Designing an Adaptive Continuous Terminal Sliding Mode Controller for a Class of Nonlinear Systems in Presence of Perturbation

Authors

Department of Electrical and computer Engineering, Babol Noshirvani University of Technology, Babol, Iran

Abstract

In this paper, an adaptive continuous terminal sliding mode controller is proposed for a class of second-order time varying perturbed systems with unknown parameters. In the proposed method, the controller is a combination of  continuous terminal sliding mode control and adaptive control. The convergence of the proposed method is based on a continuously-differentiable, homogeneous and strict Lyapunov function, and the unknown parameter of the system is estimated by an adaptive law. Zero-error convergence  of the proposed method is attained with information about the output and its derivative; furthermore, in this method, perturbation is compensated and a continuous control signal is generated which reduces the chattering. The simulation results show proper performance of the proposed method.

Keywords


[1]      P. Skruch, “Feedback stabilization of a class of nonlinear second-order systems,” Nonlinear Dynamics, vol. 59, no. 4, pp. 681-693, 2010.
[2]      M. P. Aghababa, “Fractional modeling and control of a complex nonlinear energy supply‐demand system,” Complexity, vol. 20, no. 6, pp. 74-86, 2015.
[3]      M. Yue and X. Wei, “Dynamic balance and motion control for wheeled inverted pendulum vehicle via hierarchical sliding mode approach,” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 228, no. 6, pp. 351-358, 2014.
[4]      S. Mobayen and V. J. Majd, “Robust tracking control method based on composite nonlinear feedback technique for linear systems with time-varying uncertain parameters and disturbances,” Nonlinear Dynamics, vol. 70, no. 1, pp. 171-180, 2012.
[5]      D. Efimov, A. Polyakov, L. Fridman, W. Perruquetti and J. P. Richard, “Delayed sliding mode control,” Automatica, vol. 64, no. 1, pp. 37-43, 2016.
[6]      D. Rosas, J. Alvarez and E. Alvarez, “Robust synchronization of arrays of uncertain nonlinear second-order dynamical systems,” Nonlinear Dynamics, vol. 67, no. 4, pp. 2735-2746, 2012.
[7]      علیرضا  مدیر روستا و مهدی خدابنده، «طراحی یک روش کنترل مد لغزشی انتگرالی تطبیقی برای پایدارسازی زمان محدود و مقاوم پرنده چهارملخه» مجله مهندسی برق دانشگاه تبریز، جلد 46، شماره 1، صفحه 321- 332، بهار 1395.
[8]      S. Mobayen, “Design of LMI‐based global sliding mode controller for uncertain nonlinear systems with application to Genesio's chaotic system,” Complexity, vol. 21, no. 1, pp. 94-98, 2015.
[9]      S. Mobayen, “Design of a robust tracker and disturbance attenuator for uncertain systems with time delays,” Complexity, vol. 21, no. 1, pp. 340-348, 2015.
[10]      S. Mobayen, “Finite-time robust-tracking and model-following controller for uncertain dynamical systems,” Journal of Vibration and Control, vol. 22, no. 4, pp. 1117-1127, 2016.
[11]      یاشار شب‌بویی، امیر ریخته‌گری غیاثی و سهراب خان‌محمدی، «طراحی کنترل‌کننده تحمل‌پذیر خطای مد لغزشی ترمینال غیرتکین برای سیستم‌های غیرخطی بر مبنای فیلتر کالمن توسعه‌یافته تطبیقی» مجله مهندسی برق دانشگاه تبریز، جلد 46، شماره 4، صفحه 173-183، زمستان 1395.
[12]      L. Wang, Y. Sheng and X. Liu, “A novel adaptive high-order sliding mode control based on integral sliding mode,” International Journal of Control, Automation and Systems, vol. 12, no. 3, pp. 459-472, 2014.
[13]      S. Mobayen, V. J. Majd and M. Sojoodi, “An LMI-based composite nonlinear feedback terminal sliding-mode controller design for disturbed MIMO systems,” Mathematics and Computers in Simulation, vol. 85, no. 1,
pp. 1-10, 2012.
[14]      S. Mobayen, “An LMI-based robust controller design using global nonlinear sliding surfaces and application to chaotic systems,” Nonlinear Dynamics, vol. 79, no. 2, pp. 1075-1084, 2015.
[15]      S. Kamal, J. A. Moreno, A. Chalanga, B. Bandyopadhyay and L. M. Fridman, “Continuous terminal sliding-mode controller,” Automatica, vol. 69, no. 1, pp. 308-314, 2016.
[16]      G. Bartolini, A. Ferrara and E. Usani, “Chattering avoidance by second-order sliding mode control,” IEEE Transactions on Automatic Control, vol. 43, no. 2, pp. 241-246, 1998.
[17]      L. Fridman, Sliding Mode Enforcement after 1990: Main Results and Some Open Problems, Springer Berlin Heidelberg, 2011.
[18]      A. Levant, “Principles of 2-sliding mode design,” Automatica, vol. 43, no. 4, pp. 576–586, 2007.
[19]      A. Polyakov and A. Poznyak, “Unified Lyapunov function for a finite–time stability analysis of relay second–order sliding mode control systems,” IMA Journal of Mathematical Control and Information, vol. 29, no. 4, pp. 529–550, 2012.
[20]      T. Sanchez and J. A. Moreno, “Lyapunov functions for twisting and terminal controllers,” In: Proceedings of the 13th International Workshop on Variable Structure Systems Nantes, pp. 1-6, 2014.
[21]      A. Levant, “Sliding order and sliding accuracy in sliding mode control,” International Journal of Control, vol. 58, no. 6, pp. 1247-1263, 1993.
[22]      A. Levant, “Quasi-continuous high-order sliding-mode controllers,” IEEE Transactions on Automatic Control, vol. 50, no. 11, pp. 1812-1816, 2005.
[23]      M. V. Basin and P. C. R. Ramírez, “A supertwisting algorithm for systems of dimension more than one,” IEEE Transactions on Industrial Electronics, vol. 61, no. 11, pp. 6472-6480, 2014.
[24]      C. Edwards and Y. B. Shtessel, “Continuous higher order sliding mode control based on adaptive disturbance compensation,” In Variable Structure Systems (VSS), 13th International Workshop on, pp. 1-5, 2014.
[25]      A. Levant, “Homogeneity approach to high-order sliding mode design,” Automatica, vol. 41, no. 5, pp. 823-830, 2005.
[26]      S.P. Bhat, D. S. Bernstein, Inequalities, London: Cambridge Unversity Press, 1951.
[27]      E. J. McShane and T. A. Botts, Real Analysis, vanNostrand. Princeton, NJ, 1959.
[28]      S. P. Bhat and D. S. Bernstein, “Geometric homogeneity with applications to finite-time stability,” Mathematics of Control, Signals, and Systems (MCSS), vol. 17, no. 2, pp. 101-127, 2005.
[29]      Y. John, Y, G. Weibing and J. C. Hung, “Variable Structure Control: A Survey,” IEEE Transaction on industrial electronics, vol.50, no. 1, pp.2-22, 2003.