications
,
Taylor & Francis Group
, Boca Raton, FL.
21.
Nagashio
,
T.
,
Kida
,
T.
,
Hamada
,
Y.
, and
Ohtani
,
T.
,
2014
, “
Robust Two-Degrees-of-Freedom Attitude Controller Design and Flight Test Result for Engineering Test Satellite-VIII Spacecraft
,”
IEEE Trans. Control Syst. Technol.
,
22
(
1
), pp.
157
168
.10.1109/TCST.2013.2248009
22.
Corti
,
A.
, and
Lovera
,
M.
,
2012
,
Control of Linear Parameter Varying Systems With Applications
,
Springer
,
New York/Dordrecht, The Netherlands/Heidelberg, Germany/London
, pp.
339
335
.
23.
Okasha
,
H.
,
2020
, “
Design of a Linear Parameter Varying Control System for a Delivery Quadrotor
,” M.Sc. dissertation,
The Faculty of the Department of Aerospace Engineering, San José State University
, San José, CA.
24.
Sasaki
,
T.
, and
Shimomura
,
T.
,
2017
, “
Gain-Scheduled Control/Steering Design for a Spacecraft With Variable-Speed Control Moment Gyros
,”
SICE J. Control, Meas., Syst. Integr.
,
10
(
3
), pp.
237
242
.10.9746/jcmsi.10.237
25.
Jin
,
R.
,
Chen
,
X.
,
Geng
,
Y.
, and
Hou
,
Z.
,
2018
, “
LPV Gain-Scheduled Attitude Control for Satellite With Time-Varying Inertia
,”
Aerosp. Sci. Technol.
,
80
, pp.
424
432
.10.1016/j.ast.2018.07.020
26.
Bolandi
,
H.
,
Abedi
,
M.
, and
Haghparast
,
M.
,
2012
, “
A Robust Fault Detection Algorithm Using q-LPV Interval Observer Together With an Accommodation System Based on Actuators Reconfiguration
,”
IFAC Proc. Vol.
,
45
(
31
), pp.
91
96
.10.3182/20121122-2-ES-4026.00009
27.
Kim
,
J.
,
Jung
,
Y.
, and
Bang
,
H.
,
2018
, “
Linear Time-Varying Model Predictive Control of Magnetically Actuated Satellites in Elliptic Orbits
,”
Acta Astronaut.
,
151
, pp.
791
804
.10.1016/j.actaastro.2018.07.029
28.
Yang
,
Y.
,
2016
, “
Controllability of Spacecraft Using Only Magnetic Torques
,”
IEEE Trans. Aerosp. Electron. Syst.
,
52
(
2
), pp.
954
961
.10.1109/TAES.2015.150520
29.
Ovchinnikov
,
M. Y.
,
Penkov
,
V. I.
,
Roldugin
,
D. S.
, and
Pichuzhkina
,
A. V.
,
2018
, “
Geomagnetic Field Models for Satellite Angular Motion Studies
,”
Acta Astronaut.
,
144
, pp.
171
180
.10.1016/j.actaastro.2017.12.026
30.
Yang
,
Y.
,
2010
, “
Quaternion-Based Model for Momentum Biased Nadir Pointing Spacecraft
,”
Aerosp. Sci. Technol.
,
14
(
3
), pp.
199
202
.10.1016/j.ast.2009.12.006
31.
Apkarian
,
P.
,
Gahinet
,
P.
, and
Becker
,
G.
,
1995
, “
Self-Scheduled Control of Linear Parameter-Varying Systems: A Design Example H
,”
Automatica
,
31
(
9
), pp.
1251
1261
.10.1016/0005-1098(95)00038-X
32.
Gu
,
D.-W.
,
Petkov
,
P. H.
, and
Konstantinov
,
M. M.
,
2013
,
Robust Control Design With MATLAB
, 2nd ed.,
Springer
,
London
.
33.
Apkarian
,
P.
, and
Gahinet
,
P.
,
1995
, “
A Convex Characterization of Gain-Scheduled Controllers H
,”
IEEE Trans. Autom. Control
,
40
(
5
), pp.
853
864
.10.1109/9.384219
34.
Burgin
,
E.
,
Biertümpfel
,
F.
, and
Pfifer
,
H.
,
2023
, “
Linear Parameter Varying Controller Design for Satellite Attitude Control
,”
IFAC-PapersOnLine
,
56
(
2
), pp.
3112
3117
.10.1016/j.ifacol.2023.10.1443
35.
Jan
,
Y. W.
, and
Chiou
,
J. C.
,
2005
, “
Attitude Control System for ROCSAT-3 Microsatellite: A Conceptual Design
,”
Acta Astronaut.
,
56
(
4
), pp.
439
452
.10.1016/j.actaastro.2004.05.066
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