Skip to main content
Log in

Second-Order Sliding Mode Control with PI Sliding Surface and Experimental Application to an Electromechanical Plant

  • Research Article - Electrical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

In this article, a second-order sliding mode control (2-SMC) is proposed for second-order uncertain plants using equivalent control approach to improve performance of control systems. A Proportional+Integral (PI) sliding surface is defined for the sliding mode. The sliding mode control law is derived using direct Lyapunov stability approach and asymptotic stability is proved theoretically. The second-order plant parameters are experimentally determined using input-output measured data. Performance of the closed-loop system is analysed through an experimental application to an electromechanical plant to show feasibility and effectiveness of the proposed 2-SMC and factors involved in the design. Results of the experimental application are presented to make a quantitative comparison with the traditional (first-order) sliding mode control and PID control. It is demonstrated that the proposed 2-SMC system improves performance of the closed-loop system with better tracking specifications in the case of external disturbances, better behavior of the output and faster convergence of the sliding surface while maintaining the stability.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ferrara A., Vecchico C.: Second order sliding mode control of vehicles with distributed collision avoidance capabilities. Mechatronics 19, 471–477 (2009)

    Article  Google Scholar 

  2. Biswas P.P., Srivastava R., Ray S., Samanta N.N.: Sliding mode control of quadruple tank process. Mechatronics 19, 548–561 (2009)

    Article  Google Scholar 

  3. Capisani L.M., Ferrara A., Magnani L.: Design and experimental validation of second-order sliding-mode motion controller for robot manipulators. Int. J. Control 82, 365–377 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cavallo A., Natale C.: High-order sliding control of mechanical systems: theory and experiments. Control Eng. Pract. 12, 1139–1149 (2004)

    Article  Google Scholar 

  5. Slotine J.J., Li W.: Applied Nonlinear Control. Prentice Hall, Englewood Cliffs (1991)

    MATH  Google Scholar 

  6. Bartolini G., Pisano A., Punta E., Usai E.: A survey of applications of second-order sliding mode control to mechanical systems. Int. J. Control 76, 875–892 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Mihoub M., Nouri A.S., Abdennour R.R.: Real-time application of discrete second order sliding mode control to a chemical reactor. Control Eng. Pract. 17, 1089–1095 (2009)

    Article  Google Scholar 

  8. Oaiser S., Bhatti A.I., Iqbal M., Samar R., Qadir J.: Estimation of precursor concentration in a research reactor by using second order sliding mode observer. Nuclear Eng. Design 239, 2134–2140 (2009)

    Article  Google Scholar 

  9. Ferrara A., Magnani L.: Motion control of rigid robot manipulators via first and second order sliding modes. J. Intell. Robot. Syst. 48, 23–36 (2007)

    Article  Google Scholar 

  10. Eker İ., Akınal Ş.A.: Sliding mode control with integral augmented sliding surface: design and experimental application to an electromechanical system. Electr. Eng. 90, 189–197 (2008)

    Article  Google Scholar 

  11. Boiko I., Fridman L., Iriarte R., Pisano A., Usai E.: Parameter tuning of second-order sliding mode controllers for linear plants with dynamic actuators. Automatica 42, 833–839 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Janardhanan, S.: Relay-free second order sliding mode control. In: Proceedings of IEEE International Conference on Industrial Technology (ICIT 2006), Mumbai, India, pp. 2206–2210 (2006)

  13. Kaya İ.: Sliding mode control of stable processes. Ind. Eng. Chem. Res. 46, 571–578 (2007)

    Article  Google Scholar 

  14. Alfaro-Cid E., McGookin E.W., Murray-Smith D.J., Fossen T.I.: Genetic algorithms optimization of decoupled sliding mode controllers: simulated and real results. Control Eng. Pract. 13, 739–748 (2005)

    Article  Google Scholar 

  15. Levant A.: Sliding order and sliding accuracy in sliding mode control. Int. J. Control 58, 1247–1263 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  16. Ferrara A., Rubagotti M.A.: Sub-optimal second order sliding mode controller for systems with saturating actuators. IEEE Trans. Autom. Control 54, 1082–1087 (2009)

    Article  MathSciNet  Google Scholar 

  17. Defoort M., Floquet T., Kokosyd A., Perruquetti W.: A novel higher order sliding mode control scheme. Syst. Control Lett. 58, 102–108 (2009)

    Article  MATH  Google Scholar 

  18. Almutairi N.B., Zribi M.: Sliding mode control of coupled tanks. Mechatronics 16, 427–441 (2006)

    Article  Google Scholar 

  19. Bartolini G., Farrara A., Usai E.: Applications of sub-optimal discontinuous control algorithm for uncertain second order systems. Int. J. Robust Nonlinear Control 7, 299–319 (1997)

    Article  MATH  Google Scholar 

  20. Shtessel Y.B., Shkolnikov I.A., Brown M.D.J.: An asymptotic second-order smooth sliding mode control. Asian J. Control 5, 498–504 (2003)

    Article  Google Scholar 

  21. Davila J., Fridman L., Levant A.: Second-order sliding mode observer for mechanical systems. IEEE Trans. Autom. Control 50, 1785–1789 (2005)

    Article  MathSciNet  Google Scholar 

  22. Khan M.K., Spurgeon S.K.: Robust MIMO water level control in interconnected twin-tanks using second order sliding mode control. Control Eng. Pract. 14, 375–386 (2006)

    Article  Google Scholar 

  23. Nollet F., Floquet T., Perruquetti W.: Observer-based second order sliding mode control laws for stepper motors. Control Eng. Pract. 16, 429–443 (2008)

    Article  Google Scholar 

  24. Bartolini G., Pisano A., Usai E.: On the second-order sliding mode control of nonlinear systems with uncertain control direction. Automatica 45, 2982–2985 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Perruquetti, W.; Barbot, J.P.: Sliding mode control in engineering. In: Automation and Control Series. Higher Order Sliding Modes, chap. 3, Routledge, New York (2002)

  26. Jimenez, S.; Jouvencel, T.: Using a high order sliding modes for diving control a torpedo autonomous underwater vehicle. In: Proceedings of Ocean 2003, OCEANS 2003 MTS/IEEE Conference, 22–26 Sept., San Diego, California, vol. 2, pp. 934–939 (2003)

  27. Eker İ.: Experimental on-line identification of an electromechanical system. ISA Trans. 43, 13–22 (2004)

    Article  Google Scholar 

  28. Damiano A., Gatto G.L., Morungiu I., Pisano A.: Second-order sliding mode control of DC drives. IEEE Trans. Ind. Electron. 51, 354–373 (2004)

    Article  Google Scholar 

  29. Bartolini, G.; Orani, N.; Pisano, A.; Usai, E.: Higher-order sliding mode approaches for control and estimation in electrical drives. Advances in Variable Structure, 2006, pp. 423–445 (2006)

  30. Utkin V.I.: Sliding Modes in Optimization and Control Problems. Springer, New York (1992)

    Book  Google Scholar 

  31. Hung L.C., Chung H.Y.: Decoupled control using neural network-based sliding-mode controller for nonlinear systems. Exp. Syst. Appl. Int. J. 32, 1168–1182 (2007)

    Article  Google Scholar 

  32. Yorgancıoğlu F., Kömürcügil H.: Single-input fuzzy-like moving sliding surface approach to the sliding mode control. Electr. Eng. 90, 199–207 (2008)

    Article  Google Scholar 

  33. Shtessel Y.B., Kaveh P., Ashrafi A.: Harmonic oscillator utilizing double-fold integral, traditional and second-order sliding mode control. J. Franklin Inst. 346, 872–888 (2009)

    Article  MathSciNet  Google Scholar 

  34. Lin F.J., Wai R.J., Kuo R.H., Liu D.C.: A comparative study of sliding mode and model reference adaptive observers for induction motor drive. Electr. Power Syst. Res. 44, 163–174 (1998)

    Article  Google Scholar 

  35. Su J.P., Chen T.M., Wang C.C.: Adaptive fuzzy sliding mode control with GA-based reaching laws. Fuzzy Sets Syst. 120, 145–158 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  36. Ha Q.P., Nguyen Q.H., Rye D.C., Whyte H.F.D.: Fuzzy sliding mode controllers with applications. IEEE Trans. Ind. Electron. 30, 2–21 (2001)

    Google Scholar 

  37. Eva P.E.: The MATLAB Handbook. Addison-Wesley, Harlow (1996)

    MATH  Google Scholar 

  38. Eker İ.: Second-order sliding mode control with experimental application. ISA Trans. 49, 394–405 (2010)

    Article  Google Scholar 

  39. Jang J.O., Jeon G.J.: A parallel neuro-controller for DC motors containing nonlinear friction. Neurocomputing 30, 233–248 (2000)

    Article  Google Scholar 

  40. Seborg D.E., Edgar T.F., Mellichamp D.A.: Process Dynamics and Control. Wiley, New York (1989)

    Google Scholar 

  41. Chen C.T., Peng S.T.: Design of a sliding mode control system for chemical processes. J. Process Control 15, 515–530 (2006)

    Article  MathSciNet  Google Scholar 

  42. Hsiao M.Y., Li T.H.S., Lee J.Z., Chao C.H., Tsai S.H.: Design of interval type-2 fuzzy sliding-mode controller. Inf. Sci. 178, 1696–1716 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  43. Roopaei M., Jahromi M.Z., John R., Lin T.C.: Unknown nonlinear chaotic gyros synchronization using adaptive fuzzy sliding mode control with unknown dead-zone input. Commun. Nonlinear Sci. Numer. Simul. 15, 2536–2545 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to İlyas Eker.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eker, İ. Second-Order Sliding Mode Control with PI Sliding Surface and Experimental Application to an Electromechanical Plant. Arab J Sci Eng 37, 1969–1986 (2012). https://doi.org/10.1007/s13369-012-0290-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-012-0290-6

Keywords

Navigation