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On Inherent Gain Margins of Sliding-Mode Control Systems

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Book cover Advances in Variable Structure Systems and Sliding Mode Control—Theory and Applications

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 115))

Abstract

In this book chapter, analysis of first-order and second-order sliding-mode (SM) control systems from the perspective of the gain margins of the averaged dynamics is done. These averaged dynamics result from the fact of the existence of chattering, so that averaging on the period of chattering can be considered. Analysis is done via the describing function method and the locus of a perturbed relay system method. First-order SM, hysteresis relay control, twisting algorithm and sub-optimal algorithm are compared in terms of the gain margins of the averaged dynamics that can describe the propagation of external signals through a SM control system.

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References

  1. Boiko, I.: Analysis of closed-loop performance and frequency-domain design of compensating filters for sliding mode control systems. IEEE Trans. Autom. Control. 52(10), 1882–1891 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Atherton, D.: Nonlinear Control Engineering - Describing Function Analysis and Design, Workingham, Berks. Van Nostrand Company Limited, UK (1975)

    Google Scholar 

  3. Boiko, I.: Oscillations and transfer properties of relay servo systems - the locus of a perturbed relay system approach. Automatica 41(4), 677–683 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fridman, L.: An averaging approach to chattering. IEEE Trans. Autom. Control. 46(8), 1260–1265 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  6. Levant, A.: Universal SISO sliding-mode controllers with finite-time convergence. IEEE Trans. Autom. Control. 46(9), 1447–1451 (2001)

    Article  MATH  Google Scholar 

  7. Bartolini, G., Ferrara, A., Pisano, A., Usai, E.: On the convergence properties of a 2-sliding control algorithm for nonlinear uncertain systems. Int. J. Control. 74, 718–731 (2001)

    Article  MATH  Google Scholar 

  8. Man, Z., Paplinski, A.P., Wu, H.R.: A robust MIMO terminal sliding mode control for rigid robotic manipulators. IEEE Trans. Autom. Control. 39(12), 2464–2468 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  9. Shtessel, Y.B., Shkolnikov, I.A., Brown, M.J.: An asymptotic second-order smooth sliding mode control. Asian J. Control. 5(4), 498–504 (2003)

    Article  Google Scholar 

  10. Boiko, I., Fridman, L., Pisano, A., Usai, E.: On the transfer properties of the generalized sub-optimal second-order sliding mode control algorithm. IEEE Trans. Autom. Control. 54(2), 399–403 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Boiko, I.: Input-output analysis of limit cycling relay feedback control systems. In: Proceedings of 1999 American Control Conference. San Diego, USA, 542–546 (1999)

    Google Scholar 

  12. Hsu, J.C., Meyer, A.U.: Modern Control Principles and Applications. McGraw Hill, New York (1968)

    MATH  Google Scholar 

  13. 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(9/10), 875–892 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Bartolini, G., Ferrara, A., Usai, E.: Output tracking control of uncertain nonlinear second-order systems. Automatica 33(12), 2203–2212 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  15. Boiko, I., Fridman, L., Pisano, A., Usai, E.: Analysis of chattering in systems with second-order sliding mode. IEEE Trans. Autom. Control. 52(11), 2085–2102 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Boiko, I., Fridman, L., Pisano, A., Usai, E.: Analysis of input-output performance of second-order sliding mode control algorithms. IEEE Trans. Autom. Control. 54(2), 399–403 (2009)

    Article  MATH  Google Scholar 

  17. Boiko, I., Fridman, L., Castellanos, M.: Analysis of second order sliding mode algorithms in the frequency domain. IEEE Trans. Autom. Control. 49(6), 946–950 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. The Petroleum Institute, Abu Dhabi, United Arab Emirates

    Igor Boiko

Authors
  1. Igor Boiko
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Correspondence to Igor Boiko .

Editor information

Editors and Affiliations

  1. School of Automation, Southeast University, Nanjing, China

    Shihua Li

  2. Research & Innovation Portfolio, RMIT University, Melbourne, Victoria, Australia

    Xinghuo Yu

  3. Division of Electrical Engineering, National Autonomous University of Mexico, Mexico City, Distrito Federal, Mexico

    Leonid Fridman

  4. Faculty of Science, Engineering and Technology, Swinburne University of Technology, Melbourne, Victoria, Australia

    Zhihong Man

  5. School of Automation, Southeast University, Nanjing, China

    Xiangyu Wang

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Boiko, I. (2018). On Inherent Gain Margins of Sliding-Mode Control Systems. In: Li, S., Yu, X., Fridman, L., Man, Z., Wang, X. (eds) Advances in Variable Structure Systems and Sliding Mode Control—Theory and Applications. Studies in Systems, Decision and Control, vol 115. Springer, Cham. https://doi.org/10.1007/978-3-319-62896-7_5

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  • DOI: https://doi.org/10.1007/978-3-319-62896-7_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62895-0

  • Online ISBN: 978-3-319-62896-7

  • eBook Packages: EngineeringEngineering (R0)

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