Digital Sliding-Mode Control of Second-Order Systems

  • Qingsong XuEmail author
  • Kok Kiong Tan
Part of the Advances in Industrial Control book series (AIC)


This chapter presents the precision motion control of a piezoelectric bimorph actuator without using a hysteresis model and a state observer.


Tracking Error Convergence Condition State Observer Piezoelectric Actuator Output Displacement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Abidi, K., Xu, J.X., Yu, X.: On the discrete-time integral sliding mode control. IEEE Trans. Autom. Control 52(4), 709–715 (2007)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bandyopadhyay, B., Fulwani, D.: High-performance tracking controller for discrete plant using nonlinear sliding surface. IEEE Trans. Ind. Electron. 56(9), 3628–3637 (2009)CrossRefGoogle Scholar
  3. 3.
    Bibian, S., Jin, H.: Time delay compensation of digital control for DC switchmode power supplies using prediction techniques. IEEE Trans. Power Electron. 15(5), 835–842 (2000)CrossRefzbMATHGoogle Scholar
  4. 4.
    Chen, X., Hisayama, T.: Adaptive sliding-mode position control for piezo-actuated stage. IEEE Trans. Ind. Electron. 55(11), 3927–3934 (2008)CrossRefGoogle Scholar
  5. 5.
    Elmali, H., Olgac, N.: Implementation of sliding mode control with perturbation estimation (SMCPE). IEEE Trans. Control Syst. Technol. 4(1), 79–85 (1996)CrossRefzbMATHGoogle Scholar
  6. 6.
    Furuta, K.: Sliding mode control of a discrete system. Syst. Control Lett. 14(2), 145–152 (1990)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Galias, Z., Yu, X.: Euler’s discretization of single input sliding-mode control systems. IEEE Trans. Autom. Control 52(9), 1726–1730 (2007)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Huang, S., Tan, K.K., Lee, T.H.: Adaptive sliding-mode control of piezoelectric actuators. IEEE Trans. Ind. Electron. 56(9), 3514–3522 (2009)CrossRefGoogle Scholar
  9. 9.
    Mitic, D., Milojkovic, M., Antic, D.: Tracking system design based on digital minimum variance control with fuzzy sliding mode. In: Proceedings of the 8th International Conference on Telecommunications in Modern Satellite, Cable and Broadcasting Services (TELSIKS 2007), pp. 494–497. Nis, Serbia (2007)Google Scholar
  10. 10.
    Mitic, D., Milosavljevic, C.: Sliding mode-based minimum variance and generalized minimum variance controls with \({O(T^2)}\) and \({O(T^3)}\) accuracy. Electr. Eng. 86(4), 229–237 (2004)CrossRefGoogle Scholar
  11. 11.
    Monsees, G.: Discrete-time sliding mode control. Ph.D. thesis, Delft University of Technology (2002)Google Scholar
  12. 12.
    Sarpturk, S., Istefanopulos, Y., Kaynak, O.: On the stability of discrete-time sliding mode control systems. IEEE Trans. Autom. Control 32(10), 930–932 (1987)CrossRefzbMATHGoogle Scholar
  13. 13.
    Sha, D., Bajic, V.B.: Robust discrete adaptive input-output-based sliding mode controller. Int. J. Syst. Sci. 31(12), 1601–1614 (2000)CrossRefGoogle Scholar
  14. 14.
    Sha, D., Bajic, V.B., Yang, H.: New model and sliding mode control of hydraulic elevator velocity tracking system. Simul. Pr. Theory 9(6), 365–385 (2002)CrossRefGoogle Scholar
  15. 15.
    Tarokh, M.: A discrete-time adaptive control scheme for robot manipulators. J. Robot. Syst. 7(2), 145–166 (1990)CrossRefzbMATHGoogle Scholar
  16. 16.
    Veselic, B., Perunicic-Drazenovic, B., Milosavljevic, C.: Improved discrete-time sliding-mode position control using Euler velocity estimation. IEEE Trans. Ind. Electron. 57(11), 3840–3847 (2010)CrossRefGoogle Scholar
  17. 17.
    Xi, Z., Hesketh, T.: Discrete time integral sliding mode control for overhead crane with uncertainties. IET Control Theory Appl. 4(10), 2071–2081 (2010)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Xu, J.X., Abidi, K.: Discrete-time output integral sliding-mode control for a piezomotor-driven linear motion stage. IEEE Trans. Ind. Electron. 55(11), 3917–3926 (2008)CrossRefGoogle Scholar
  19. 19.
    Xu, Q., Jia, M.: Model reference adaptive control with perturbation estimation for a micropositioning system. IEEE Trans. Control Syst. Technol. 22(1), 352–359 (2014)Google Scholar
  20. 20.
    Xu, Q., Li, Y.: Micro-/nanopositioning using model predictive output integral discrete sliding mode control. IEEE Trans. Ind. Electron. 59(2), 1161–1170 (2012)CrossRefGoogle Scholar
  21. 21.
    Xu, Q., Li, Y.: Model predictive discrete-time sliding mode control of a nanopositioning piezostage without modeling hysteresis. IEEE Trans. Control Syst. Technol. 20(4), 983–994 (2012)CrossRefGoogle Scholar
  22. 22.
    Young, K.D., Utkin, V.I., Ozguner, U.: A control engineer’s guide to sliding mode control. IEEE Trans. Control Syst. Technol. 7(3), 328–342 (1999)CrossRefGoogle Scholar
  23. 23.
    Zhu, Y.: Multivariable System Identification for Process Control. Elsevier Science Inc., New York (2001)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Electromechanical EngineeringUniversity of MacauMacauChina
  2. 2.Department of Electrical and Computer EngineeringNational University of SingaporeSingaporeSingapore

Personalised recommendations