Using Sliding Mode Control to Set Up a Rotating Electrodynamic Space Tether System

Abstract

The paper considers the process of imparting rotation at a given angular velocity to an electrodynamic space tether system in a near-Earth orbit. The tether system is a linear cluster of three microsatellites connected by insulated conductive cables. Initially the system is gravitationally stabilised in the approximate vertical direction. Electromagnetic forces generated in the conductive cables by the geomagnetic field impart rotation to the system. We stated the equations of motion for the system in the Earth-fixed coordinate system, taking into account distributed load produced by gravitational and electromagnetic forces. The system is moving in a fairly high, almost circular orbit, so aerodynamic forces are not taken into account. Adjusting the current will reduce the strain in the tethers. The model under consideration represents those as a set of material points connected by unilateral elastic links. We propose a feedback current controller based on sliding mode control. The system variables lie on a single surface, moving across which ensures asymptotic stability of the control process. We used a simplified system motion model to synthesise the controller parameters. We analysed the angular motion of microsatellites with respect to the tether direction while rotation is imparted to the system. Numerical examples confirm the efficiency of our approach to setting up a rotating space tether system

The study was supported by RFBR and National Natural Science Foundation of China as part of the research projects no. 21-51-53002 and no. 61803307

Please cite this article in English as:

Lu H., Wang C., Zabolotnov Yu.M. Using sliding mode control to set up a rotating electrodynamic space tether system. Herald of the Bauman Moscow State Technical University, Series Mechanical Engineering, 2022, no. 2 (141), pp. 4--19 (in Russ.). DOI: https://doi.org/10.18698/0236-3941-2022-2-4-19

References

[1] Bekey I., Penzo P.A. Tether propulsion. Aerosp. Am., 1986, vol. 24, pp. 40--43.

[2] Beletskiy V.V., Levin E.M. Dinamika kosmicheskikh trosovykh system [Dynamics of space tether systems]. Moscow, Nauka Publ., 1990.

[3] Van Pelt M. Space tethers and space elevators. New York, Springer, 2009.

[4] Zhong R., Zhu Z.H. Optimal control of nanosatellite fast deorbit using electrodynamic tether. J. Guid. Control Dyn., 2014, vol. 37, no. 4, pp. 1182--1194. DOI: https://doi.org/10.2514/1.62154

[5] Williams P. Optimal control of electrodynamic tether orbit transfers using timescale separation. J. Guid. Control Dyn., 2010, vol. 33, no. 1, pp. 88--98. DOI: https://doi.org/10.2514/1.45250

[6] Li A., Lu H., Zabolotnov Y. Impact analysis and orbit reboost of payload tossing using spinning electrodynamic tether system. Int. J. Eng. Syst. Model. Simul., 2020, vol. 11, no. 4, pp. 176--185.

[7] Sanmartin J.R., Pelaez J. Tether capture of spacecraft at Neptune. Acta Astronaut., 2020, vol. 177, pp. 906--911. DOI: https://doi.org/10.1016/j.actaastro.2020.03.024

[8] Ohkawa Y., Kawamoto S., Okumura T., et al. Review of KITE --- electrodynamic tether experiment on the H-II Transfer Vehicle. Acta Astronaut., 2020, vol. 177, pp. 750--758. DOI: https://doi.org/10.1016/j.actaastro.2020.03.014

[9] Osipov V.G., Shoshunov N.L. Space tether systems: history and prospects. Zemlya i Vselennaya, 1998, no. 4, pp. 19--29 (in Russ.).

[10] Kul’kov V.M., Egorov Yu.G., Tuzikov S.A. Investigation of integral energy characteristics of the space electrodynamic tether system designed for orbital experiments. Izv. RAN. Energetika [Proceedings of the Russian Academy of Sciences. Power Engineering], 2017, no. 3, pp. 114--127 (in Russ.).

[11] Sedwick R.J., Schweighart S.A. Propellantless spin-up of tethered or electromagnetically coupled sparse apertures. Proc. SPIE, 2002, vol. 4849. DOI: https://doi.org/10.1117/12.460559

[12] Cai Z., Li X., Wu Z. Deployment and retrieval of a rotating triangular tethered satellite formation near libration points. Acta Astronaut., 2014, vol. 98, pp. 37--49. DOI: https://doi.org/10.1016/j.actaastro.2014.01.015

[13] Levin E.M. Dynamic analysis of space tether missions. San Diego, California, AAS, 2007.

[14] Voevodin P.S., Zabolotnov Yu.M. Stabilizing the motion of a low-orbit electrodynamic tether system. J. Comput. Syst. Sc. Int., 2019, vol. 58, no. 2, pp. 270--285. DOI: https://doi.org/10.1134/S1064230719020175

[15] Lu H., Li A., Wang C., et al. Stability analysis and motion control of spinning electrodynamic tether system during transition into spin. Acta Astronaut., 2020, vol. 177, pp. 871--881. DOI: https://doi.org/10.1016/j.actaastro.2019.11.032

[16] Lu H., Li A., Wang C., et al. Tether deformation of spinning electrodynamic tether system and its suppression with an optimal controller. J. Aerosp. Eng., 2021, vol. 34, no. 2, art. 04021003. DOI: http://dx.doi.org/10.1061/(ASCE)AS.1943-5525.0001233

[17] Van Ch., Zabolotnov Yu.M. Analysis of the dynamics of the formation of a tether group of three nanosatellites taking into account their motion around the centers of mass. Mech. Solids, 2021, vol. 56, no. 7, pp. 1181--1198.DOI: https://doi.org/10.3103/S0025654421070244