First-Order Sliding Mode Concepts

  • Halim Alwi
  • Christopher Edwards
  • Chee Pin Tan
Part of the Advances in Industrial Control book series (AIC)


In this chapter a brief introduction to the concept of sliding mode control is given and the properties of sliding mode systems are discussed. The chapter also highlights the benefits of sliding modes when applied to the fields of FTC and FDI. A simple pendulum example is used to introduce the concept. The unit vector approach for multi-input systems, sliding surface design and tracking requirements (integral action and model reference based tracking) are also discussed. The chapter ends with some discussions on the benefits and motivation for sliding mode control in the fields of FTC and FDI.


Phase Portrait Slide Mode Control Slide Mode Controller Switching Function Reachability Condition 
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. 17.
    Balestrino, A., DeMaria, G., Zinober, A.S.I.: Nonlinear adaptive model-following control. Automatica 20, 559–568 (1984) MathSciNetCrossRefMATHGoogle Scholar
  2. 56.
    Choi, H.H.: A new method for variable structure control system design: a linear matrix inequality approach. Automatica 33, 2089–2092 (1997) CrossRefMATHGoogle Scholar
  3. 58.
    Corradini, M.L., Orlando, G., Parlangeli, G.: A fault tolerant sliding mode controller for accommodating actuator failures. In: 44th IEEE Conference on Decision and Control, Seville, Spain, pp. 3091–3096 (2005) CrossRefGoogle Scholar
  4. 72.
    Dorling, C.M., Zinober, A.S.I.: Two approaches to hyperplane design in multivariable variable structure control systems. Int. J. Control 44, 65–82 (1986) CrossRefMATHGoogle Scholar
  5. 73.
    Dorling, C.M., Zinober, A.S.I.: Robust hyperplane design in multivariable variable structure control systems. Int. J. Control 48, 2043–2054 (1988) MathSciNetCrossRefMATHGoogle Scholar
  6. 79.
    Edwards, C.: A practical method for the design of sliding mode controllers using linear matrix inequalities. Automatica 40, 1761–1769 (2004) CrossRefMATHGoogle Scholar
  7. 85.
    Edwards, C., Spurgeon, S.K.: Sliding Mode Control: Theory and Applications. Taylor & Francis, London (1998) Google Scholar
  8. 88.
    El-Ghezawi, O.M.E., Billings, S.A., Zinober, A.S.I.: Variable-structure systems and system zeros. IEE Proc. Part D 130, 1–5 (1983) MATHGoogle Scholar
  9. 99.
    Franklin, G.F., Powell, J.D., Emami-Naeini, A.: Feedback Control of Dynamic Systems. 4th edn. Prentice Hall, New York (2002) Google Scholar
  10. 127.
    Hess, R.A., Wells, S.R.: Sliding mode control applied to reconfigurable flight control design. J. Guid. Control Dyn. 26, 452–462 (2003) CrossRefGoogle Scholar
  11. 211.
    Perruquetti, W., Barbot, J.P.: Sliding Mode Control in Engineering. Dekker, New York (2002) CrossRefGoogle Scholar
  12. 217.
    Ryan, E.P., Corless, M.: Ultimate boundedness and asymptotic stability of a class of uncertain dynamical systems via continuous and discontinuous control. IMA J. Math. Control Inf. 1, 223–242 (1984) CrossRefMATHGoogle Scholar
  13. 225.
    Shtessel, Y., Buffington, J., Banda, S.: Multiple time scale flight control using re-configurable sliding modes. J. Guid. Control Dyn. 22, 873–883 (1999) CrossRefGoogle Scholar
  14. 226.
    Shtessel, Y., Buffington, J., Banda, S.: Tailless aircraft flight control using multiple time scale re-configurable sliding modes. IEEE Trans. Control Syst. Technol. 10(2), 288–296 (2002) CrossRefGoogle Scholar
  15. 230.
    Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice Hall, Englewood Cliffs (1991) MATHGoogle Scholar
  16. 255.
    Utkin, V., Guldner, J., Shi, J.: Sliding Mode Control in Electromechanical Systems. Taylor & Francis, London (1999) Google Scholar
  17. 256.
    Utkin, V.I.: Sliding Modes in Control Optimization. Springer, Berlin (1992) MATHGoogle Scholar
  18. 257.
    Utkin, V.I., Young, K.K.D.: Methods for constructing discontinuity planes in multidimensional variable structure systems. Autom. Remote Control 39, 1466–1470 (1978) MATHGoogle Scholar
  19. 263.
    Vetter, T.K., Wells, S.R., Hess, R.A.: Designing for damage-robust flight control design using sliding mode techniques. Proc. Inst. Mech. Eng., G J. Aerosp. Eng. 217, 245–261 (2003) CrossRefGoogle Scholar
  20. 269.
    Wells, S.R., Hess, R.A.: Multi-input/multi-output sliding mode control for a tailless fighter aircraft. J. Guid. Control Dyn. 26(3), 463–473 (2003) CrossRefGoogle Scholar
  21. 285.
    Young, K.-K.D.: Asymptotic stability of model reference systems with variable structure control. IEEE Trans. Autom. Control 22, 279–281 (1977) CrossRefMATHGoogle Scholar
  22. 286.
    Young, K.K.D.: Design of variable structure model-following control systems. IEEE Trans. Autom. Control 23, 1079–1085 (1978) CrossRefMATHGoogle Scholar
  23. 299.
    Zinober, A.S.I.: An introduction to variable structure control. In: Zinober, A.S.I. (ed.) Deterministic Control of Uncertain Systems, pp. 1–26. Peter Peregrinus, Stevenage (1990) Google Scholar
  24. 300.
    Zinober, A.S.I.: An introduction to sliding mode variable structure control. In: Zinober, A.S.I. (ed.) Variable Structure and Lyapunov Control, pp. 1–22. Springer, Berlin (1994) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Halim Alwi
    • 1
  • Christopher Edwards
    • 1
  • Chee Pin Tan
    • 2
  1. 1.Department of EngineeringUniversity of LeicesterLeicesterUK
  2. 2.School of EngineeringMonash University Sunway CampusBandar SunwayMalaysia

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