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Discussions on Smooth Modifications of Integral Sliding Mode Control

  • Yongping Pan
  • Young Hoon Joo
  • Haoyong Yu
Regular Paper Control Theory and Applications

Abstract

Sliding mode control (SMC) contains two phases, namely reaching and sliding phases, where the invariance of SMC is not guaranteed during the reaching phase. Integral SMC (ISMC) eliminates the reaching phase such that the invariance is guaranteed from the initial time instant. Several smoothing techniques have been applied to reduce chattering in the ISMC, including boundary layer, high-order SMC, low-pass filtering, etc. In this study, we discuss pros and cons of these techniques and suggest a simple and effective solution to attenuate chattering in the ISMC. In the suggested solution, the discontinuous part of the ISMC law is smoothed by a low-pass filter based on the equivalent control method. The resultant ISMC can not only avoid the trade-off among chattering, tracking accuracy, and robustness, but also act as a disturbance observer to exactly estimate and reject uncertainties. Numerical results have been provided to verify the arguments of this study.

Keywords

Continuous sliding mode control disturbance rejection integral sliding surface uncertainty estimation 

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References

  1. [1]
    Y. Shtessel, C. Edwards, L. Fridman, and A. Levant, Sliding Mode Control and Observation, Springer, New York, NY,USA, 2014.CrossRefGoogle Scholar
  2. [2]
    J. Y. Hung, W. Gao, and J. C. Hung, “Variable structure control: a survey,” IEEE Transactions on Industrial Electronics, vol. 40, no. 1, pp. 2–22, Feb. 1993. [click]CrossRefGoogle Scholar
  3. [3]
    V. Utkin and J. Shi, “Integral sliding mode in systems operating under uncertainty conditions,” Proceeding of IEEE Conference on Decision and Control, Kobe, Japan, pp. 4591–4596, 1996. [click]CrossRefGoogle Scholar
  4. [4]
    J. Shi, H. Liu, and N. Bajcinca, “Robust control of robotic manipulators based on integral sliding mode,” International Journal of Control, vol. 81, no. 10, pp. 1537–1548, 2008. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    V. Utkin, J. Guldner, and J. Shi, Sliding Mode Control in Electro-Mechanical Systems, 2nd ed., CRC Press, Boca Raton, FL, USA, 2009.CrossRefGoogle Scholar
  6. [6]
    J. Komsta, N. van Oijen, and P. Antoszkiewicz, “Integral sliding mode compensator for load pressure control of diecushion cylinder drive,” Control Engineering Practice, vol. 21, no. 5, pp. 708–718, May. 2013. [click]CrossRefGoogle Scholar
  7. [7]
    R. J. Liu and S. H. Li, “Optimal integral sliding mode control scheme based on pseudospectral method for robotic manipulators,” International Journal of Control, vol. 87, no. 6, pp. 1131–1140, Jun. 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Y. W. Liang, C. C. Chen, D. C. Liaw, Y. C. Feng, C. C. Cheng, and C. H. Chen, “Robust guidance law via integralsliding- mode scheme,” Journal of Guidance, Control and Dynamics, vol. 37, no. 3, pp. 1038–1041, May 2014.CrossRefGoogle Scholar
  9. [9]
    C. C. Chen, S. S. D. Xu, and Y. W. Liang, “Study of nonlinear integral sliding mode fault-tolerant control,” IEEEASME Transactions on Mechatronics, vol. 21, no. 2, pp. 1160–1168, Apr. 2016.CrossRefGoogle Scholar
  10. [10]
    J.-J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, NJ, USA, 1991.zbMATHGoogle Scholar
  11. [11]
    J. H. Lee and M. J. Youn, “A new improved continuous variable structure controller for accurately prescribed tracking control of BLDD servo motors,” Automatica, vol. 40, no. 12, pp. 2069–2074, Dec. 2004. [click]MathSciNetzbMATHGoogle Scholar
  12. [12]
    M. Asad, A. I. Bhatti, S. Iqbal, and Y. Asfia, “A smooth integral sliding mode controller and disturbance estimator design,” International Journal of Control, Automation and Systems, vol. 13, no. 6, pp. 1326–1336, Dec. 2015. [click]CrossRefGoogle Scholar
  13. [13]
    K. D. Young, V. I. Utkin, and U. Ozguner, “A control engineer’s guide to sliding mode control,” IEEE Transactions on Control Systems Technology, vol. 7, no. 3, pp. 328–342, May 1999. [click]CrossRefGoogle Scholar
  14. [14]
    S. Laghrouche, F. Plestan, and A. Glumineau, “Higher order sliding mode control based on integral sliding mode,” Automatica, vol. 43, no. 3, pp. 531–537, Mar. 2007.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Q. Zong, J. Zhang, and Z. S. Zhao, “Higher order sliding mode control with self-tuning law based on integral sliding mode,” IET Control Theory and Applications, vol. 4, no. 7, pp. 1282–1289, Jul. 2010.MathSciNetCrossRefGoogle Scholar
  16. [16]
    M. Furat and I. Eker, “Second-order integral sliding-mode control with experimental application,” ISA Transactions, vol. 53, no. 5, pp. 1661–9, Sep. 2014.CrossRefGoogle Scholar
  17. [17]
    M. Das and C. Mahanta, “Optimal second order sliding mode control for nonlinear uncertain systems,” ISA Transactions, vol. 53, no. 4, pp. 1191–1198, Jul. 2014. [click]CrossRefGoogle Scholar
  18. [18]
    L. Qi, S. Bao, and H. B. Shi, “Permanent-magnet synchronous motor velocity control based on second-order integral sliding mode control algorithm,” Transactions of the Institute of Measurement and Control, vol. 37, no. 7, pp. 875–882, Aug. 2015.CrossRefGoogle Scholar
  19. [19]
    A. Chalanga, S. Kamal, and B. Bandyopadhyay, “A new algorithm for continuous sliding mode control with implementation to industrial emulator setup,” IEEE-ASME Transactions on Mechatronics, vol. 20, no. 5, pp. 2194–2204, Oct. 2015. [click]CrossRefGoogle Scholar
  20. [20]
    A. Ferrara and G. P. Incremona, “Design of an integral suboptimal second-order sliding mode controller for the robust motion control of robot manipulators,” IEEE Transactions on Control Systems Technology, vol. 23, no. 6, pp. 2316–2325, Nov. 2015. [click]CrossRefGoogle Scholar
  21. [21]
    H. Rios, S. Kamal, L. M. Fridman, and A. Zolghadri, “Fault tolerant control allocation via continuous integral sliding-modes: A HOSM-observer approach,” Automatica, vol. 51, pp. 318–325, Jan. 2015. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    P. R. Kumar, A. Chalanga, and B. Bandyopadhyay, “Smooth integral sliding mode controller for the position control of Stewart platform,” ISA Transactions, vol. 58, pp. 543–551, Sep. 2015.CrossRefGoogle Scholar
  23. [23]
    P. M. Tiwari, S. Janardhanan, and M. un Nabi, “Rigid spacecraft attitude control using adaptive integral second order sliding mode,” Aerospace Science and Technology, vol. 42, pp. 50–57, 2015. [click]CrossRefGoogle Scholar
  24. [24]
    X. Y. Zhang, H. Y. Su, and R. Q. Lu, “Second-order integral sliding mode control for uncertain systems with control input time delay based on singular perturbation approach,” IEEE Transactions on Automatic Control, vol. 60, no. 11, pp. 3095–3100, Nov. 2015. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    M. Taleb, F. Plestan, and B. Bououlid, “An adaptive solution for robust control based on integral high-order sliding mode concept,” International Journal of Robust and Nonlinear Control, vol. 25, pp. 1201–1213, May 2015. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    V. Utkin, “Discussion aspects of high-order sliding mode control,” IEEE Transactions on Automatic Control, vol. 61, no. 3, pp. 829–833, Mar. 2016. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    I. Khan, A. I. Bhatti, A. Arshad, and Q. Khan, “Robustness and performance parameterization of smooth second order sliding mode control,” International Journal of Control, Automation and Systems, vol. 14, no. 3, pp. 681–690, Jun. 2016. [click]CrossRefGoogle Scholar
  28. [28]
    C. T. Heng, Z. Jamaludin, A. Y. B. Hashim, L. Abdullah, and N. A. Rafan, “Design of super twisting algorithm for chattering suppression in machine tools,” International Journal of Control, Automation and Systems, vol. 15, no. 3, pp. 1259–1266, Jun. 2017. [click]CrossRefGoogle Scholar
  29. [29]
    S. Mobayen and F. Tchier, “A novel robust adaptive second-order sliding mode tracking control technique for uncertain dynamical systems with matched and unmatched disturbances,” International Journal of Control, Automation and Systems, vol. 15, no. 3, pp. 1097–1106, Jun. 2017. [click]CrossRefGoogle Scholar
  30. [30]
    W. B. Gao and J. C. Hung, “Variable structure control of nonlinear systems: A new approach,” IEEE Transactions on Industrial Electronics, vol. 40, no. 1, pp. 45–55, Feb. 1993. [click]CrossRefGoogle Scholar
  31. [31]
    J. Yang, S. H. Li, and X. H. Yu, “Sliding-mode control for systems with mismatched uncertainties via a disturbance observer,” IEEE Transactions on Industrial Electronics, vol. 60, no. 1, pp. 160–169, Jan 2013. [click]CrossRefGoogle Scholar
  32. [32]
    J. Yang, S. H. Li, J. Y. Su, and X. H. Yu, “Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances,” Automatica, vol. 49, no. 7, pp. 2287–2291, Jul 2013. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    J. Yang, J. Y. Su, S. H. Li, and X. H. Yu, “High-order mismatched disturbance compensation for motion control systems via a continuous dynamic sliding-mode approach,” IEEE Transactions on Industrial Informatics, vol. 10, no. 1, pp. 604–614, Feb 2014. [click]CrossRefGoogle Scholar
  34. [34]
    Y. Pan and H. Yu, “Composite learning from adaptive dynamic surface control,” IEEE Transactions on Automatic Control, vol. 61, no. 9, pp. 2603–2609, Sep. 2016. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    Y. Pan, J. Zhang, and H. Yu, “Model reference composite learning control without persistency of excitation,” IET Control Theory and Applications, vol. 10, no. 16, pp. 1963–1971, Oct. 2016. [click]MathSciNetCrossRefGoogle Scholar
  36. [36]
    Y. Pan and H. Yu, “Biomimetic hybrid feedback feedforward neural-network learning control,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 6, pp. 1481–1487, Jun 2017. [click]CrossRefGoogle Scholar
  37. [37]
    C. K. Ahn, P. Shi, and M. V. Basin, “Two-dimensional dissipative control and filtering for roesser model,” IEEE Transactions on Automatic Control, vol. 60, no. 7, pp. 1745–1759, Jul. 2015. [click]MathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    C. K. Ahn, P. Shi, and M. V. Basin, “Deadbeat dissipative FIR filtering,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 63, no. 8, pp. 1210–1221, Aug. 2016. [click]MathSciNetCrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Biomedical EngineeringNational University of SingaporeSingaporeSingapore
  2. 2.Department of Control and Robotics EngineeringKunsan National UniversityKunsanKorea

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