Triaxial electrodynamic stabilization of a satellite via PID controller
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 20 (2024) no. 2, pp. 244-254 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A satellite moving on a circular equatorial orbit is considered. The satellite is equipped with a controlled magnetic moment and a controlled electrostatic charge. The problem of triaxial stabilization in the orbital frame is studied. The electrodynamic control system is proposed. In addition, to improve characteristics of transient processes, PID controller of a special form is used. With the aid of the Lyapunov direct method, asymptotic stability conditions of the program mode are obtained. The results of computer simulation are provided demonstrating the efficiency of the developed approach.
Keywords: electrodynamic control, triaxial stabilization, Lyapunov — Krasovskii functional, PID controller.
Mots-clés : satellite
@article{VSPUI_2024_20_2_a8,
     author = {A. Yu. Aleksandrov and S. B. Ruzin},
     title = {Triaxial electrodynamic stabilization of a satellite via {PID} controller},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {244--254},
     year = {2024},
     volume = {20},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2024_20_2_a8/}
}
TY  - JOUR
AU  - A. Yu. Aleksandrov
AU  - S. B. Ruzin
TI  - Triaxial electrodynamic stabilization of a satellite via PID controller
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2024
SP  - 244
EP  - 254
VL  - 20
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2024_20_2_a8/
LA  - en
ID  - VSPUI_2024_20_2_a8
ER  - 
%0 Journal Article
%A A. Yu. Aleksandrov
%A S. B. Ruzin
%T Triaxial electrodynamic stabilization of a satellite via PID controller
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2024
%P 244-254
%V 20
%N 2
%U http://geodesic.mathdoc.fr/item/VSPUI_2024_20_2_a8/
%G en
%F VSPUI_2024_20_2_a8
A. Yu. Aleksandrov; S. B. Ruzin. Triaxial electrodynamic stabilization of a satellite via PID controller. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 20 (2024) no. 2, pp. 244-254. http://geodesic.mathdoc.fr/item/VSPUI_2024_20_2_a8/

[1] Schaub H., Junkins J. L., Analytical mechanics of space systems, American Institute of Aeronautics Astronautics, Reston, Virginia, 2009, 744 pp. | MR | Zbl

[2] Hughes P. C., Spacecraft attitude dynamics, Wiley, New York, 1986, 584 pp.

[3] Kane T. R., Likins P. W., Levinson D. A., Spacecraft dynamics, McGraw-Hill Book Co, New York, 1983, 454 pp.

[4] Zhou K., Huang H., Wang X., Sun L., Zhong R., “Magnetic attitude control for Earth-pointing satellites in the presence of gravity gradient”, Aerospace Science and Technology, 60 (2017), 115–123 | DOI

[5] Silani E., Lovera M., “Magnetic spacecraft attitude control: A survey and some new results”, Control Engeneering Practic, 13:3 (2005), 357–371 | DOI

[6] Ignatov A. I., Sazonov V. V., “Stabilization of the solar orientation mode of an artificial earth satellite by an electromagnetic control system”, Cosmic Research, 56:5 (2018), 388–399 | DOI

[7] Guelman M., Waller R., Shiryaev A., Psiaki M., “Design and testing of magnetic controllers for satellite stabilization”, Acta Astronautica, 56 (2005), 231–239 | DOI

[8] Xia X., Guo C., Xie G., “Investigation on magnetic-based attitude de-tumbling algorithm”, Aerospace Science and Technology, 84 (2019), 1106–1115 | DOI

[9] Giri D. K., Sinha M., Kumar K. D., “Fault-tolerant attitude control of magneto-Coulombic satellites”, Acta Astronautica, 116 (2015), 254–270 | DOI

[10] Kovalenko A. P., Magnetic control systems for spacecraft, Mashinostroenie Publ, M., 1975, 248 pp. (In Russian)

[11] Antipov K. A., Tikhonov A. A., “Parametric control in the problem of spacecraft stabilization in the geomagnetic field”, Automation Remote Control, 68:8 (2007), 1333–1345 | DOI | MR

[12] Aleksandrov A. Yu., Tikhonov A. A., “Electrodynamic stabilization of earth-orbiting satellites in equatorial orbits”, Cosmic Research, 50:4 (2012), 313–318 | DOI

[13] Zhao C., Guo L., “PID controller design for second order nonlinear uncertain systems”, Science China Information Science, 60:2 (2017), 022201 | DOI | MR

[14] Tkhai V. N., “Stabilization of oscillations of a controlled reversible mechanical system”, Automation Remote Control, 83:9 (2022), 1404–1416 | DOI | MR | Zbl

[15] Anan'evskii I. M., Kolmanovskii V. B., “On stabilization of some control systems with an after-effect”, Automation Remote Control, 1989, no. 9, 1174–1181 | MR | Zbl

[16] Formal'sky A. M., “On a modification of the PID controller”, Dynamics and Control, 7:3 (1997), 269–277 | DOI | MR | Zbl

[17] Zhao C., Guo L., “Towards a theoretical foundation of PID control for uncertain nonlinear systems”, Automatica, 142 (2022), 110360 | DOI | MR | Zbl

[18] Dong W., Zhao Y., Cong Y., “Reduced-order observer-based controller design for quasi-one-sided Lipschitz nonlinear systems with time-delay”, International Journal Robust and Nonlinear Control, 31:3 (2021), 817–831 | DOI | MR | Zbl

[19] Zhabko A. P., Provotorov V. V., Sergeev S. M., “Optimal control of the Navier — Stokes system with a space variable in a network-like domain”, Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 19:4 (2023), 549–562 | DOI | MR

[20] Subbarao K., “Nonlinear PID-like controllers for rigid-body attitude stabilization”, The Journal of the Austronautical Sciences, 52:1–2 (2004), 61–74 | DOI | MR

[21] Moradi M., “Self-tuning PID controller to three-axis stabilization of a satellite with unknown parameters”, International Journal Non-Linear Mechanics, 49 (2013), 50–56 | DOI

[22] Li Y., Zhaowei S., Dong Y., “Time efficient robust PID plus controller for satellite attitude stabilization control considering angular velocity and control torque constraint”, Journal Aerospace Engeneering, 30:5 (2017), 04017030 | DOI

[23] Alexandrov A. Yu., Tikhonov A. A., “Electrodynamic control with distributed delay for AES stabilization in an equatorial orbit”, Cosmic Research, 60:5 (2022), 366–374 | DOI | MR

[24] Fridman E., Introduction to time-delay systems: Analysis and control, Birkhäuser, Basel, 2014, 362 pp. | MR

[25] Aleksandrov A. Yu., Kosov A. A., Chen Y., “Stability and stabilization of mechanical systems with switching”, Automation Remote Control, 72:6 (2011), 1143–1154 | DOI | MR | Zbl

[26] Efimov D., Aleksandrov A., “Analysis of robustness of homogeneous systems with time delays using Lyapunov — Krasovskii functionals”, International Journal Robust Nonlinear Control, 31 (2021), 3730–3746 | DOI | MR | Zbl

[27] Aleksandrov A., Efimov D., Fridman E., “Stability of homogeneous systems with distributed delay and time-varying perturbations”, Automatica, 153 (2023), 111058 | DOI | MR | Zbl

[28] Kalinina E. A., Kamachkin A. M., Stepenko N. A., Tamasyan G. Sh., “On the question of a constructive controllability criterion. Pt I. Cyclic invariant subspaces”, Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 19:2 (2023), 283–299 (In Russian) | DOI | MR

[29] Aleksandrov A. Y., Aleksandrova E. B., Tikhonov A. A., “Stabilization of a programmed rotation mode for a satellite with electrodynamic attitude control system”, Advances in Space Research, 62:1 (2018), 142–151 | DOI