Skip to main content
SpringerLink
Log in

Quantization Behaviors in Equivalent-Control Based Sliding-Mode Control Systems

  • Chapter
Advances in Sliding Mode Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 440))

Abstract

In this chapter, we study the quantization behaviors of the equivalent control based second order single-input sliding-mode control (SMC) systems in the presence of quantized state feedback.We show that the class of SMC systems with both uniform and logarithmic quantizers can make the system states converge into a band, which relates to the quantization parameters. Properties of the system trajectories with quantized state feedback are characterized by using the concepts of quantized sliding mode (QSM) and quantized sliding-mode control (QSMC) system. We show that the QSM is piecewise constant. Various simulations illustrate the behaviors of the equivalent-control based SMC system under uniform and logarithmic quantized state feedback.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chakrabarty, S., Bandyopadhyay, B.: Quasi sliding mode control with quantization in state measurement. In: Proceedings of 37th Annual Conference on IEEE Industrial Electronics Society, Australia, pp. 3971–3976 (2011)

    Google Scholar 

  2. Corradini, M., Ippoliti, G., Orlando, G., et al.: Robust control of hybrid plants in the presence of quantization errors. In: Proceedings of IEEE International Conference on Control and Automation, New Zealand, pp. 234–239 (2009)

    Google Scholar 

  3. Delchamps, D.F.: Stabilizing a linear system with quantized state feedback. IEEE Transactions on Automatic Control 35(8), 916–924 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  4. Edwards, C., Spurgeon, S.K.: Sliding mode control, theory and applications. CRC Press, Taylor & Francis Group (1998)

    Google Scholar 

  5. Elia, N., Mitter, S.K.: Stabilization of linear systems with limited information. IEEE Transactions on Automatic Control 4, 1384–1400 (2001)

    Article  MathSciNet  Google Scholar 

  6. Furuta, K., Pan, Y.: Discrete-time VSS control for continuous-time systems. In: Proceedings of the First Asian Control Conference, Tolyo, Japan, pp. 337–380 (1994)

    Google Scholar 

  7. Galias, Z., Yu, X.: Analysis of zero-order holder discretization of two dimensional sliding-mode control systems. IEEE Transactions on Circuits and Systems-II: Express Briefs 55(12), 1269–1273 (2008)

    Article  Google Scholar 

  8. Gao, W., Wang, Y., Homaifa, A.: Discrete-time variable structure control systems. IEEE Transactions on Industrial Electronics 42(2), 117–122 (1995)

    Article  Google Scholar 

  9. Hung, J.Y., Gao, W., Hung, J.C.: Variable structure control: a survey. IEEE Transactions on Industrial Electronics 40(1), 2–22 (1993)

    Article  Google Scholar 

  10. Levant, A.: Sliding order and sliding accuracy in sliding mode control. International Journal of Control 58(6), 1247–1263 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  11. Liberzon, D.: Hybrid feedback stabilization of systems with quantized signals. Automatica 39, 1543–1554 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu, T., Jiang, Z., Hill, D.J.: Small-gain based output-feedback controller design for a class of nonlinear systems with actuator dynamic quantization. IEEE Transactions on Automatic Control 57(5), 1326–1332 (2012)

    Article  MathSciNet  Google Scholar 

  13. Milosavljevic, C.: General conditions for the existence of a quasi-sliding mode on the switching hyperplane in discrete variable structure systems. Automation and Remote Control 3, 36–44 (1985)

    Google Scholar 

  14. Rasool, F., Nguang, S.K.: Quantised robutst H  ∞  output feedback control of discrete-time systems with random communication delays. Control Theory and Applications 4, 2252–2262 (2010)

    Article  MathSciNet  Google Scholar 

  15. Shkolnikov, I.A., Shtessel, Y.B., Adhami, R.: Digital sliding modes and quasi-exact tracking discrete-valued signals. In: Proceedings of IEEE 9th International Workshop on Variable Structure Systems, Italy, pp. 17–22 (2006)

    Google Scholar 

  16. Su, W.C., Drakunov, S., Özgüner, Ü.: An \(\textit{O}\)(T 2) boundary layer in sliding mode for sampled-data systems. IEEE Transactions on Automatic Control 45, 482–485 (2000)

    Article  MATH  Google Scholar 

  17. Utkin, V.I.: Variable structure systems with sliding mode. IEEE Transactions on Automatic Control 22(2), 212–222 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  18. Utkin, V.I., Drakunov, S.: On discrete-time sliding mode control. In: Proceedings of IFAC Symposium on Nonlinear Control Systems, Capri, Italy, pp. 384–389 (1989)

    Google Scholar 

  19. Wang, B., Yu, X., Chen, G.: ZOH discretization effect on single-input sliding mode control systems with matched uncertainties. Automatica 45, 119–125 (2009)

    MathSciNet  Google Scholar 

  20. Xia, X., Zinober, A.S.I.: Periodic orbits from delta-modulation of stable linear systems. IEEE Transactions on Automatic Control 49(6), 1376–1380 (2004)

    Article  MathSciNet  Google Scholar 

  21. Yan, Y., Yu, X., Yu, S.: Quantization effect on sliding-mode control of a second-order dynamical system. In: Proceedings of IEEE 12th International Workshop on Variable Structure Systems, India, pp. 243–247 (2012)

    Google Scholar 

  22. Yan, Y., Yu, X., Yu, S.: Quantization effect on a second-order dynamical system under sliding-mode control. International Journal of Bifurcation and Chaos (2012) (accepted)

    Google Scholar 

  23. Xu, J.X., Zheng, F., Lee, T.: On Sampled Data Variable Structure Control Systems. In: Young, K.D., Özgüner, Ü. (eds.) Variable Structure Systems, Sliding Mode and Nonlinear Control. LNCIS, vol. 247, pp. 69–92. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  24. Yu, S., Yu, X., Qian, W.: Time delayed discrete variable structure control with quasi-sliding modes. In: Yu, X., Xu, J.-X. (eds.) Advances in Variable Structure Systems: Analysis, Integration and Applications, pp. 84–92. World Scientific, Singapore (2000)

    Google Scholar 

  25. Yu, S.H., Tsai, Y.H.: Sliding-mode quantized control of a class-D audio power amplifier. In: Proceedings of the 2010 International Power Electronics Conference, Japan, pp. 553–556 (2010)

    Google Scholar 

  26. Yu, X., Chen, G.: Discretization behaviors of equivalent control based variable structure systems. IEEE Transactions on Automatic Control 48(9), 1641–1646 (2003)

    Article  MathSciNet  Google Scholar 

  27. Yu, X., Wang, B., Galias, Z., et al.: Discretization effect on equivalent control based multi-input sliding mode control systems. IEEE Transactions on Automatic Control 53(6), 1563–1569 (2008)

    Article  MathSciNet  Google Scholar 

  28. Yu, X., Wang, B., Li, X.: Computer-controlled variable structure systems: The state of the art. IEEE Transactions on Industrial Informatics 8(2), 197–205 (2012)

    Article  Google Scholar 

  29. Yun, S.W., Choi, Y.J., Park, P.: Dynamic output-feedback guaranteed cost control for linear systems with uniform input quantization. Nonlinear Dynamics 62, 95–104 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  30. Zheng, B.C., Yang, G.H.: Quantised feedback stabilisation of planar systems via switching-based sliding-mode control. IET Control Theory and Applications 6, 149–156 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Science and Technology, Dalian Maritime University, 116026, Dalian, Liaoning, China

    Yan Yan

  2. School of Electrical and Computer Engineering, RMIT University, Melbourne, VIC, 3000, Australia

    Xinghuo Yu

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

    Xinghuo Yu

Authors
  1. Yan Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xinghuo Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan Yan .

Editor information

Editors and Affiliations

  1. , Interdisciplinary Programme in Systems, Indian Institute of Technology Bombay, ACRE Building 114 B, Mumbai, 400 076, Maharashtra, India

    B Bandyopadhyay

  2. , Dept. of Electrical Engineering, Indian Institute of Technology Delhi, Room No : II/335, New Delhi, 110 016, India

    S Janardhanan

  3. , Department of Electronics, University of Kent, Jennison Building - Room 1.54, Kent, CT2 7NT, United Kingdom

    Sarah K. Spurgeon

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Yan, Y., Yu, X. (2013). Quantization Behaviors in Equivalent-Control Based Sliding-Mode Control Systems. In: Bandyopadhyay, B., Janardhanan, S., Spurgeon, S. (eds) Advances in Sliding Mode Control. Lecture Notes in Control and Information Sciences, vol 440. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36986-5_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-36986-5_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36985-8

  • Online ISBN: 978-3-642-36986-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation