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AIMS Mathematics

2023, Volume 8, Issue 4: 7899-7916. doi: 10.3934/math.2023398
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Research article

Controllability and observability of discretized satellite magnetic attitude control system

  • School of Mathematics, Jilin University, Changchun, 130000, China
  • Received: 20 October 2022 Revised: 02 January 2023 Accepted: 12 January 2023 Published: 31 January 2023

  • MSC : 93B05, 34A25

  • In this paper, two different discrete schemes of the second-order linear time-varying system represented by the linearized satellite magnetic attitude control motion equation are obtained by Euler method. Then, the controllability and observability conditions of a new discrete second-order linear time-varying system are proposed and the validity of these conditions is further verified by some numerical examples. Next, the theoretical results are applied to investigate the controllability and observability of the discretized satellite magnetic control system. Different periods $ \tau $ are chosen to investigate the effect on the controllability and observability of the resulting discrete system. The corresponding conclusions are obtained.

    Citation: Sihui Liu, Qingdao Huang. Controllability and observability of discretized satellite magnetic attitude control system[J]. AIMS Mathematics, 2023, 8(4): 7899-7916. doi: 10.3934/math.2023398

    Related Papers:

  • In this paper, two different discrete schemes of the second-order linear time-varying system represented by the linearized satellite magnetic attitude control motion equation are obtained by Euler method. Then, the controllability and observability conditions of a new discrete second-order linear time-varying system are proposed and the validity of these conditions is further verified by some numerical examples. Next, the theoretical results are applied to investigate the controllability and observability of the discretized satellite magnetic control system. Different periods $ \tau $ are chosen to investigate the effect on the controllability and observability of the resulting discrete system. The corresponding conclusions are obtained.


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    [1] M. Reyhanoglu, J. R. Hervas, Three-axis magnetic attitude control algorithms for small satellites, Proceedings of 5th International Conference on Recent Advances in Space Technologies, (2011), 897–902. https://dx.doi.org/10.1109/RAST.2011.5966973 doi: 10.1109/RAST.2011.5966973
    [2] A. L. Rodriquez-Vazquez, M. A. Martin-Prats, F. Bernelli-Zazzera, Spacecraft magnetic attitude control using approximating sequence Riccati equations, IEEE T. Aero. Elec. Sys., 51 (2015), 3374–3385. https://dx.doi.org/10.1109/TAES.2015.130478 doi: 10.1109/TAES.2015.130478
    [3] G. Dipak, M. Bijoy, T. N. Bidul, S. Manoranjan, Three-axis global magnetic attitude control of Earth-pointing satellites in circular orbit, Asian J. control, 19 (2017), 2028–2041. https://doi.org/10.1002/asjc.1506 doi: 10.1002/asjc.1506
    [4] E. I. Ergin, P. C. Wheeler, Magnetic control of a spinning satellite, J. Spacecraft Rockets, 2 (1965), 846–850. https://doi.org/10.2514/3.28302 doi: 10.2514/3.28302
    [5] M. L. Renard, Command laws for magnetic attitude control of spin-stabilized earth satellites, J. Spacecraft Rockets, 4 (1967), 156–163. https://doi.org/10.2514/3.28828 doi: 10.2514/3.28828
    [6] J. Kim, Y. Jung, H. Bang, Linear time-varying model predictive control of magnetically actuated satellites in elliptic orbits, Acta Astronaut., 151 (2018), 791–804. https://doi.org/10.1016/j.actaastro.2018.07.029 doi: 10.1016/j.actaastro.2018.07.029
    [7] R. Q. Chai, A. TsourdosH, J. Gao, Y. Q. Xia, S. C. Chai, Dual-Loop Tube-Based Robust Model Predictive Attitude Tracking Control for Spacecraft With System Constraints and Additive Disturbances, IEEE T. Ind. Electron., 69 (2022), 4022–4033. https://doi.org/10.1109/TIE.2021.3076729 doi: 10.1109/TIE.2021.3076729
    [8] H. Y. Yang, Q. L. Hu, H. Y. Dong, X. W. Zhao, ADP-Based Spacecraft Attitude Control Under Actuator Misalignment and Pointing Constraints, IEEE T. Ind. Electron., 69 (2022), 9342–9352. https://doi.org/10.1109/TIE.2021.3116571 doi: 10.1109/TIE.2021.3116571
    [9] K. Zhou, H. Huang, X. Wang, L. Sun, Magnetic attitude control for Earth-pointing satellites in the presence of gravity gradient , Aerosp. Sci. Technol., 60 (2017), 115–123. https://doi.org/10.1016/j.ast.2016.11.003 doi: 10.1016/j.ast.2016.11.003
    [10] V. V. Beletskii, Dvizhenie iskusstvennogo sputnika otnositel'no tsentra mass(Artificial satellite motion relative to center of mass), Moscow: Nauka, 1965.
    [11] M. L. Psiaki, Magnetic torquer attitude control via asymptotic periodic linear quadratic regulation, J. Guid. Control Dynam., 24 (2001), 386–394. https://doi.org/10.2514/2.4723 doi: 10.2514/2.4723
    [12] S. P. Bhat, Controllability of nonlinear time-varying systems: Applications to spacecraft attitude control using magnetic acutation, IEEE T. Automat. Contr., 50 (2005), 1725–1735. https://doi.org/0.1109/TAC.2005.858686
    [13] R. Sutherland, I. Kolmanovsky, A. R. Girard, Attitude control of a 2U cubesat by magnetic and air drag torques, IEEE T. Contr. Syst. T., 27 (2018), 1047–1059. https://doi.org/10.1109/TCST.2018.2791979 doi: 10.1109/TCST.2018.2791979
    [14] Y. Yang, Controllability of spacecraft using only magnetic torques, IEEE T. Aero. Elec. Sys., 52 (2016), 954–961. https://doi.org/10.1109/TAES.2015.150520 doi: 10.1109/TAES.2015.150520
    [15] V. M. Morozov, V. I. Kalenova, Satellite control using magnetic moments: Controllability and stabilization algorithms, Cosmic Research, 58 (2020), 158–166. https://doi.org/10.1134/S0010952520030041 doi: 10.1134/S0010952520030041
    [16] Y. Q. Wang, D. Zhao, Y. Y. Li, S. X. Ding, Unbiased Minimum Variance Fault and State Estimation for Linear Discrete Time-Varying Two-Dimensional Systems, IEEE T. Automat. Contr., 62 (2017), 5463–5469. https://doi.org/10.1109/TAC.2017.2697210 doi: 10.1109/TAC.2017.2697210
    [17] D. Zhao, H. K. Lam, Y. Y. Li, S. X. Ding, S. Liu, A Novel Approach to State and Unknown Input Estimation for Takagi-Sugeno Fuzzy Models With Applications to Fault Detection, IEEE Transactions on Circuits and Systems-I: Regular Papers, 67 (2020), 2053–2063. https://doi.org/10.1109/TCSI.2020.2968732 doi: 10.1109/TCSI.2020.2968732
    [18] Y. Y. Li, M. Yuan, M. Chadli, Z. P. Wang, D. Zhao, Unknown Input Functional Observer Design for Discrete-Time Interval Type-2 Takagi-Sugeno Fuzzy Systems, IEEE T. Fuzzy Syst., 30 (2022), 4690–4701. https://doi.org/10.1109/TFUZZ.2022.3156735 doi: 10.1109/TFUZZ.2022.3156735
    [19] G. Reissig, C. Hartung, F. Svaricek, Strong stuctural controllability and observability of linear time-varying systems, IEEE T. Automat. Contr., 59 (2014), 3087–3092. https://doi.org/10.1109/TAC.2014.2320297 doi: 10.1109/TAC.2014.2320297
    [20] E. N. Mahmudov, Controllability and observability of second order linear time invariant systems, Optimization and Control, 39 (2019), 16–25.
    [21] A. Babiarz, A. Czornik, S. Siegmund, On Stabilization of discrete time-varying systems, SIAM J. Control Optim., 59 (2021), 242–266. https://doi.org/10.1137/20M1324326 doi: 10.1137/20M1324326
    [22] M. Witczak, V. Puig, D. Rotondp, P. Witczak, A necessary and sufficient condition for total observability of discrete-time linear time-varying systems, International Federation Of Automatic Control, 50 (2017), 729–734. https://doi.org/10.1016/j.ifacol.2017.08.232 doi: 10.1016/j.ifacol.2017.08.232
    [23] E. N. Mahmudov, Second order discrete time-varying and time-invariant linear continuous systems and kalman type conditions, Numerical Algebra, Control And Optimization, 12 (2022), 353–371. https://doi.org/10.3934/naco.2021010 doi: 10.3934/naco.2021010
    [24] G. D. Meena, S. Janardhanan, Discretization of Linear Time-Varying Systems, 2020 International Conference on Emerging Frontiers in Electrical and Electronic Technologies (ICEFEET), (2020), 1–6.
    [25] V. I. Kalenova, V. M. Morozov, The reducibility of linear second-order time-varying systems with control and observation, Journal of Applied Mathematics and Mechanic, 76 (2012), 413–422. https://doi.org/10.1016/j.jappmathmech.2012.09.008 doi: 10.1016/j.jappmathmech.2012.09.008
    [26] C. Liu, C. Li, Reachability and observability of switched linear systems with continuous-time and discrete-time subsystems, International Journal Of Control, Automation And Systems, 11 (2013), 200–205. https://doi.org/10.1007/s12555-011-0169-4 doi: 10.1007/s12555-011-0169-4
    [27] D. S. Ivanov, M. Yu. Ovchinnikov, V. I. Penkov, D. S. Roldugin, D. M. Doronin, A. V. Ovchinnikov, Advanced numerical study of the three-axis magnetic attitude control and determination with uncertainties, Acta Astronaut., 132 (2017), 103–110. https://doi.org/10.1016/j.actaastro.2016.11.045 doi: 10.1016/j.actaastro.2016.11.045
    [28] M. G. Frost, Controllability, observability and the transfer function matrix for a delay-differential system, Int. J. Control, 35 (1982), 175–182. https://doi.org/10.1080/00207178208922610 doi: 10.1080/00207178208922610
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