Finite-Time Disturbance Observer Based Fractional Order Nonsingular Terminal Sliding Mode Attitude Control of Satellites

Piri, Shirkoo; Beyramzad, Jalil; Khanmirza, Esmaeel

doi:10.22034/jsst.2024.1509

Finite-Time Disturbance Observer Based Fractional Order Nonsingular Terminal Sliding Mode Attitude Control of Satellites

Document Type : Original Research Paper

Authors

Shirkoo Piri ¹

Jalil Beyramzad ²

Esmaeel khanmirza ³

¹ PhD, Candidate, School of Mechanical Engineering, University of Science and Technology, Tehran, Iran

² PhD Candidate, School of Mechanical Engineering, University of Science and Technology, Tehran, Iran

³ School of Mechanical Engineering, University of Science and Technology. Tehran, Iran

10.22034/jsst.2024.1509

Abstract

This study presents a method for implementing rigid satellite output feedback control that considers dynamic uncertainties and external disturbances, all while avoiding the need for velocity state measurement. The dynamics of a rigid satellite are first represented using the modified Rodrigues parameter (MRP), and then transformed into Euler-Lagrangian form to provide the state-space representation of the dynamics. The availability of angular velocity data for practical applications is often limited by cost or technical limitations. Consequently, angular velocity is considered to be immeasurable. In order to minimize the need for extra mathematical calculations and the creation of separate observers to estimate uncertainties and system states, a finite time disturbance observer (third order sliding mode (TOSM) observer) was used to simultaneously estimate both uncertainties and system states. The main component of the suggested controller incorporates the fractional order nonsingular terminal sliding mode technique, which guarantees stability within a finite time and avoids chattering. The simulation results of the proposed methodology have been presented and compared with the results of techniques available in the literature, showcasing the efficacy of the method described in this study and the enhancement of the findings of previous relevant research.

Keywords

Fractional order SMC

Attitude control

Disturbance observer

Terminal sliding mode

Finite time stability

Subjects

Space subsystems design: (navigation, control, structure and…)

Article Title Persian

Finite time disturbance observer based output feedback fractional order nonsingular terminal sliding mode attitude control of satellites

Authors Persian

شیرکو پیری ¹

Jalil Beyramzad ²

اسماعیل خان میرزا ³

¹ دانشکده مهندسی مکانیک، دانشگاه علم و صنعت ایران، تهران، ایران

² دانشجوی دکتری، دانشکده مهندسی مکانیک، دانشگاه علم و صنعت ایران، تهران، ایران

³ دانشکده مهندسی مکانیک، دانشگاه علم و صنعت ایران، تهران، ایران

Abstract Persian

Keywords Persian

Fractional order SMC

Attitude control

Disturbance observer

Terminal sliding mode

Finite time stability

[1] N. Nazari, H. Moladavoudi, and J. Beyramzad, "Finite time sliding mode control for agile rigid satellite with CMG actuators using fast high-order sliding mode observer," Aerospace Systems, vol. 7, pp. 363-383, 2024, https://doi.org/10.1007/s42401-024-00283-4.

[2] Y. Guo, B. Huang, J. H. Guo, A. J. Li, and C. Q. Wang, "Velocity-free sliding mode control for spacecraft with input saturation," Acta Astronautica, vol. 154, pp. 1-8, 2019, https://doi.org/10.1016/j.actaastro.2018.10.045.

[3] K. Zhang, G. R. Duan, and M. D. Ma, "Dynamic output feedback sliding mode control for spacecraft hovering without velocity measurements," Journal of the Franklin Institute, vol. 356, no. 4, pp. 1991-2014, 2019, https://doi.org/10.1016/j.jfranklin.2019.01.030.

[4] L. Yuan, G. Ma, C. Li, and B. Jiang, "Finite-time attitude tracking control for spacecraft without angular velocity measurements," Journal of Systems Engineering and Electronics, vol. 28, no. 6, pp. 1174-1185, 2017, https://doi.org/10.21629/JSEE.2017.06.15.

[5] Q. Hu and B. Jiang, "Continuous finite-time attitude control for rigid spacecraft based on angular velocity observer," IEEE Transactions on Aerospace and Electronic Systems, vol. 54, no. 3, pp. 1082-1092, 2017, https://doi.org/10.1109/TAES.2017.2773340.

[6] M. Malekzadeh and H. Sadeghian, "Attitude control of spacecraft simulator without angular velocity measurement," Control Engineering Practice, vol. 84, pp. 72-81, 2019, https://doi.org/10.1016/j.conengprac.2018.11.011.

[7] Y. Shtessel, C. Edwards, L. Fridman, and A. Levant, Sliding Mode Control and Observation, New York: Springer, 2014, https://doi.org/10.1007/978-0-8176-4893-0.

[8] J. Liu and X. Wang, Advanced Sliding Mode Control for Mechanical Systems: Design, Analysis and MATLAB Simulation, Berlin: Springer, 2012, https://doi.org/10.1007/978-3-642-20907-9.

[9] V. Shahbahrami, M. Azimi, and A. Alikhani, "Attitude and vibration control of a flexible spacecraft using hybrid adaptive super-twisting non-singular terminal sliding mode control," Journal of Space Science and Technology, vol. 16, no. 4, pp. 1-13, 2021, https://doi.org/10.30699/jsst.2023.1365.

[10] V. Utkin, A. Poznyak, Y. Orlov, and A. Polyakov, "Conventional and high order sliding mode control," Journal of the Franklin Institute, vol. 357, no. 15, pp. 10244-10261, 2020, https://doi.org/10.1016/j.jfranklin.2020.06.018.

[11] L. Fridman, J. A. Moreno, B. Bandyopadhyay, S. Kamal, and A. Chalanga, "Continuous nested algorithms: The fifth generation of sliding mode controllers," in Recent Advances in Sliding Modes: From Control to Intelligent Mechatronics: Studies in Systems, Decision and Control 24, X. Yu, and M. ÖnderEfe, Eds. Cham: Springer, 2015, pp. 5-35, https://doi.org/10.1007/978-3-319-18290-2_2.

[12] F. Shokouhi and A. H. Davaie Markazi, "A new continuous approximation of sign function for sliding mode control," in 6^th International Conference on Robotics and Mechatronics (ICRoM 2018), Tehran, Iran, 2018.

[13] M. Navabi and M. R. Hosseini, "Investigation in to the effect of kinematic of the space craft attitude control using feedback linearization method," Journal of Space Science and Technology, vol. 11, no. 1, pp. 59-71, 2018.

[14] Y. Guo, B. Huang, S. M. Song, A. J. Li, and C. Q. Wang, "Robust saturated finite-time attitude control for spacecraft using integral sliding mode," Journal of Guidance, Control, and Dynamics, vol. 42, no. 2, pp. 440-446, 2019, https://doi.org/10.2514/1.G003520.

[15] M. Navabi and N. Safaei Hashekvaei, "Kinematic modelling without singularity and nonlinear control of satellite attitude using direct adaptive and fuzzy PD control methods," Journal of Space Science and Technology, vol. 14, no. 2, pp. 77-88, 2021, https://doi.org/10.22034/jsst.2021.1248.

[16] H. Yadegari, J. Beyramzad, and E. Khanmirza, "Magnetorquers-based satellite attitude control using interval type-II fuzzy terminal sliding mode control with time delay estimation," Advances in Space Research, vol. 69, no. 8, pp. 3204-3225, 2022, https://doi.org/10.1016/j.asr.2022.01.018.

[17] P. M. Tiwari, S. Janardhanan, and M. Nabi, "Attitude control using higher order sliding mode," Aerospace Science and Technology, vol. 54, pp. 108-113, 2016, https://doi.org/10.1016/j.ast.2016.04.012.

[18] M. Javaheripour, A. R. Vali, V. Behnam Gol, and F. Allahverdizadeh, "Design of an nonlinear extended state observer to estimate unmeasurable information on the problem of flying objects guidance," Journal of Space Science and Technology, vol. 15, no. 3, pp. 67-78, 2022, https://doi.org/10.30699/jsst.2022.1352.

[19] M. Alipour, M. Malekzadeh, and A. Ariaei, "Practical fractional-order nonsingular terminal sliding mode control of spacecraft," ISA Transactions, vol. 128, Part A, pp. 162-173, 2022, https://doi.org/10.1016/j.isatra.2021.10.022.

[20] Z. Ismail, R. Varatharajoo, and Y.C. Chak, "A fractional-order sliding mode control for nominal and underactuated satellite attitude controls," Advances in Space Research, vol. 66, no. 2, pp. 321-334, 2020, https://doi.org/10.1016/j.asr.2020.02.022.

[21] G. Zhao, "Fractional-order fast terminal sliding mode control for a class of dynamical systems," Mathematical Problems in Engineering, vol. 2013, no. 1, 2013, Art. no. 384921, https://doi.org/10.1155/2013/384921.

[22] C. A. Monje, Y. Q. Chen, B. M. Vinagre, D. Xue, and V. Feliu-Batlle, Fractional-Order Systems and Controls: Fundamentals and Applications, Springer, London, 2010.

[23] D. Xue, Fractional-Order Control Systems: Fundamentals and Numerical Implementations, Walter de Gruyter, 2017.

[24] V. C. Nguyen, A. T. Vo, and H. J. Kang, "A finite-time fault-tolerant control using non-singular fast terminal sliding mode control and third-order sliding mode observer for robotic manipulators," IEEE Access, vol. 9, pp. 31225-31235, 2021, https://doi.org/10.1109/ACCESS.2021.3059897.

[25] M. Van, H. J. Kang, Y. S. Suh, and K. S. Shin, "Output feedback tracking control of uncertain robot manipulators via higher-order sliding-mode observer and fuzzy compensator," Journal of Mechanical Science and Technology, vol. 27, pp. 2487-2496, 2013, https://doi.org/10.1007/s12206-013-0636-3.

[26] M. Van, P. Franciosa, and D. Ceglarek, "Fault diagnosis and fault-tolerant control of uncertain robot manipulators using high-order sliding mode," Mathematical Problems in Engineering, vol. 2016, no. 1, 2016, Art. no. 7926280, https://doi.org/10.1155/2016/7926280.

[27] T. M. Duc, N. V. Hoa, and T. P. Dao, "Adaptive fuzzy fractional-order nonsingular terminal sliding mode control for a class of second-order nonlinear systems," Journal of Computational and Nonlinear Dynamics, vol. 13, no. 3, 2018, Art. no. 31004, https://doi.org/10.1115/1.4038642.

[28] Y. Li, Y. Q. Chen, and I. Podlubny, "Mittag–Leffler stability of fractional order nonlinear dynamic systems," Automatica, vol. 45, no. 8, pp. 1965-1969, 2009, https://doi.org/10.1016/j.automatica.2009.04.003.

[29] D. Cao and J. Fei, "Adaptive fractional fuzzy sliding mode control for three-phase active power filter," IEEE Access, vol. 4, pp. 6645-6651, 2016, https://doi.org/10.1109/ACCESS.2016.2586958.

[30] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, 1^st ed, Elsevie, 2006.

[31] G. Sun, L. Wu, Z. Kuang, Z. Ma, and J. Liu, "Practical tracking control of linear motor via fractional-order sliding mode," Automatica, vol. 94, pp. 221-235, 2018, https://doi.org/10.1016/j.automatica.2018.02.011.

[32] J. Fei and H. Wang, "Experimental investigation of recurrent neural network fractional-order sliding mode control of active power filter," IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 67, no. 11, pp. 2522-2526, 2019, https://doi.org/10.1109/TCSII.2019.2953223.

[33] C. Izaguirre‐Espinosa, A. J. Muñoz‐Vázquez, A. Sánchez‐Orta, V. Parra‐Vega, and P. Castillo, "Attitude control of quadrotors based on fractional sliding modes: Theory and experiments," IET Control Theory & Applications, vol. 10, no. 7, pp. 825-832, 2016, https://doi.org/10.1049/iet-cta.2015.1048.

[34] H. P. Ren, X. Wang, J. T. Fan, and O. Kaynak, "Fractional order sliding mode control of a pneumatic position servo system," Journal of the Franklin Institute, vol. 356, no. 12, pp. 6160-6174, 2019, https://doi.org/10.1016/j.jfranklin.2019.05.024.

[35] S. Li, H. Lu, J. Li, T. Zheng, and Y. He, "Fractional-order sliding mode controller based on ESO for a buck converter with mismatched disturbances: Design and experiments," IEEE Transactions on Industrial Electronics (Early Access), pp. 1-12, 2025, https://doi.org/10.1109/TIE.2024.3525110.