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A novel robust adaptive second-order sliding mode tracking control technique for uncertain dynamical systems with matched and unmatched disturbances

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Abstract

This paper investigates a robust adaptive second-order sliding mode control method for tracking problem of a class of uncertain linear systems with matched and unmatched disturbances. The fundamental idea of the suggested control method is that the discontinuous sign function is used for the time-derivative of the control signal and hence the smooth control input achieved after an integration process is continuous and removes the chattering problem. Using a PID sliding surface, the finite-time convergence of output tracking errors is obtained. The adaptive gain-tuning control law removes the necessity of gaining information about the upper bounds of the external disturbances. The control system is in the sliding mode and then, tracking errors converge to the origin in a finite time under the presence of the external disturbances. Simulation results on an uncertain numerical system and a turntable servo-system are presented to indicate the effectiveness and feasibility of the proposed scheme.

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References

  1. S. Mobayen, M. H. Asemani and V. J. Majd, “Transient performance improvement using composite nonlinear feedback and integral sliding surface for matched and unmatched uncertain MIMO linear systems,” Proc. of the 3rd International Conference on Control, Instrumentation, and Automation (ICCIA 2013), Tehran, Iran, pp. 83–88, 2013.

    Google Scholar 

  2. S. Mondal and C. Mahanta, “Chattering free adaptive multivariable sliding mode controller for systems with matched and mismatched uncertainty,” ISA Transactions, vol. 52, no. 3, pp. 335–341, 2013.

    Article  Google Scholar 

  3. S. Mobayen and D. Baleanu, “Linear matrix inequalities design approach for robust stabilization of uncertain nonlinear systems with perturbation based on optimally-tuned global sliding mode control,” Journal of Vibration and Control, 2015, doi: 10.1177/1077546315592516

  4. X. Liu and P. Stechlinski, “Hybrid control of impulsive systems with distributed delays,” Nonlinear Analysis: Hybrid Systems, vol. 11, pp. 57–70, 2014. [click]

    MathSciNet  MATH  Google Scholar 

  5. Z. M. Ge and C. H. Yang, “Chaos synchronization and chaotization of complex chaotic systems in series form by optimal control,” Chaos Solitons & Fractals, vol. 42, no. 2, pp. 994–1002, 2009. [click]

    Article  MATH  Google Scholar 

  6. S. Mobayen, “An adaptive chattering-free PID sliding mode control based on dynamic sliding manifolds for a class of uncertain nonlinear systems,” Nonlinear Dynamics, vol. 82, no. 1-2, pp. 53–60, 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  7. S. Mobayen and F. Tchier, “A new LMI-based robust finitetime sliding mode control strategy for a class of uncertain nonlinear systems,” Kybernetika, vol. 51, no. 6, pp. 1035–1048, 2015. [click]

    MathSciNet  MATH  Google Scholar 

  8. C. K. Ahn, “Receding horizon disturbance attenuation for Takagi–Sugeno fuzzy switched dynamic neural networks,” Information Sciences, vol. 280, pp. 53–63, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  9. S. Mobayen and S. Javadi, “Disturbance observer and finite-time tracker design of disturbed third-order nonholonomic systems using terminal sliding mode,” Journal of Vibration and Control, vol. 23, no. 2, pp. 181–189, 2017.

    Article  MathSciNet  Google Scholar 

  10. S. Mobayen, “A novel global sliding mode control based on exponential reaching law for a class of under-actuated systems with external disturbances,” Journal of Computational and Nonlinear Dynamics, vol. 11, no. 2, pp. 021011 (9 pages), 2015.

    Article  MathSciNet  Google Scholar 

  11. S. Mobayen, “An adaptive fast terminal sliding mode control combined with global sliding mode scheme for tracking control of uncertain nonlinear third-order systems,” Nonlinear Dynamics, vol. 82, no. 1, pp. 599–610, 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  12. F. Yorgancioglu and H. Komurcugil, “Decoupled slidingmode controller based on time-varying sliding surface for forth-order systems,” Expert Systems with Applications, vol. 37, no. 10, pp. 6764–6774, 2010. [click]

    Article  Google Scholar 

  13. S. Ganjefar, M. H. Sarajchi and S. M. Hoseini, “Teleoperation systems design using singular perturbation method and sliding mode controllers,” Journal of Dynamic Systems, Measurement, and Control, vol. 136, no. 5, pp. 051005–051005-8, 2014.

    Article  Google Scholar 

  14. 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, pp. 1–10, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  15. 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.

    Article  MathSciNet  MATH  Google Scholar 

  16. S. Mobayen, “Robust tracking controller for multivariable delayed systems with input saturation via composite nonlinear feedback,” Nonlinear Dynamics, vol. 76, no. 1, pp. 827–838, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  17. S. Mondal and C. Mahanta, “A fast converging robust controller using adaptive second order sliding mode,” ISA Transactions, vol. 51, no. 6, pp. 713–721, 2012.

    Article  Google Scholar 

  18. S. Mobayen, “Design of CNF-based nonlinear integral sliding surface for matched uncertain linear systems with multiple state-delays,” Nonlinear Dynamics, vol. 77, no. 3, pp. 1047–1054, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  19. 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. [click]

    Article  MathSciNet  Google Scholar 

  20. D. Efimov and L. Fridman, “Global sliding-mode observer with adjusted gains for locally Lipschitz systems,” Automatica, vol. 47, no. 3, pp. 565–570, 2011. [click]

    Article  MathSciNet  MATH  Google Scholar 

  21. S. Mobayen, D. Baleanu, and F. Tchier, “Second-order fast terminal sliding mode control design based on LMI for a class of non-linear uncertain systems and its application to chaotic systems,” Journal of Vibration and Control, 2016, doi: 10.1177/1077546315623887

    Google Scholar 

  22. M. K. Khan and S. K. Spurgeon, “Robust MIMO water level control in interconnected twin-tanks using second order sliding mode control,” Control Engineering Practice, vol. 14, no. 4, pp. 375–386, 2006. [click]

    Article  Google Scholar 

  23. H. Joe, M. Kim, and S. C. Yu, “Second-order sliding-mode controller for autonomous underwater vehicle in the presence of unknown disturbances,” Nonlinear Dynamics, vol. 78, no. 1, pp. 183–196, 2014.

    Article  Google Scholar 

  24. L. Lü, M. Yu, C. Li, S. Liu, B. Yan, H. Chang, J. Zhou, and Y. Liu, “Projective synchronization of a class of complex network based on high-order sliding mode control,” Nonlinear Dynamics, vol. 73, no. 1-2, pp. 411–416, 2013. [click]

    Article  MathSciNet  MATH  Google Scholar 

  25. 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.

    Article  MathSciNet  Google Scholar 

  26. L. Lü, M. Yu, and L. Luan, “Synchronization between uncertain chaotic systems with a diverse structure based on a second-order sliding mode control,” Nonlinear Dynamics, vol. 70, no. 3, pp. 1861–1865, 2012.

    Article  MathSciNet  Google Scholar 

  27. X. Li, X. Yu, and Q. L. Han, “Stability analysis of secondorder sliding mode control systems with input-delay using Poincaré map,” IEEE Trans. Automatic Control, vol. 58, no. 9, pp. 2410–2415, 2013.

    Article  MathSciNet  Google Scholar 

  28. A. Susperregui, M. I. Martinez, G. Tapia, and I. Vechiu, “Second-order sliding-mode controller design and tuning for grid synchronization and power control of a wind turbine-driven doubly fed induction generator,” IET Renewable Power Generation, vol.7, no. 5, pp. 540–551, 2013.

    Article  Google Scholar 

  29. J. L. Chang, “Dynamic compensator-based second-order sliding mode controller design for mechanical systems,” IET Control Theory & Applications, vol. 7, no. 13, pp. 1675–1682, 2013.

    Article  MathSciNet  Google Scholar 

  30. A. L. Shang and Z. Wang, “Adaptive backstepping second order sliding mode control of non-linear systems,” International Journal of Modeling, Identification and Control, vol. 19, no. 2, pp. 195–201, 2013.

    Article  MathSciNet  Google Scholar 

  31. I. Eker, “Second-order sliding mode control with experimental application,” ISA Transactions, vol. 49, no. 3, pp. 394–405, 2010. [click]

    Article  Google Scholar 

  32. M. Defoort and T. Murakami, “Second order sliding mode control with disturbance observer for bicycle stabilization,” Proc. of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2008), pp. 2822–2827, 2008.

    Google Scholar 

  33. L. Peng, P. Xuefeng, M. Jianjun, and T. Shuai, “Nonhomogeneous disturbance observer-based second order sliding mode control for a tailless aircraft,” Proc. Chinese Automation Congress (CAC), pp. 120–125, 2013.

    Google Scholar 

  34. A. Rosales and I. Boiko, “Disturbance attenuation for systems with second-order sliding modes via linear compensators,” IET Control Theory & Applications, vol. 9, no. 4, pp. 526–537, 2014.

    Article  MathSciNet  Google Scholar 

  35. S. P. Bhat and D. S. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM Journal on Control and Optimization, vol. 38, no. 3, pp. 751–766, 2000. [click]

    Article  MathSciNet  MATH  Google Scholar 

  36. W. Xiang and Y. Huangpu, “Second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 11, pp. 3241–3247, 2010. [click]

    Article  MathSciNet  MATH  Google Scholar 

  37. I. Eker, “Sliding mode control with PID sliding surface and experimental application to an electromechanical plant,” ISA Transactions, vol. 45, no. 1, pp. 109–118, 2006.

    Article  Google Scholar 

  38. W. J. Cao and J. X. Xu, “Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems,” IEEE Trans. Automatic Control, vol. 49, no. 8, pp. 1355–1360, 2004.

    Article  MathSciNet  Google Scholar 

  39. J. Wang and J. Zhao, “On improving transient performance in tracking control for switched systems with input saturation via composite nonlinear feedback,” International Journal of Robust and Nonlinear Control, vol. 26, no. 3, pp. 509–518, 2016.

    Article  MathSciNet  MATH  Google Scholar 

Download references

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Correspondence to Saleh Mobayen.

Additional information

Recommended by Associate Editor Sing Kiong Nguang under the direction of Editor PooGyeon Park. This research project was supported by a grant from the “Research Center of the Center for Female Scientific and Medical Colleges”, Deanship of Scientific Research, King Saud University.

Saleh Mobayen received his doctorate in Control Engineering from Tarbiat Modares University, Iran (2009-2012), and is currently an Assistant Professor of Control Engineering at University of Zanjan. He has published several papers in the national and international Journals. His research interests include sliding mode control, robust tracking, non-holonomic robots and chaotic systems.

Fairouz Tchier received her Ph.D. in Mathematics (Theoretical Computer Science) from Université Laval, Quebec City, Québec, Canada (1992-1996), and is currently an Associate Professor in Mathematics Department, King Saud University. Her research interests include theoretical computer science, software engineering, fixed point theory, formal methods and Fuzzy set theory.

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Mobayen, S., Tchier, F. A novel robust adaptive second-order sliding mode tracking control technique for uncertain dynamical systems with matched and unmatched disturbances. Int. J. Control Autom. Syst. 15, 1097–1106 (2017). https://doi.org/10.1007/s12555-015-0477-1

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