Skip to main content
SpringerLink
Log in

Time-Delayed Control (TDC): Design Issues and Solutions

  • Chapter
  • First Online:
Adaptive-Robust Control with Limited Knowledge on Systems Dynamics

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 257))

  • 738 Accesses

Abstract

This chapter primarily tries to bridge the pertaining gaps in the literature regarding the design issues of a conventional time-delayed Control (TDC). A Razumikhin-theorem based new stability analysis of TDC is introduced in this chapter that establishes a relation between system stability and the choice of controller gains as well as sampling interval. Especially, the stability analysis allows the continuous-time system to absorb the sampled past data used in time-delayed estimation (TDE) method. Further, the obtained stability result empowers the designer with a range of sampling intervals for fixed choice of controller gains in different application scenarios without violating the system stability. This particular contribution provides a rostrum towards the system applications, which require high sampling intervals due to operational/application constraints. Finally, the design solutions of TDC introduced in this chapter are experimentally validated under various sampling intervals, using ‘PIONEER-3’ wheeled mobile robot.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and 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
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Notes

  1. 1.

    Throughout this book, system stability refers closed-loop system stability, even if they are not mentioned explicitly.

  2. 2.

    Note that \(K_P=K_D=4\) indeed make \(\mathbf {A}\) Hurwitz for system (1.11).

References

  1. Hsia, T., Gao, L.: Robot manipulator control using decentralized linear time-invariant time-delayed joint controllers. In: Proceedings IEEE International Conference on Robotics and Automation, pp. 2070–2075. IEEE (1990)

    Google Scholar 

  2. Youcef-Toumi, K., Ito, O.: A time delay controller for systems with unknown dynamics. ASME J. Dyn. Syst. Meas. Control 112, 133 (1990)

    Article  Google Scholar 

  3. Lee, J., Dallali, H., Jin, M., Caldwell, D., Tsagarakis, N.: Robust and adaptive whole-body controller for humanoids with multiple tasks under uncertain disturbances. In: Proceedings IEEE International Conference on Robotics and Automation, pp. 5683–5689. IEEE (2016)

    Google Scholar 

  4. Roy, S., Kar, I.N.: Robust time-delayed control of a class of uncertain nonlinear systems. IFAC-PapersOnLine 49(1), 736–741 (2016)

    Article  Google Scholar 

  5. Roy, S., Nandy, S., Shome, S.N., Ray, R.: Robust position control of an autonomous underwater vehicle: a comparative study. In: EEE Conference on Automation Science and Engineering, pp. 1002–1007. IEEE (2013)

    Google Scholar 

  6. Roy, S., Nandy, S., Kar, I.N., Ray, R., Shome, S.N.: Robust control of nonholonomic wheeled mobile robot with past information: theory and experiment. Proc. Inst. Mech. Eng. J. Syst. Control Eng. 231(3), 178–188 (2017)

    Google Scholar 

  7. Jin, M., Lee, J., Tsagarakis, N.G.: Model-free robust adaptive control of humanoid robots with flexible joints. IEEE Trans. Ind. Electron. 64(2), 1706–1715 (2017)

    Article  Google Scholar 

  8. Jin, M., Lee, J., Ahn, K.K.: Continuous nonsingular terminal sliding-mode control of shape memory alloy actuators using time delay estimation. IEEE/ASME Trans. Mechatron. 20(2), 899–909 (2015)

    Article  Google Scholar 

  9. Roy, S., Nandy, S., Ray, R., Shome, S.N.: Time delay sliding mode control of nonholonomic wheeled mobile robot: experimental validation. In: Proceedings IEEE International Conference on Robotics and Automation, pp. 2886–2892. IEEE (2014)

    Google Scholar 

  10. Jin, M., Lee, J., Chang, P.H., Choi, C.: Practical nonsingular terminal sliding-mode control of robot manipulators for high-accuracy tracking control. IEEE Trans. Ind. Electron. 56(9), 3593–3601 (2009)

    Article  Google Scholar 

  11. Jin, M., Kang, S.H., Chang, P.H.: Robust compliant motion control of robot with nonlinear friction using time-delay estimation. IEEE Trans. Ind. Electron. 55(1), 258–269 (2008)

    Article  Google Scholar 

  12. Lee, J., Chang, P.H., Jamisola, R.S.: Relative impedance control for dual-arm robots performing asymmetric bimanual tasks. IEEE Trans. Ind. Electron. 61(7), 3786–3796 (2014)

    Article  Google Scholar 

  13. Baek, J., Jin, M., Han, S.: A new adaptive sliding-mode control scheme for application to robot manipulators. IEEE Trans. Ind. Electron. 63(6), 3628–3637 (2016)

    Article  Google Scholar 

  14. Roy. S., Kar, I.N.: Adaptive-robust control of uncertain Euler-Lagrange systems with past data: a time-delayed approach. In: Proceedings 2007 IEEE International Conference on Robotics and Automation, pp. 5715–5720. IEEE (2016)

    Google Scholar 

  15. Mukherjee, J., Roy, S., Kar, I.N., Mukherjee, S.: A double-layered artificial delay-based approach for maneuvering control of planar snake robots. J. Dyn. Syst. Meas. Control 141(4), 1–10 (2019)

    Article  Google Scholar 

  16. Roy, S., Nandy, S., Ray, R., Shome, S.N.: Robust path tracking control of nonholonomic wheeled mobile robot: experimental validation. Int. J. Control Autom. Syst. 13(4), 897–905 (2015)

    Article  Google Scholar 

  17. Roy, S., Roy, S.B., Kar, I.N.: Adaptive-robust control of Euler-Lagrange systems with linearly parametrizable uncertainty bound. IEEE Trans. Control Syst. Technol. 26(5), 1842–1850 (2018)

    Article  Google Scholar 

  18. Roy, S., Kar, I.N.: Adaptive sliding mode control of a class of nonlinear systems with artificial delay. J. Franklin Inst. 354(18), 8156–8179 (2017)

    Article  MathSciNet  Google Scholar 

  19. Roy, S., Lee, J., Baldi, S.: A new continuous-time stability perspective of time-delay control: introducing a state-dependent upper bound structure. IEEE Control Syst. Lett. 3(2), 475–480 (2019)

    Article  Google Scholar 

  20. Roy, S., Roy, S.B., Lee, J., Baldi, S.: Overcoming the underestimation and overestimation problems in adaptive sliding mode control. IEEE/ASME Trans, Mechatron. (2019)

    Google Scholar 

  21. Spong, M.W., Vidyasagar, M.: Robot Dynamics and Control. Wiley, New York (2008)

    Google Scholar 

  22. Roy, S., Roy, S.B., Kar, I.N.: A new design methodology of adaptive sliding mode control for a class of nonlinear systems with state dependent uncertainty bound. In: 15th International Workshop on Variable Structure Systems (VSS), pp. 414–419. IEEE (2018)

    Google Scholar 

  23. Roy, S., Baldi, S.: A simultaneous adaptation law for a class of nonlinearly parametrized switched systems. IEEE Control Syst. Lett. 3(3), 487–492 (2019)

    Article  Google Scholar 

  24. Roy, S., Kar, I.N.: Adaptive robust tracking control of a class of nonlinear systems with input delay. Nonlinear Dyn. 85(2), 1127–1139 (2016)

    Article  MathSciNet  Google Scholar 

  25. Hale, J.: Theory of Functional Differential Equations (1977)

    Google Scholar 

  26. Fridman, E.: Introduction to Time-delay Systems: Analysis and Control. Springer, Berlin (2014)

    Book  Google Scholar 

  27. Coelho, P., Nunes, U.: Path-following control of mobile robots in presence of uncertainties. IEEE Trans. Robot. 21(2), 252–261 (2005)

    Article  Google Scholar 

  28. Das, T., Kar, I.N.: Design and implementation of an adaptive fuzzy logic-based controller for wheeled mobile robots. IEEE Trans. Control Syst. Technol. 14(3), 501–510 (2006)

    Article  Google Scholar 

  29. Roy, S., Patel, A., Kar, I.N.: Analysis and design of a wide-area damping controller for inter-area oscillation with artificially induced time delay. IEEE Trans. Smart Grid 10(4), 3654–3663 (2019)

    Article  Google Scholar 

  30. Roy, S., Kar, I.N.: Robust control of uncertain Euler-Lagrange systems with time-varying input delay. In: Proceedings of the Advances in Robotics, p. 16. ACM (2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Robotics Research Center, International Institute of Information Technology, Hyderabad, Telangana, India

    Spandan Roy

  2. Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India

    Indra Narayan Kar

Authors
  1. Spandan Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Indra Narayan Kar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Spandan Roy .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Roy, S., Kar, I.N. (2020). Time-Delayed Control (TDC): Design Issues and Solutions. In: Adaptive-Robust Control with Limited Knowledge on Systems Dynamics. Studies in Systems, Decision and Control, vol 257. Springer, Singapore. https://doi.org/10.1007/978-981-15-0640-6_2

Download citation

Publish with us

Policies and ethics

Search

Navigation