A robust asymptotic tracking controller for an uncertain 2DOF underactuated mechanical system motivated by a satellite attitude control problem

• Autorzy: Emirsajłow Zbigniew , Barciński Tomasz

Identyfikatory

DOI

10.61822/amcs-2025-0008

• Języki publikacji: EN

Abstrakty

EN

The paper is devoted to the theoretical problem of designing a robust asymptotic tracking control system for a rotational motion of a 2DOF underactuated linear mechanical system with parametric uncertainties. The mathematical formulation of the problem is motivated by the attitude control problem of an earth observation satellite with a solar panel. It is assumed that all the parameters of the plant model are uncertain and the plant single input is additively disturbed by an unknown constant torque. By employing the general regulator theory in the state space setup combined with the concept of the structured singular value, we develop a robustly stabilizing and robustly asymptotically tracking error feedback controller. The rotation of the main rigid body of the mechanical system is to asymptotically track a harmonically changing reference signal. The obtained theoretical results are successfully tested on two numerical examples and computations are performed in Matlab.

Słowa kluczowe

EN

underactuated 2DOF mechanical system; rotational motion control; robust asymptotic tracking; robust error feedback controller

PL

sterowanie ruchem; śledzenie asymptotyczne; kontroler sprzężenia zwrotnego

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2025
• Tom: Vol. 35, no. 1
• Strony: 97--116
• Opis fizyczny: Bibliogr. 25 poz., rys., wykr.

Twórcy

autor

Emirsajłow Zbigniew

• Department of Automatic Control and Robotics, West Pomeranian University of Technology in Szczecin, Sikorskiego 37, 70-313 Szczecin, Poland

autor

Barciński Tomasz

• Space Research Center, Polish Academy of Sciences, Bartycka 18A, 00-716 Warsaw, Poland

Bibliografia

• [1] Almeida, D., Gamez, C. and Rascon, R. (2015). Robust regulation and tracking control of a class of uncertain 2DOF underactuated mechanical systems, Mathematical Problems in Engineering 2015: 1-11, Article ID: 429476, DOI: 10.1155/2015/429476.
• [2] Angeletti, F., Gasbarri, P., Sabatini, M. and Iannelli, P. (2020). Design and performance assessment of a distributed vibration suppression system of a large flexible antenna during attitude manoeuvres, Acta Astronautica 176: 542-557, DOI: 10.1016/j.actaastro.2020.04.015.
• [3] Angeletti, F., Iannelli, P., Gasbarri, P. and Sabatini, M. (2021). End-to-end design of a robust attitude control and vibration suppression system for large space smart structures, Acta Astronautica 187: 416-428, DOI: 10.1016/j.actaastro.2021.04.007.
• [4] Emirsajłow, Z., Barciński, T. and Bukowiecka, N. (2023). Attitude control of an earth observation satellite with a solar panel, in M. Pawelczyk et al. (Eds), Advanced Contemporary Control, Springer Nature, Cham, pp. 393-402, DOI: 10.1007/978-3-031-35170-9-37.
• [5] Francis, B. and Wonham, W. (1975). The internal model principle for linear multivariable regulators, Applied Mathematics and Optimization 2(2): 170-194.
• [6] Iannelli, P., Angeletti, F. and Gasbarri, P. (2022). A model predictive control for attitude stabilization and spin control of a spacecraft with a flexible rotating payload, Acta Astronautica 199: 401-411, DOI: 10.1016/j.actaastro.2022.07.024.
• [7] Isidori, A., Marconi, L. and Serrani, A. (2003). Robust Autonomous Guidance An Internal Model Approach, Springer, London.
• [8] Liu, Y. and Yu, H. (2013). A survey of underactuated mechanical systems, IET Control Theory and Applications 7(7): 921-935, DOI: 10.1049/iet-cta.2012.0505.
• [9] MathWorks (2020a). MATLAB Control System Toolbox R2020b, MathWorks, Natick.
• [10] MathWorks (2020b). MATLAB Robust Control Toolbox R2020b, MathWorks, Natick.
• [11] MathWorks (2020c). MATLAB Symbolic Math Toolbox R2020b, MathWorks, Natick.
• [12] Mohsenipour R., Nemati, H., Nasirian, M. and Nia, A.K. (2013). Attitude control of a flexible satellite by using robust control design methods, Intelligent Control and Automation 4(3): 313-326, DOI: 10.4236/ica.2013.43037.
• [13] Muñoz-Arias, M. (2019). An energy-based approach to satellite attitude control in presence of disturbances, Proceedings of the 8th European Conference for Aeronautics and Aerospace Sciences (EUCASS), Madrid, Spain, pp. 1-7, DOI: 10.13009/EUCASS2019-1052.
• [14] Narkiewicz, J., Grunvald, S. and Sochacki, M. (2024). Attitude control system for an earth observation satellite, Bulletin of the Polish Academy of Sciences: Technical Sciences 72(2): 1-8, DOI: 10.24425/bpasts.2024.148612.
• [15] Narkiewicz, J., Sochacki, M. and Zakrzewski, B. (2020). Generic model of a satellite attitude control system, International Journal of Aerospace Engineering 2020(1): 5352019, DOI: 10.1155/2020/5352019.
• [16] Ohtani, T., Hamada, Y., Nagashio, T., Kida, T., Mitani, S., Yamaguchi, I., Kasai, T. and Igawa, H. (2011). Robust attitude control using mu-synthesis for the large flexible satellite ETS-VIII, Journal of Space Technology and Science 25(1): 27-40, DOI: 10.1155/2020/5352019.
• [17] Ordaz, P., Romero-Trejo, H., Cuvas, C. and Sandre, O. (2024). Dynamic sliding mode control based on a full-order observer: Underactuated electro-mechanical system regulation, International Journal of Applied Mathematics and Computer Science 34(1): 29-43, DOI: 10.61822/amcs-2024-0003.
• [18] Saberi, A., Stoorvogel, A. and Sannuti, P. (2000). Control of Linear Systems with Regulation and Input Constraints, Springer, London.
• [19] Scherer, C. (2001). Theory of Robust Control, Delft University of Technology, Delft.
• [20] Sumithra, S. and Vadivel, S. (2021). An optimal innovation based adaptive estimation Kalman filter for accurate positioning in a vehicular ad-hoc network, International Journal of Applied Mathematics and Computer Science 31(1): 45-57, DOI: 10.34768/amcs-2021-0004.
• [21] Wang, L., Li, Z. and Wang, B. (2012). Robust satellite attitude control, in D. Jin and S. Lin (Eds), Advances in Computer Science and Information Engineering, Vol. 1, Springer, Berlin, Heidelberg, pp. 649-654, DOI: 10.1007/978-3-642-30126-1-102.
• [22] Wang, Y., Zhang, D. and Dai, G. (2020). Classification of high resolution satellite images using improved U-Net, International Journal of Applied Mathematics and Computer Science 30(3): 399-413, DOI: 10.34768/amcs-2020-0030.
• [23] Williams, R. and Lawrence, D. (2007). Linear State-Space Control Systems, Wiley, Hoboken, NJ.
• [24] Xie, Y., Huang, H., Hu, Y. and Zhang, G. (2016). Applications of advanced control methods in spacecrafts - Progress, challenges, and future prospects, Frontiers of Information Technology & Electronic Engineering 17(9): 416-428, DOI: 10.1631/FITEE.1601063.
• [25] Zhou, K. and Doyle, J. (1998). Essentials of Robust Control, Prentice Hall, Upper Saddle River.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).