Adaptive Controller Design Based On Predicted Time-delay for Teleoperation Systems Using Lambert W Function

  • Mohammad hadi Sarajchi
  • Soheil Ganjefar
  • Seyed Mahmoud Hoseini
  • Zhufeng ShaoEmail author


This study develops an approach of controller design, on the basis of Lambert W function structure for Internet-based bilateral teleoperation systems. Actually, time-delay terms in bilateral teleoperation systems lead to an infinite number of characteristic equation roots making difficulty in analysis of systems by classical methods. As delay differential equations (DDEs) have infinite eigenspectrums, all closed-loop eigenvalues are not feasible to locate in desired positions by using classical control methods. Therefore, this study suggests a new feedback controller for assignment of eigenvalues, in compliance with Lambert W function. In this regard, an adaptive controller is accurately employed in order to provide the controller with updated predicted time-delay and robust the system against the time-delay. This novel control approach causes the rightmost eigenvalues to locate exactly in desired positions in the stable left hand of the imaginary axis. The simulation results show strong and robust closed-loop performance and better tracking in constant and time-varying delay.


Adaptive controller delay differential equations(DDEs) eigenvalue assignment Lambert W function teleoperation systems time-delay 


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  1. [1]
    T. B. Sheridan, “Teleoperation, Telerobotics and Telepresence,” A progress Report, Control Engineering Practice, vol. 3, No. 2, pp. 2–204, 1995.Google Scholar
  2. [2]
    L. Zhao, H. Zhang, Y. Yang, and H. Yang, “Integral sliding mode control of a bilateral teleoperation system based on extended state observers,” International Journal of Control, Automation and Systems, vol. 15, No. 5, pp. 5–2118, 2017.Google Scholar
  3. [3]
    H. G. Lee, H. J. Hyung, and D. W. Lee, “Egocentric teleoperation approach,” International Journal of Control, Automation and Systems, vol. 15, no. X, pp. 2744–2753, 2017.Google Scholar
  4. [4]
    O. Penaloza-Mejfa, L. A. Marquez-Martmez, J. Alvarez-Gallegos, and J. Alvarez, “Master-slave teleoperation of underactuated mechanical systems with communication delays,” International Journal of Control, Automation and Systems, vol. 15, No. 2, pp. 2–827, 2017.Google Scholar
  5. [5]
    R. Mellah, S. Guermah, and R. Toumi, “Adaptive control of bilateral teleoperation system with compensatory neural-fuzzy controllers,” International Journal of Control, Automation and Systems, vol. 15, No. 4, pp. 4–1949, 2017.Google Scholar
  6. [6]
    J. Xie, Y. Kao, and J. H. Park, “H∞ performance for neutral-type Markovian switching systems with general uncertain transition rates via sliding mode control method,” Nonlinear Analysis: Hybrid Systems, vol. 27, p. 416–436, 2018.MathSciNetzbMATHGoogle Scholar
  7. [7]
    B. Jiang, Y. Kao, C. Gao, and X. Yao, “Passification of uncertain singular semi-Markovian jump systems with actuator failures via sliding mode approach,” IEEE Transactions on Automatic Control, vol. 62, No. 8, pp. 8–4138, 2017.MathSciNetzbMATHGoogle Scholar
  8. [8]
    Z. Du, Z. Yan, and Z. Zhao, “Interval type-2 fuzzy tracking control for nonlinear systems via sampled-data controller,” Fuzzy Sets and Systems, vol. 356, pp. 92–112, 2019.MathSciNetGoogle Scholar
  9. [9]
    Z. Lu, P. Huang, P. Dai, Z. Liu, and Z. Meng, “Enhanced transparency dual-user shared control teleoperation architecture with multiple adaptive dominance factors,” International Journal of Control, Automation and Systems, vol. 15, No. 5, pp. 5–2301, 2017.Google Scholar
  10. [10]
    R. Uddin, S. Park, S. Park, and J. Ryu, “Projected predictive Energy-Bounding Approach for multiple degree-of-freedom haptic teleoperation,” International Journal of Control, Automation and Systems, vol. 14, No. 6, pp. 6–1561, 2016.Google Scholar
  11. [11]
    J. J. Craig, Introduction to Robotics Mechanics and Control, Addison-Wesley, 1989.zbMATHGoogle Scholar
  12. [12]
    F. Janabi-Sharifi, “Collision: modelling, simulation and identification of robotic manipulators interacting with environments,” Journal of Intelligent and Robotic Systems, vol. 13, No. 1, pp. 1–1, 1995.Google Scholar
  13. [13]
    K. Gu, and S. I. Niculescu, Stability Analysis of Time-delay Systems: A Lyapunov Approach, Springer, London, 2006.zbMATHGoogle Scholar
  14. [14]
    P. Liu, “Exponential stability for linear time-delay systems with delay,” Journal of the Franklin Institute, vol. 340, No. 6, pp. 6–481, 2003.MathSciNetGoogle Scholar
  15. [15]
    G. H. Gonnet, D. Hare, D. J. Jeffrey, D. E. Knuth, and R. M. Corless, “On the Lambert W function,” Advances in Computational Mathematics, vol. 5, No. 4, pp. 4–329, 1996.MathSciNetzbMATHGoogle Scholar
  16. [16]
    P. W. Nelson, A. G. Ulsoy, and S. Yi, Time-delay Systems: Analysis and Control Using the Lambert W function, World Scientific, 2010.zbMATHGoogle Scholar
  17. [17]
    F. M. Asl, and A. G. Ulsoy, “Analysis of a system of linear delay differential equations,” Journal of Dynamic Systems Measurement and Control, vol. 12, No. 5, pp. 5–215, 2003.Google Scholar
  18. [18]
    P. W. Nelson, A. G. Ulsoy, and S. Yi, “Eigenvalue assignment via the Lambert W function for control for time-delay systems,” Journal of Vibration and Control, vol. 16, No. 7, pp. 7–961, 2010.MathSciNetzbMATHGoogle Scholar
  19. [19]
    S. Yi and A. G. Ulsoy, “Solution of a system of linear delay differential equations using the matrix Lambert function,” Proceedings of American Control Conference, Minneapolis, MN, USA, pp. 2433–2438, 2006.Google Scholar
  20. [20]
    R. E. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York, USA, 1963.zbMATHGoogle Scholar
  21. [21]
    P. W. Nelson, A. G. Ulsoy, and S. Yi, “Delay differential equations via the matrix Lambert W function and bifurcation analysis application to machine tool chatter,” Math. Biosci Eng., vol. 4, No. 2, pp. 2–355, 2007.MathSciNetzbMATHGoogle Scholar
  22. [22]
    H. Shinozaki and T. Mori, “Robust stability analysis of linear time-delay systems by Lambert W function,” Some Extreme Point Results submitted to Automatica, vol. 42, No. 10, pp. 10–1791,2006.zbMATHGoogle Scholar
  23. [23]
    A. Manitius and A. W. Olbrot, “Finite spectrum assignment problem for systems with delays,” IEEE Transaction on Automatic Control, vol. 24, No. 4, pp. 4–541, 1979.MathSciNetzbMATHGoogle Scholar
  24. [24]
    J. E. Colgate, “Robust impedance shaping telemanipula-tion,” IEEE Transaction on Robotics and Automation, vol. 9, No. 4, pp. 4–374, 1993.Google Scholar
  25. [25]
    O. Reinoso, J. M. Sabater, and C. Perez, and J. M. Azorin, “A new control method of teleoperators with time delay,” Proc. of 11th International Conference on Advanced Robotics, Coimbra, Portugal, pp. 100–105, 2003.Google Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  • Mohammad hadi Sarajchi
    • 1
    • 2
  • Soheil Ganjefar
    • 3
  • Seyed Mahmoud Hoseini
    • 3
  • Zhufeng Shao
    • 1
    • 2
    Email author
  1. 1.State Key Laboratory of Tribology & Institute of Manufacturing EngineeringTsinghua UniversityBeijing ShiChina
  2. 2.Beijing Key Lab of Precision/Ultra-precision Manufacturing Equipment and ControlTsinghua UniversityBeijing ShiChina
  3. 3.Department of Electrical EngineeringBu-Ali Sina UniversityHamedanIran

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