International Journal of Nonlinear Analysis and Applications

A newly proposed super-twisting backstepping sliding mode controller

Document Type : Research Paper

Authors

Department of Electrical Engineering, Mashhad branch, Islamic Azad University, Mashhad, Iran

Abstract

The chattering phenomenon has been one of the most important controlling challenges in recent years, and efforts have been made to eliminate or control this phenomenon effectively, with various control strategies. In this article, a new super-twisting back-stepping sliding mode controller is proposed and to validate the performance of this controller, the outcomes of some well-known techniques are compared, in two aspects reducing tracking error and removing the chattering phenomenon. Also, a comparative analysis between control methods such as sliding mode,  feedback linearization and back-stepping control has been done in the sense of stability and convergence. The model discussed in this article is a non-linear, highly unstable system of the inverted pendulum. The results of applying the proposed controller on an inverted pendulum are compared in terms of the tracking speed, convergence time, error and chattering reduction. In addition, the stability analysis of the closed-loop system is presented according to the Lyapunov theorem. The results clearly show the efficiency of the proposed method not only in terms of stability and convergence improvement but also in reducing unwanted chattering.

Keywords

[1] R. Abedzadeh Maafi, S. Etemadi Haghighi, and M.J. Mahmoodabadi, Pareto optimal design of a fuzzy adaptive hierarchical sliding-mode controller for an XZ inverted pendulum system, IETE J. Res. 69 (2021), no. 5, 3052–3069.
[2] R. Afifa, S. Ali, M. Pervaiz, and J. Iqbal, Adaptive backstepping integral sliding mode control of a mimo separately excited DC motor, Robotics 12 (2023), no. 4, 1–16.
[3] W. Alam, A. Mehmood, Kh. Ali, U. Javaid, S. Alharbi, and J. Iqbal, Nonlinear control of a flexible joint robotic manipulator with experimental validation, J. Mech. Engin. 64 (2018), no. 1, 47–55.
[4] Kh.A. Alattas, O. Mofid, A.K. Alanazi, H.M. Abo-Dief, A. Bartoszewicz, M. Bakouri, and S. Mobayen, Barrier function adaptive nonsingular terminal sliding mode control approach for quad-rotor unmanned aerial vehicles, Sensors 72 (2022), no. 3, 1–20.
[5] S. Ali, A. Prado, and M. Pervaiz, Hybrid backstepping-super twisting algorithm for robust speed control of a three-phase induction motor, Electronics 12 (2023), no. 3.
[6] K. Ali, L. Khan, Q. Khan, Sh. Ullah, S. Ahmad, S. Mumtaz, F. Karam, and Naghmash, Robust integral backstepping based nonlinear MPPT control for a PV system, Energies 12 (2019), no. 16.
[7] D.J. Almakhles, Robust backstepping sliding mode control for a quadrotor trajectory tracking application, IEEE Access 8 (2020), 5515–5525.
[8] M. Andalib Sahnehsaraei and M.J. Mahmoodabadi, Approximate feedback linearization based optimal robust control for an inverted pendulum system with time-varying uncertainties, Int. J. Dyn. Control 9 (2021), 160–172.
[9] J. Ansari, M. Homayounzade, and A. Abbasi, Load frequency control in power systems by a robust backstepping sliding mode controller design, Energy Rep. 10 (2023), 1287–1298.
[10] G.R. Ansarifar and H.R. Akhavan, Sliding mode control design for a PWR nuclear reactor using sliding mode observer during load following operation, Ann. Nuclear Energy 75 (2015), 611–619.
[11] S. Coskun, Non-linear control of inverted pendulum, J. Faculty Engin. Architect. 35 (2020), 27–38.
[12] Y. Dong, G. Zhang, G. He, and W. Si, A novel control strategy for uninterruptible power supply based on backstepping and fuzzy neural network, IEEE Access 11 (2023), 5306–5313.
[13] H. Eddine Glida, L. Abdou, A. Chelihi, Ch. Sentouh, and S. Hasseni, Optimal model-free backstepping control for a quadrotor helicopter, Nonlinear Dyn. 100 (2020), 3449–3468.
[14] S. Hassan, B. Abdelmajid, Z. Mourad, S. Aicha, and B. Abdennaceur, PSO-backstepping controller of a grid connected DFIG based wind turbine, Int. J. Electric. Comput. Engin. 10 (2020), no. 1, 856–867.
[15] J. Hu, H. Zhang, H. Liu, and X. Yu, A survey on sliding mode control for networked control systems, Int. J. Syst. Sci. 52 (2021), no. 6, 1129–1147.
[16] J. Huang, T. Zhang, Y. Fan, and J.Q. Sun, Control of rotary inverted pendulum using model-free backstepping technique, IEEE Access 7 (2019), 96965–96973.
[17] S. Irfan, A. Mehmood, M. Tayyab Razzaq, and J. Iqbal, Advanced sliding mode control techniques for inverted pendulum: Modelling and simulation, Engin. Sci. Technol. Int. J. 72 (2018), no. 4, 753–759.
[18] O. Jedda, J. Ghabi, and A. Douik, Sliding mode control of an inverted pendulum, Chapter 6, Research Gate, 2017.
[19] A.A. Kabanov, Feedback linearization of nonlinear singularly perturbed Systems with state-dependent coefficients, Int. J. Control Autom. Syst. 18 (2020), 1743–1750.
[20] K. Kayisli and R.Z. Caglayan, Twisting sliding mode control based maximum power point tracking, Balkan J. Electric. Comput. Engin. 10 (2022), no. 4, 356–362.
[21] Y. Lan and F. Minrui, Design of state-feedback controller by pole placement for a coupled set of inverted pendulums, Tenth Int. Conf. Electronic Measure. Instruments, IEEE, 2011, pp. 68–72.
[22] Sh. Li, M. Zhou, and X. Yu, Design and implementation of terminal sliding mode control method for PMSM speed regulation system, IEEE Trans. Ind. Inf. 9 (2011), no. 4, 1879–1891.
[23] Y. Liang, D. Zhang, G. Li, and T. Wu, Adaptive chattering-free PID sliding mode control for tracking problem of uncertain dynamical systems, Electronics 11 (2022), no. 21, 1–18.
[24] X. Liu, X. Xu, Z. Zhu, and Y. Jiang, Dual-arm coordinated control strategy based on modified sliding mode impedance controller, Sensors 21 (2021), no. 14, 2–22.
[25] W. Liu, H. Ye, and X. Yang, Super-twisting sliding mode control for the trajectory tracking of underactuated USVs with disturbances, J. Marine Sci. Engin. 11 (2023), no. 3, 1–15.
[26] Zh. Ma and Q. Yu, Control strategy for boost converter based on adaptive integral terminal sliding-mode control, J. Phys.: Conf. Ser. 2378 (2022), 1–7.
[27] M.J. Mahmoodabadi and M. Andalib Sahnehsaraei, Parametric uncertainty handling of underactuated nonlinear systems using an online optimal input-output feedback linearization controller, Syst. Sci. Control Engin. 9 (2021), no. 1, 209–218.
[28] M.S. Mahmoud, Radhwan A.A. Saleh, and A. Maarif, Stabilizing of inverted pendulum system using Robust sliding mode control, Int. J. Robot. Control Syst. 2 (2022), no. 2, 230–239.
[29] B. Majout, B. Bossoufi, M. Bouderbala, M. Masud, J.F. Al-Amri, M. Taoussi, M. El Mahfoud, S. Motahhir, and M. Karim, Improvement of PMSG-based wind energy conversion system using developed sliding mode control, Energies 15 (2022), no. 5, 1–17.
[30] S. Mobayen, Adaptive global sliding mode control of underactuated systems using a super-twisting scheme: An experimental study, J. Vib. Control 25 (2019), no. 16, 1-19.
[31] S. Mobayen, A. Fekih, S. Vaidyanathan, and A. Sambas, Chameleon chaotic systems with quadratic nonlinearities: An adaptive finite-time sliding mode control approach and circuit simulation, IEEE Access 9 (2021), 64558–64573.
[32] S. Mobayen, F. Tchier, and L. Ragoub, Design of an adaptive tracker for n-link rigid robotic manipulators based on super-twisting global nonlinear sliding mode control, Int. J. Syst. Sci. 48 (2017), no. 9, 1990–2002.
[33] A. Nagarajan and A.A. Victoire, Optimization reinforced PID-sliding mode controller for rotary inverted pendulum, IEEE Access 11 (2023), 24420–24430.
[34] B.B. Naik and A.J. Mehta, Sliding mode controller with modified sliding function fo rDC-DC Buck converter, ISA Trans. 20 (2017), 279–287.
[35] P. Nam Dao and Y. Chen Liu, Adaptive reinforcement learning strategy with sliding mode control for unknown and disturbed wheeled inverted pendulum, Int. J. Control Automat. Syst. 19 (2021), 1139–1150.
[36] N.P. Nguyen, H. Oh, Y. Kim, J. Moon, J. Yang, and W. Chen, Fuzzy-based super-twisting sliding mode stabilization control for under-actuated rotary inverted pendulum systems, IEEE Access 8 (2020), 185079–185092.
[37] A. Norouzi, M. Masoumi, A. Barari, and S. F. Sani, Lateral control of an autonomous vehicle using integrated backstepping and sliding mode controller, Proc. Inst. Mech. Engin. Part K: J. Multi-body Dyn. 233 (2019), no. 1, 141–151.
[38] A.K. Patra, S.S. Biswal, and P. Kumar Rout, Backstepping linear quadratic Gaussian controller design for balancing an inverted pendulum, IETE J. Res. 68 (2019), no. 1, 150–164.
[39] B. Qiu, G. Wang, Y. Fan, D. Mu, and X. Sun, Adaptive sliding mode trajectory tracking control for unmanned surface vehicle with modeling uncertainties and input saturation, Appl. Sci. 9 (2019), no. 6, 1–18.
[40] Z. Qiu and S. Zhang, Fuzzy fast terminal sliding mode vibration control of a two-connected flexible plate using laser sensors, J. Sound Vibr. 380 (2016), 51-77.
[41] R. Saravanakumar and D. Jena, Validation of an integral sliding mode control for optimal control of a three blade variable speed variable pitch wind turbine, Electric. Power Energy Syst. 69 (2015), 421–429.
[42] Ch. Song, Sh. Fei, J. Cao, and Ch. Huang, Robust synchronization of fractional-order uncertain chaotic systems based on output feedback sliding mode control, Mathematics 7 (2019), no. 7, 2–10.
[43] L. Yu, J. Huang, W. Luo, Sh. Chang, H. Sun, and H. Tian, Sliding-mode control for PMLSM position control, Actuators 12 (2023), no. 1, 1–23.
[44] F.M. Zaihidee, S. Mekhilef, and M. Mubin, Robust speed control of PMSM using sliding mode control (SMC)-A review, Energies 12 (2019), no. 9, 1–27.
[45] A.R. Zare and M. Ahmadizadeh, Modified sliding mode design of passive viscous fluid control systems for nonlinear structures, Engin. Struct. 162 (2018), 245–256.
[46] S. Zeghlache, M.Z. Ghellab, A. Djerioui, B. Bouderah, and M.F. Benkhoris, Adaptive fuzzy fast terminal sliding mode control for inverted pendulum-cart system with actuator faults, Math. Comput. Simul. 210 (2023), 207–234.
[47] M. Zhang, J. Huang, and Y. Cao, Adaptive super-twisting control for mobile wheeled inverted pendulum systems, Appl. Sci. 9 (2019), no. 12.
[48] J. Zhang, N. Zhang, G. Shen, and Y. Xia, Analysis and design of chattering-free discrete-time sliding mode control, Int. J. Robust Nonlinear Control 29 (2019), no. 18, 6572–6581.
[49] M. Zhihong and X. Huo Yu, Terminal sliding mode control of MIMO linear systems, IEEE Trans. Circ. Syst. 44 (1997), no. 11, 1065–1070.
International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 4
April 2025
Pages 295-309
  • Receive Date: 19 June 2023
  • Revise Date: 31 October 2023
  • Accept Date: 09 November 2023