Design of an adaptive fixed-time control for a class of second-order nonlinear systems using sliding mode control

Document Type : Original Article

Authors

Department of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran,

Abstract

This paper addresses the problem of fixed-time control for a class of second-order nonlinear systems in the presence of model uncertainty and external disturbance. By introducing a novel form of non-singular terminal sliding mode control, a fixed-time control is designed to obtain acceptable performance, rapid convergence of the system states, high robustness and singularity elimination. Guaranteeing fixed-time convergence is a significant feature of the proposed control law under which the convergence time of the proposed surface is independent of the initial conditions. Since the upper bound of the system uncertainty and disturbance is quite difficult to obtain, an adaptive mechanism is presented under which there is no need to know this upper bound. Lyapunov analysis proves that the system states converge to small neighborhood of the origin within a fixed time. To assess efficiency of the suggested method, a flexible spacecraft attitude control system is considered and a fixed-time attitude control system is derived. Simulation results verify the effectiveness and performance of the presented approach.

Keywords


[1]     S. Mobayen, “Fast terminal sliding mode controller design for nonlinear second‐order systems with time-varying uncertainties,” Complexity, vol. 21, no. 2, pp. 239-244, 2015.
[2]     A. Galicki, “Finite-time trajectory tracking control in a task space of robotic manipulators,” Automatica, vol. 67, pp. 165-170, 2016.
[3]     M. Golestani, I. Mohammadzaman, MJ Yazdanpanah, “Robust finite-time stabilization of uncertain nonlinear systems based on partial stability,” Nonlinear Dynamics, vol. 85, no. 1, pp. 87-96, 2016.
[4]     B. Xiao, S. Yin and O. Kaynak, “Attitude Stabilization Control of Flexible Satellites with High Accuracy: An Estimator-based Approach,” IEEE/ASME Transactions on Mechatronics, vol. 22, no. 1, pp. 349-358, 2017.
[5]     C. Zhong, Z. Chen and Y. Guo, “Attitude control for flexible spacecraft with disturbance rejection,’ IEEE Transactions on Aerospace and Electronic Systems, vol. 53, no. 1, pp. 101-110, 2017.
[6]     Z. Yu, Y. Guo, L. Wang and L. Wu, “Adaptive robust attitude control and active vibration suppression of flexible spacecraft,” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 231, no. 6, pp. 1076-1087, 2017.
[7]     S. Ding and WX. Zheng, “Nonsmooth attitude stabilization of a flexible spacecraft,” IEEE Transactions on Aerospace and Electronic Systems, vol. 50, no. 2, pp. 1163-1181, 2014.
[8]     SM. Smaeilzadeh and M. Golestani, “A finite-time adaptive robust control for a spacecraft attitude control considering actuator fault and saturation with reduced steady-state error,” Transactions of the Institute of Measurement and Control, vol. 41, no. 4, pp. 1002-1009, 2018.
[9]     M. Mirshams and M. Khosrojerdi, “Attitude control of an underactuated spacecraft using tube-based MPC approach,” Aerospace Science and Technology, vol. 48, pp. 140-145, 2016.
[10]  فاطمه پیروزمند، نعمت ا... قهرمانی و محمدرضا عاروان، «طراحی کنترل‌کننده پیش‌بین مقاوم با استفاده از نامساوی‌های ماتریسی خطی برای سیستم کنترل وضعیت ماهواره»، مجله مهندسی برق دانشگاه تبریز، دوره 44، شماره 4، صفحه 9-21، 1393.
[11]  SW. Liu and T. Singh, “Robust time-optimal control of flexible structures with parametric uncertainty,” Journal of Dynamic Systems, Measurement, and Control, vol. 119, no. 4, pp. 743–738, 1997.
[12]  Q Shen, D Wang, S Zhu and EK Poh, “Integral-Type Sliding Mode Fault-Tolerant Control for Attitude Stabilization of Spacecraft." IEEE Transactions on Control Systems Technology, vol. 23, no. 3, pp. 1131-1138, 2015.
[13]  VI. Utkin, “Sliding modes in control optimization” In Springer Verlag. Berlin, 1997.
[14]  یاشار شب‌بویی، امیر ریخته‌گر غیاثی و سهراب خان‌محمدی، «طراحی کنترل‌کننده تحمل‌پذیر خطای مد لغزشی ترمینال غیرتکین برای سیستم‌های غیرخطی بر مبنای فیلتر کالمن توسعه یافته تطبیقی»، مجله مهندسی برق دانشگاه تبریز، دوره 46، شماره 4، صفحه 173-183، 1395.
[15]  Z. Man and X. Yu, “Terminal sliding mode control design of mimo linear systems,” IEEE Transactions on Circuits and Systems, vol. 44, no. 11, pp. 823–830, 1997.
[16]  S Yu, X Yu, B Shirinzadeh and Z Man, “Continuous finite-time control for robotic manipulators with terminal sliding mode,” Automatica, vol. 41, no. 11, pp. 1957-1964, 2005.
[17]  L. Yang and J. Yang, “Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems,” International Journal of Robust and Nonlinear Control, vol. 21, no. 16, pp.1865-1879, 2011.
[18]  S. Wu, G. Radice and Z. Sun, “Robust finite-time control for flexible spacecraft attitude maneuver,” Journal of Aerospace Engineering, vol. 27, no. 2, pp. 185–190, 2012.
[19]  C. Pukdeboon, “Nonsingular terminal sliding mode based finite-time control for spacecraft attitude tracking,” International Journal of Control, Automation, and Systems, vol. 12, no. 3, pp. 530–540, 2014.
[20]  K. Lu and Y. Xia, “Adaptive attitude tracking control for rigid spacecraft with finite-time convergence,” Automatica, vol. 49, no. 12, pp. 3591-3599, 2013.
[21]  A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems,” IEEE Transactions on Automatic Control, vol. 57, no. 8, pp. 2106-2110, 2012.
[22]  Z. Zuo, “Nonsingular fixed-time consensus tracking for second-order multi-agent networks,” Automatica, vol. 54, pp. 305–309, 2015.
[23]  Y. Huang and Y. Jia, “Robust adaptive fixed-time tracking control of 6-DOF spacecraft fly-around mission for noncooperative target,” International Journal of Robust and Nonlinear Control, vol. 28, no 6, pp. 2598-2618, 2018.
[24]  K. Lu, Y. Xia, M. Fu and C. Yu, “Adaptive finite-time attitude stabilization for rigid spacecraft with actuator faults and saturation constraints,” International Journal of Robust and Nonlinear Control, vol. 26, no. 1, pp. 28-46, 2016.
[25]  B. Xiao, Q. Hu, Y. Zhang and X. Huo “Fault-tolerant tracking control of spacecraft with attitude-only measurement under actuator failures,” Journal of Guidance, Control and Dynamics, vol. 37, no. 3, pp. 838-849, 2014.
[26]  L. Wang, C. Zhong, Y. Guo and Y. Wu, “Robust adaptive attitude control for flexible spacecraft in the presence of SGCMG friction nonlinearity,” International Journal of Robust and Nonlinear Control, vol. 28, pp. 3324-3341, 2018.
[27]  C. Zhong, L. Wu, J. Guo, Y. Guo and Z. Chen, “Robust adaptive attitude manoeuvre control with finite-time convergence for a flexible spacecraft,” Transactions of the Institute of Measurement and Control, vol. 40, no. 2, pp. 425-435, 2018.
[28]  SM. Smaeilzadeh and M. Golestani, “Finite-time fault-tolerant adaptive robust control for a class of uncertain non-linear systems with saturation constraints using integral backstepping approach,” IET Control Theory and Applications, vol. 12, no. 15, pp. 2109 – 2117, 2018.
[29]  C. Ton and C. Petersen, “Continuous Fixed-Time Sliding Mode Control for Spacecraft with Flexible Appendages.” IFAC-PapersOnLine, vol. 51, no. 12, pp. 1-5, 2018.