Constraining State Variables in Continuous Time Sliding Mode Control

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1196)


In this paper the continuous-time system of arbitrary order was taken into consideration. The sliding mode controller was computed using the reaching law approach. The time-varying convergence rate of the sliding variable was designed in such a manner to fulfill the control signal and state variables constraints for the whole regulation time. The sufficient condition guaranteeing the fastest, finite-time, monotonic convergence of the representative point to the predefined switching hyperplane in the presence of given limitations was stated and formally proved.


Sliding mode control Continuous-time systems State constraint Control signal constraint Reaching law 


  1. 1.
    Bartolini, G., Ferrara, A., Utkin, V.I.: Adaptive sliding mode control in discrete-time systems. Automatica 31, 769–773 (1995)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bartoszewicz, A.: A new reaching law for sliding mode control of continuous time systems with constraints. Trans. Inst. Measur. Control 37, 515–521 (2015)CrossRefGoogle Scholar
  3. 3.
    Bartoszewicz, A.: Discrete-time quasi-sliding-mode control strategies. IEEE Trans. Ind. Electron. 45, 633–637 (1998)CrossRefGoogle Scholar
  4. 4.
    Bartoszewicz, A., Kaynak, O., Utkin, V.I. (eds.): Sliding mode control in industrial applications. Special Section IEEE Trans. Ind. Electron. 55, 3805–4103 (2008)Google Scholar
  5. 5.
    Bartoszewicz, A., Latosiński, P.: Generalization of Gao’s reaching law for higher relative degree sliding variables. IEEE Trans. Autom. Control 63, 3173–3179 (2018)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Bartoszewicz, A., Latosiński, P.: Reaching law for DSMC systems with relative degree 2 switching variable. Int. J. Control 90, 1626–1638 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Bartoszewicz, A., Leśniewski, P.: Reaching law approach to the sliding mode control of periodic review inventory systems. IEEE Trans. Autom. Sci. Eng. 11, 810–817 (2014)CrossRefGoogle Scholar
  8. 8.
    Bartoszewicz, A., Leśniewski, P.: Reaching law-based sliding mode congestion control for communication networks. IET Proc. Control Theory Appl. 8, 1914–1920 (2014)CrossRefGoogle Scholar
  9. 9.
    Chakrabarty, S., Bandyopadhyay, B.: A generalized reaching law with different convergence rates. Automatica 63, 34–37 (2016)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Emelyanov, S.V.: Variable Structure Control Systems. Nauka, Moscow (1967)zbMATHGoogle Scholar
  11. 11.
    Fallaha, C.J., Saad, M., Kanaan, H.Y., Al-Haddad, K.: Sliding-mode robot control with exponential reaching law. IEEE Trans. Ind. Electron. 58, 600–610 (2011)CrossRefGoogle Scholar
  12. 12.
    Gao, W., Hung, J.C.: Variable structure control of nonlinear systems: a new approach. IEEE Trans. Ind. Electron. 40, 45–55 (1993)CrossRefGoogle Scholar
  13. 13.
    Gao, W., Wang, Y., Homaifa, A.: Discrete-time variable structure control systems. IEEE Trans. Ind. Electron. 42, 117–122 (1995)CrossRefGoogle Scholar
  14. 14.
    Jaskuła, M., Pietrala, M., Leśniewski, P.: The problem of state constraints in designing the discrete time sliding mode controller. Pomiary Automatyka Robotyka 4, 15–22 (2017)CrossRefGoogle Scholar
  15. 15.
    Jaskuła, M., Leśniewski, P.: Discrete time sliding mode control in the presence of state and control signal constraints. In: 24th International Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, pp. 201–204 (2019)Google Scholar
  16. 16.
    Milosavljević, C̆.: General conditions for the existence of a quasi-sliding mode on the switching hyperplane in discrete variable structure systems. Autom. Remote Control 46, 307–314 (1985)Google Scholar
  17. 17.
    Niu, Y., Ho, D.W.C., Wang, Z.: Improved sliding mode control for discrete-time systems via reaching law. IET Control Theory Appl. 4, 2245–2251 (2010)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Utkin, V.I.: Variable structure systems with sliding modes. IEEE Trans. Autom. Control 22, 212–222 (1977)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Utkin, V.I., Drakunow, S.V.: On discrete-time sliding mode control. In: IFAC Conference Nonlinear Control, pp. 484–489 (1989)Google Scholar
  20. 20.
    Wang, A., Jia, X., Dong, S.: A new exponential reaching law of sliding mode control to improve performance of permanent magnet synchronous motor. IEEE Trans. Magn. 49, 2409–2412 (2013)CrossRefGoogle Scholar
  21. 21.
    Zhang, X., Sun, L., Zhao, K., Sun, L.: Nonlinear speed control for PMSM system using sliding-mode control and disturbance compensation techniques. IEEE Trans. Power Electron. 28, 1358–1365 (2013)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Automatic ControlŁodź University of TechnologyŁodźPoland

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