Improving a Satellite Attitude Control Using Fractional-Order Controller in the Presence of Environmental Disturbances

Khatoonabadi, Elahe; Bohlouri, Vahid

doi:10.22034/joae.2022.320999.1080

Improving a Satellite Attitude Control Using Fractional-Order Controller in the Presence of Environmental Disturbances

Document Type : Original Article

Authors

Elahe Khatoonabadi ¹

Vahid Bohlouri ²

¹ Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran

² Department of Electrical Engineering, Technical and Vocational University, Tehran, Iran

10.22034/joae.2022.320999.1080

Abstract

In this paper, attitude control of a rigid satellite in the presence of external perturbations and considering the parametric uncertainties with the fractional order controller is investigated. To control the attitude of the satellite, a reaction wheel actuator with a first-order dynamic model is used and uncertainty is considered in the parameters of the satellite’s moment of inertia, the actuator model and external perturbations. For comparative purposes, in addition to the fractional order controller, the integer order controller is also used. Numerical solution is performed by Euler method and Granwald-Letinkov definition is used to solve the fractional order integral and derivative. The coefficients of the integer order and fractional order controllers were extracted by the particle swarm optimization method with the performance criterion of mean of absolute value of error. Fractional order controllers have more degree of freedom than integer order controllers due to their more design parameters. Therefore, according to the results, the appropriate performance of fractional order controllers can be seen in overshoot, settling time and against of perturbations and uncertainty in the satellite attitude control.

Keywords

Satellite Attitude Control

Fractional-order Controller

Uncertainty

Disturbance

20.1001.1.17359449.1401.24.2.6.8

[1] M. J. Sidi, Spacecraft dynamics and control: A practical engineering approach. 2014.

[2] M. Massoumnia,, "Linear Controllers Design," Sharif Univercity of Technology, 1394, (in persian),Accessed: Dec. 28, 2020. [Online]. Available: http://ganjineh.sharif.ir/resource/425314.

[3] A. Ghaedi and M. A. Nekoui, “3-Axes satellite attitude control based on biased angular momentum,” in 2008 13th International Power Electronics and Motion Control Conference, EPE-PEMC 2008, 2008, pp. 1054–1057, doi: 10.1109/EPEPEMC.2008.4635407.

[4] P. Sharma and V. G. Nair, “Tuning of PID controller using glowworm swarm optimisation on a satellite attitude control reaction wheel,” Int. J. Recent Technol. Eng., vol. 8, no. 2, pp. 4205–4210, 2019, doi: 10.35940/ijrte.B3404.078219.

[5] C. Pukdeboon, “Robust optimal pid controller design for attitude stabilization of flexible spacecraft,” Kybernetika, vol. 54, no. 5, pp. 1049–1070, 2018, doi: 10.14736/kyb-2018-5-1049.

[6] S. S. Kumar, C. Shreesha, and N. K. Philip, “Robust PID controller design for rigid uncertain spacecraft using Kharitonov theorem and vectored particle swarm optimization,” Int. J. Eng. Technol., vol. 7, no. 2, pp. 9–14, 2018, doi: 10.14419/ijet.v7i2.21.11825.

[7] Y. Li, Z. Sun and D. Ye, “Robust linear PID controller for satellite attitude stabilisation and attitude tracking control,” Int. J. Sp. Sci. Eng., vol. 4, no. 1, p. 64, 2016, doi: 10.1504/ijspacese.2016.078581.

[8] A. Kosary, A. Maani and H. Nejat Pishkonary, "Three-axis Satellite Atittude with a combination of Thruster and Reaction wheels," (in persian), vol. 11, no. 3, pp. 63–71, Dec. 2018, Accessed: Dec. 28, 2020. [Online]. Available: http://jsst.ias.ir/article_81073.html.

[9] S. M. Bazaz, V. Bohlouri, S. Hamid and J. Naini, “Attitude Control of a Rigid Satellite with Pulse-Width Pulse-Frequency Modulation Using Observer-based Modified PID Controller,” Fac. Mech. Eng. Tarbiat Modares Univ. Tehran, Iran., vol. 16, no. 8, pp. 139–148, 2016, Accessed: Dec. 28, 2020. [Online]. Available: http://journals.modares.ac.ir/article-15-1094-en.html.

[10] V. Bohlouri, Z. Khodamoradi and S. H. Jalali-Naini, “Spacecraft attitude control using model-based disturbance feedback control strategy,” J. Brazilian Soc. Mech. Sci. Eng., vol. 40, no. 12, pp. 1–18, Dec. 2018, doi: 10.1007/s40430-018-1478-9.

[11] V. Bohlouri, M. Ebrahimi, and S. H. J. Naini, “Robust optimization of satellite attitude control system with on-off thruster under uncertainty,” in 2017 International

Conference on Mechanical, System and Control Engineering, ICMSC 2017, 2017, pp. 328–332, doi: 10.1109/ICMSC.2017.7959495.

[12] V. Bohlouri and S. H. Jalali-Naini, “Application of reliability-based robust optimization in spacecraft attitude control with PWPF modulator under uncertainties,” J. Brazilian Soc. Mech. Sci. Eng., vol. 41, no. 10, pp. 1–15, Oct. 2019, doi: 10.1007/s40430-019-1955-9.

[13] M. Tavazoei and M. Tavakoli-Kakhaki, “Fractional Order Systems and Controllers.” (in persian), http://press.kntu.ac.ir/book_388060.html (accessed Dec. 28, 2020).

[14] F. Mainardi, “Short survey: An historical perspective on fractional calculus in linear viscoelasticity,” Fractional Calculus and Applied Analysis, vol. 15, no. 4. pp. 712–717, 2012, doi: 10.2478/s13540-012-0048-6.

[15] R. El-Khazali, “Fractional-order PI λdμ controller design,” Comput. Math. with Appl., vol. 66, no. 5, pp. 639–646, Sep. 2013, doi: 10.1016/j.camwa.2013.02.015.

[16] H. Li, Y. Luo and Y. Chen, “A fractional order proportional and derivative (FOPD) motion controller: Tuning rule and experiments,” IEEE Trans. Control Syst. Technol., vol. 18, no. 2, pp. 516–520, 2010, doi: 10.1109/TCST.2009.2019120.

[17] C. A. Monje, B. M. Vinagre, V. Feliu and Y. Q. Chen, “Tuning and auto-tuning of fractional order controllers for industry applications,” Control Eng. Pract., vol. 16, no. 7, pp. 798–812, 2008, doi: 10.1016/j.conengprac.2007.08.006.

[18] D. Valério and J. S. Da Costa, “Ziegler-nichols type tuning rules for fractional pid controllers,” in Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005, 2005, vol. 6 B, pp. 1431–1440, doi: 10.1115/detc2005-84344.

[19] S. M. Baviskar, P. Shah and S. D. Agashe, “Tuning of fractional PID controllers for higher order systems,” Int. J. Appl. Eng. Res., vol. 9, no. 11, pp. 1581–1590, 2014, Accessed: Dec. 28, 2020. [Online]. Available: http://www.ripublication.com.

[20] M. T. Nasri and W. Kinsner, “An evaluation of integer- and fractional-order controllers for small satellites,” in Proceedings of 2014 IEEE 13th International Conference on Cognitive Informatics and Cognitive Computing, ICCI*CC 2014, 2014, pp. 30–38, doi: 10.1109/ICCI-CC.2014.6921437.

[21] M.Nasri and W. Kinsner, “A comparison between fuzzy, fractional-, and integer-order controllers for small satellites attitude control,” ieeexplore.ieee.org, 2014, Accessed: Dec. 28, 2020. [Online]. Available: https://ieeexplore.ieee.org/abstract/document/6901125/.

[22] N. Sarafnia, M. Malekzadeh, and J. Askari, “Fractional order PDD control of spacecraft rendezvous,” Adv. Sp. Res., vol. 62, no. 7, pp. 1813–1825, 2018, doi: 10.1016/j.asr.2018.06.040.

[23] G. Xing-wang, L. Ai-jun, G. Yang-yang and W. Chang-qing, “Fractional order attitude stability control for sub-satellite of tethered satellite system during deployment,” Appl. Math. Model., vol. 62, pp. 272–286, 2018, doi: 10.1016/j.apm.2018.04.005.

[24] G. Sun and Z. H. Zhu, “Fractional order controlof tethered satellite system deployment and retrieval,” 2014, doi: 10.2514/6.2014-4132.

[25] D. Chakrabarti and N. Selvaganesan, “PD and PDβ based sliding mode control algorithms with modified reaching law for satellite attitude maneuver,” Adv. Sp. Res., vol. 65, no. 4, pp. 1279–1295, 2020, doi: 10.1016/j.asr.2019.11.005.

[26] D. Chakrabarti and N. Selvaganesan, “PD and PDβ based sliding mode control algorithms with modified reaching law for satellite attitude maneuver,” Adv. Sp. Res., vol. 65, no. 4, pp. 1279–1295, 2020, doi: 10.1016/j.asr.2019.11.005.

[27] P. N. Paraskevopoulos, Modern control engineering. 2017.