Model reference adaptive control of a small satellite in the presence of parameter uncertainties

Document Type : Research Note

Authors

1 Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Department of Aerospace Engineering, K.N. Toosi University of Technology, Tehran, Iran

Abstract

An accurate control algorithm for small satellites is critical to the mission's success. In this paper, a novel discrete-time Model Reference Adaptive Control algorithm (MRAC) is developed based on unified approach for attitude control of a three-axis stabilized nonlinear satellite model. The linearized model of satellite with unknown dynamic parameters is derived and Recursive Least Squares (RLS) algorithm is used to identify the linear model’s unknown parameters. In order to take into account the nonlinear model of satellite dynamics, the proposed MRAC strategy is used considering the linear model, the estimation error; and the difference between the actual nonlinear system and the linear model outputs. The actual nonlinear model of satellite includes moments of inertia uncertainties, external disturbances, and sensor noise on the outputs. The introduced controller performance is compared with a conventional discrete -time MRAC which demonstrates excellent simultaneous regulation and tracking capabilities.

Keywords

Main Subjects


References:
1. Arzen, K.-E. "A simple event-based PID controller", 14th IFAC World Congress (1999).
2. Psiaki, M.L. "Magnetic torquer attitude control via asymptotic periodic linear quadratic regulation", Journal of Guidance, Control, and Dynamics, 24(2), pp. 386-394 (2001).
3. Binette, M.R., Damaren, C.J., and Pavel, L. "Nonlinear H1 attitude control using modified Rodrigues parameters", Journal of Guidance, Control, and Dynamics, 37(6), pp. 2017-2021 (2014).
4. Liu, C., Vukovich, G., Shi, K., and Sun, Z. "Robust fault tolerant nonfragile H1 attitude control for spacecraft via stochastically intermediate observer", Advances in Space Research, 62(9), pp. 2631-2648 (2018).
5. Giri, D.K. and Sinha, M. "Robust backstepping magnetic attitude control of satellite subject to unsymmetrical mass properties", Journal of Spacecraft and Rockets, 56(1), pp. 298-305 (2019).
6. Mori, K. and Takahashi, M. "Minimum-time attitude maneuver and robust attitude control of small satellite mounted with communication antenna", AIAA Scitech 2019 Forum, American Institute of Aeronautics and Astronautics (2019).
7. Lu, K. and Xia, Y. "Adaptive attitude tracking control for rigid spacecraft with finite-time convergence", Automatica, 49(12), pp. 3591-3599 (2013).
8. Ioannou, P.A. and Kokotovic, P.V. "Instability analysis and improvement of robustness of adaptive control", Automatica, 20(5), pp. 583-594 (1984).
9. Rohrs, C., Valavani, L., Athans, M., and Stein, G. "Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics", IEEE Transactions on Automatic Control, 30(9), pp. 881-889 (1985).
10. Sastry, S. and Bodson, M., Adaptive Control: Stability, Convergence and Robustness, Courier Corporation (2011).
11. Yoon, H. and Tsiotras, P. "Adaptive spacecraft attitude tracking control with actuator uncertainties", The Journal of the Astronautical Sciences, 56(2), pp. 251- 268 (2008).
12. Kim, D., MacKunis, W., Fitz-Coy, N., and Dixon, W. "Precision Integrated Power and Attitude Control System (IPACS) in the presence of dynamic uncertainty", The Journal of the Astronautical Sciences, 58(1), pp. 99-120 (2011).
13. Ioannou, P.A. and Sun, J., Robust Adaptive Control, Courier Corporation (2012).
14. Jin, X., Zhu, S., Zhu, X., Chen, Q., and Zhang, X. "Single-input adaptive fuzzy sliding mode control of the lower extremity exoskeleton based on humanrobot interaction", Advances in Mechanical Engineering, 9(2), pp. 1-9 (2017).
15. Jiao, X. and Jiang, J. "Design of adaptive switching control for hypersonic aircraft", Advances in Mechanical Engineering, 7(10), pp. 1-10 (2015).
16. Torabi, M., Sharifi, M., and Vossoughi, G. "Robust adaptive sliding mode admittance control of exoskeleton rehabilitation robots", Scientia Iranica, 25(5), pp. 2628-2642 (2018).
17. Sun, R., Wang, J., Zhang, D., and Shao, X. "Neuralnetwork-based sliding-mode adaptive control for spacecraft formation using aerodynamic forces", Journal of Guidance, Control, and Dynamics, 41(3), pp. 757-763 (2017).
18. Sun, L. and Zheng, Z. "Adaptive sliding mode control of cooperative spacecraft rendezvous with coupled uncertain dynamics", Journal of Spacecraft and Rockets, 54(3), pp. 652-661 (2017).
19. Bolandi, H., Haghparast, M., and Abedi, M. "A reliable fault tolerant attitude control system based on an adaptive fault detection and diagnosis algorithm together with a backstepping fault recovery controller", Scientia Iranica, Transaction D, Computer Science & Engineering, Electrical, 20(6) (2013).
20. Imran, A., Radice, G., and Kim, J. "Backstepping control design with actuator torque bound for spacecraft attitude maneuver", Journal of Guidance, Control, and Dynamics, 33(1), pp. 254-259 (2010).
21. Jiang Y., Hu Q., and Ma, G. "Adaptive backstepping fault-tolerant control for  flexible spacecraft with unknown bounded disturbances and actuator failures", ISA Transactions, 49(1), pp. 57-69 (2010).
22. Sun, L. and Huo, W. "6-DOF integrated adaptive backstepping control for spacecraft proximity operations", IEEE Transactions on Aerospace and Electronic Systems, 51(3), pp. 2433-2443 (2015).
23. Cruz, G. and Bernstein D.S. "Retrospective cost adaptive control of spacecraft attitude using magnetic actuators", Proc. AIAA Guid. Nav. Contr. Conf., Boston, MA (2013).
24. Landau, I. and Lozano, R. "Unification of discrete time explicit model reference adaptive control designs", Automatica, 17(4), pp. 593-611 (1981).
25. Saberi, F.F., Dastgerdi, S.A., and Zandieh, M. "Unified model reference adaptive attitude control of a satellite in presence of uncertain parameters: Design and implementation", International Journal of Computer Applications, 121(12), pp. 25-32 (2015).
26. Wie, B., Space Vehicle Dynamics and Control, AIAA (1998).
27. Sidi, M.J., Spacecraft Dynamics and Control: A Practical Engineering Approach, Cambridge University Press (1997).
28. Chalam, V., Adaptive Control Systems: Techniques and Applications, Marcel Dekker, Inc. (1987).
29. Popov, V.-M., Hyperstability of Control Systems, Springer-Verlag Berlin Heidelberg (1973).