80
Views
3
CrossRef citations to date
0
Altmetric
Articles

On the attitude stabilization of a rigid body under control with distributed delay

ORCID Icon & ORCID Icon
Pages 2241-2250 | Received 24 Dec 2020, Accepted 14 Feb 2021, Published online: 01 Mar 2021

References

  • Ajorkar, A., A. Fazlyab, F. F. Saberi, and M. Kabganian. 2015. Design of an adaptive-neural network attitude controller of a satellite using reaction wheels. Journal of Applied and Computational Mechanics 1 (2):67–73.
  • Aleksandrov, A. Y. 2020. Stability analysis and synthesis of stabilizing controls for a class of nonlinear mechanical systems. Nonlinear Dynamics 100 (4):3109–19. doi:10.1007/s11071-020-05709-0.
  • Aleksandrov, A. Y., E. B. Aleksandrova, and A. A. Tikhonov. 2018. Stabilization of a programmed rotation mode for a satellite with electrodynamic attitude control system. Advances in Space Research 62 (1):142–51. doi:10.1016/j.asr.2018.04.006.
  • Aleksandrov, A. Y., Y. Chen, A. A. Kosov, and L. Zhang. 2011. Stability of hybrid mechanical systems with switching linear force fields. Nonlinear Dynamics and Systems Theory 11 (1):53–64.
  • Aleksandrov, A. Y., A. A. Kosov, and Y. Chen. 2011. Stability and stabilization of mechanical systems with switching. Automation and Remote Control 72 (6):1143–54. doi:10.1134/S0005117911060026.
  • Aleksandrov, A. Y., and O. Mason. 2016. Diagonal Riccati stability and applications. Linear Algebra and Its Applications. 492:38–51. doi:10.1016/j.laa.2015.11.004.
  • Aleksandrov, A. Y., and A. A. Tikhonov. 2018. Attitude stabilization of a rigid body under the action of a vanishing control torque. Nonlinear Dynamics 93 (2):285–93. doi:10.1007/s11071-018-4191-4.
  • Aleksandrov, A. Y., and A. A. Tikhonov. 2020. Averaging technique in the problem of Lorentz attitude stabilization of an Earth-pointing satellite. Aerospace Science and Technology 104:105963. doi:10.1016/j.ast.2020.105963.
  • Anan’evskii, I. M., and V. B. Kolmanovskii. 1989. On stabilization of some control systems with an after-effect. Automation and Remote Control 50 (9):1174–81.
  • Behjameh, M. R., H. Delavari, and A. Vali. 2015. Global finite time synchronization of two nonlinear chaotic gyros using high order sliding mode control. Journal of Applied and Computational Mechanics 1 (1):26–34.
  • De Souza, L. C. G. 2006. Design of satellite control system using optimal nonlinear theory. Mechanics Based Design of Structures and Machines 34 (4):351–64. doi:10.1080/15397730601044853.
  • Deriglazov, A. P., and A. A. Tikhonov. 2020. The effect of the nonuniformity of the Earth’s magnetic field on electrodynamic space tether system dynamics. Vestnik St. Petersburg University: Mathematics 53 (3):366–75.
  • Dosaev, M. 2019. Interaction between internal and external friction in rotation of vane with viscous filling. Applied Mathematical Modelling 68:21–8. doi:10.1016/j.apm.2018.11.002.
  • Formal’sky, A. M. 1997. On a modification of the PID controller. Dynamics and Control 7:269–77.
  • Fridman, E. 2014. Introduction to time-delay systems: Analysis and control. Basel: Birkhauser.
  • He, B., B. R. Wang, T. H. Yan, and Y. Y. Han. 2013. A distributed parallel motion control for the multi-thruster autonomous underwater vehicle. Mechanics Based Design of Structures and Machines 41 (2):236–57. doi:10.1080/15397734.2012.726847.
  • Ivanov, D. S., M. Y. Ovchinnikov, V. I. Penkov, and T. A. Ivanova. 2020. Modeling a nanosatellite’s angular motion damping using a hysteresis plate. Mathematical Models and Computer Simulations 12 (5):816–23. doi:10.1134/S2070048220050075.
  • Joshi, R. P., H. Qiu, and R. K. Tripathi. 2013. Configuration studies for active electrostatic space radiation shielding. Acta Astronautica 88:138–45. doi:10.1016/j.actaastro.2013.03.011.
  • Kępiński, R., J. Awrejcewicz, and D. Lewandowski. 2015. Dynamical simulation of a nonlinear stepper motor system. International Journal of Dynamics and Control 3 (1):31–5. doi:10.1007/s40435-014-0093-6.
  • Krasil’nikov, P. S. 2011. On the average of differential equations with two independent small parameters. Doklady Physics 56 (1):58–61. doi:10.1134/S1028335811010113.
  • Mashtakov, Y. V., M. Y. Ovchinnikov, and S. S. Tkachev. 2016. Study of the disturbances effect on small satellite route tracking accuracy. Acta Astronautica 129:22–31. doi:10.1016/j.actaastro.2016.08.028.
  • Melnikov, G. I., N. A. Dudarenko, K. S. Malykh, L. N. Ivanova, and V. G. Melnikov. 2017. Mathematical models of nonlinear oscillations of mechanical systems with several degrees of freedom. Nonlinear Dynamics and Systems Theory 17 (4):369–75.
  • Nikitin, D. Y., and A. A. Tikhonov. 2018. Attitude stabilization of a spacecraft equipped with large electrostatic protection screens. AIP Conference Proceedings 1959 (040011).
  • Pavlikov, S. V. 2007a. Constant-sign Lyapunov functionals in the problem of the stability of a functional differential equation. Journal of Applied Mathematics and Mechanics 71 (3):339–50. doi:10.1016/j.jappmathmech.2007.07.014.
  • Pavlikov, S. V. 2007b. Stabilization of the motions of controlled mechanical systems by a regulator with delay. Doklady Mathematics 75 (1):174–6. doi:10.1134/S1064562407010462.
  • Shen, J., and J. Lam. 2014. Decay rate constrained stability analysis for positive systems with discrete and distributed delays. Systems Science & Control Engineering 2 (1):7–12. doi:10.1080/21642583.2013.870054.
  • Su, Y. X., and C. H. Zheng. 2017. PID control for global finite-time regulation of robotic manipulators. International Journal of Systems Science 48 (3):547–58. doi:10.1080/00207721.2016.1193256.
  • Sur, A., and M. Kanoria. 2020. Memory response on thermal wave propagation in an elastic solid with voids. Mechanics Based Design of Structures and Machines 48 (3):326–47. doi:10.1080/15397734.2019.1652647.
  • Tikhonov, A. A. 2020. A control method for angular stabilization of an electrodynamic tether system. Automation and Remote Control 81 (2):269–86. doi:10.1134/S0005117920020071.
  • Tikhonov, A. A., K. A. Antipov, D. G. Korytnikov, and D. Yu. Nikitin. 2017. Electrodynamical compensation of disturbing torque and attitude stabilization of a satellite in J2 perturbed orbit. Acta Astronautica 141:219–27. doi:10.1016/j.actaastro.2017.10.009.
  • You, B., X. Yu, D. Liang, X. Liu, and X. Yang. 2020. Numerical and experimental investigation on dynamics of deployable space telescope experiencing deployment and attitude adjustment motions coupled with laminated composite shell. Mechanics Based Design of Structures and Machines. doi:10.1080/15397734.2020.1717341.
  • Zahariev, E., K. Delchev, and S. Karastanev. 2006. Suppression of deviations and vibrations of tethered satellite. Mechanics Based Design of Structures and Machines 34 (4):389–408. doi:10.1080/15397730601044887.
  • Zubov, V. I. 1975. Lectures on control theory (Russian). Moscow: Nauka.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.