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Design Principles

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Book cover Road Map for Sliding Mode Control Design

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Abstract

This chapter discusses the main principles of sliding mode design. Regular form of the controlled system is introduced. Reaching and existence conditions are presented. The decoupling procedure and invariance notion are discussed. The basic principles of output, unit, and integral SMC are presented. Second-order sliding mode (SOSM) controllers (such as twisting and super-twisting) are analyzed. Suboptimal controllers are also discussed.

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References

  1. Levant, A.: Sliding order and sliding accuracy in sliding mode control. Int. J. Control. 58(6), 1247–1263 (1993)

    Article  MathSciNet  Google Scholar 

  2. Shtessel, Y., Edwards, C., Fridman, L., Levant, A.: Sliding Mode Control and Observation. Control Engineering Series. Birkhauser, NY (2014)

    Google Scholar 

  3. Loukyanov, A., Utkin, V.: Methods of reducing equations of dynamic systems to a regular form. Autom. Remote. Control. 42(4), 413–420 (1981)

    MathSciNet  Google Scholar 

  4. Utkin, V.: Sliding Modes in Control and Optimization. Springer, Berlin (1992)

    Book  Google Scholar 

  5. Utkin, V., Guldner, J., Shi, J.: Sliding Mode Control in Electro-Mechanical Systems. CRC Press (2009)

    Google Scholar 

  6. Drazenovic, B.: The invariance conditions in variable structure systems. Automatica 5(3), 287–295 (1969)

    Article  MathSciNet  Google Scholar 

  7. Atassi, A.N., Khalil, H.K.: Separation results for stabilization of nonlinear systems using different high-gain observer designs. Syst. Control. Lett. 39, 183–191 (2000)

    Article  MathSciNet  Google Scholar 

  8. Oh, S., Khalil, H.K.: Nonlinear output feedback tracking using high-gain observer and variable structure control. Automatica 33, 1845–1856 (1997)

    Article  MathSciNet  Google Scholar 

  9. Edwards, C., Spurgeon, S.: Sliding Mode Control: Theory and Applications. Taylor and Francis (1998)

    Google Scholar 

  10. Poznyak, A.: Advanced Mathematical Tools for Automatic Control Engineers. Deterministic Technique, vol. 1. Elsevier, Amsterdam, Netherlands (2008)

    Google Scholar 

  11. Utkin, V.I., Shi, J.: Integral sliding mode in systems operating under uncertainty conditions. In: Proceedings of IEEE CDC, vol. 4, Kobe, Japan, pp. 4591–4596 (1996)

    Google Scholar 

  12. Fridman, L., Poznyak, A., Bejarano, F.J.: Robust Output LQ Optimal Control via Integral Sliding Modes. Birkhäuser, Springer Science, Series Systems and Control: Foundations and Applications, New York (2014)

    Google Scholar 

  13. Gutman, S.: Uncertain dynamic systems—a lyapunov min-max approach. IEEE Trans. Autom. Control AC-24, 437–449 (1979)

    Google Scholar 

  14. Gutman, S. Leitmann, G.: Stabilizing feedback control for dynamic systems with bounded uncertainties. In: Confrence on Decision and Control, pp. 94–99 (1976)

    Google Scholar 

  15. Orlov, Y., Utkin, V.: Unit sliding mode control in infinite-dimensional systems. J. Appl. Math. Comput. Sci. 8, 7–20 (1998)

    MathSciNet  MATH  Google Scholar 

  16. Khalil, H.: Nonlinear Systems. Prentice Hall (2002)

    Google Scholar 

  17. Levant, A.: Principles of 2-sliding mode control design. Automatica 43(4), 576–586 (2007)

    Article  MathSciNet  Google Scholar 

  18. Bhat, S.P., Bernstein, D.S.: Geometric homogeneity with applications to finite-time stability. Math. Control Signals Syst. 17(2), 101–127 (2005)

    Article  MathSciNet  Google Scholar 

  19. Utkin, V.: Mechanical energy-based lyapunov function design for twisting and super-twisting sliding mode control. IMA J. Math. Control Inf. 32(4), 675–688 (2015)

    MathSciNet  MATH  Google Scholar 

  20. Orlov, Y.: Finite time stability and robust control synthesis of uncertain switched systems. SIAM J. Control Optim. 43(4), 1253–1271 (2005)

    Article  MathSciNet  Google Scholar 

  21. Bartolini, G., Ferrara, A., Usai, E.: Chattering avoidance by second-order sliding mode control. IEEE Trans. Autom. Control 43(2), 241–246 (1998)

    Article  MathSciNet  Google Scholar 

  22. Bartolini, G., Pisano, A., Punta, E., Usai, E.: A survey of application of second-order sliding mode control to mechanical systems. Int. J. Control 76(9/10), 875–892 (2003)

    Article  MathSciNet  Google Scholar 

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Correspondence to Vadim Utkin .

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Utkin, V., Poznyak, A., Orlov, Y.V., Polyakov, A. (2020). Design Principles. In: Road Map for Sliding Mode Control Design. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-41709-3_3

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