Discrete-Time Sliding Mode Control with Disturbance Estimator for NCS Having Random Fractional Delay and Multiple Packet Loss

  • Dipesh H. ShahEmail author
  • Axaykumar Mehta
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 132)


The concept of remotely controlling a system through communication network gave birth to Networked Control Systems (NCSs). The NCSs are traditional feedback control loops closed through a real-time communication network. It is evident that the performance of closed-loop system deteriorates due to network delay and information loss in communication channel due to bandwidth limitation or congestion. Hence, it is mandatory to improvise the existing control strategies for NCS. In this chapter, we propose an approach for designing discrete-time sliding mode controller for NCS having random fractional delay and multiple packet loss simultaneously. The fractional delay that occurs within sampling period is modelled using Poisson’s distribution function and is approximated using Thiran’s delay approximation technique. The multiple packet loss that occurs in communication channel between sensor and controller is treated with uniform probability distribution function and compensated at controller end. Based on the proposed approach, a sliding surface is designed and is used to derive discrete-time sliding mode control law that computes the control actions in the presence of random network delay and multiple packet loss. Further, a second-order disturbance estimator is incorporated at the plant side to estimate the disturbance that occurs in the plant. The disturbance estimator guarantees the width of quasi-sliding mode band (QSMB) of order \(O(h^{3})\) with decreasing reaching steps. Hence, the robustness properties of closed-loop NCS are improved. The stability of the closed-loop NCS is also derived using Lyapunov approach that assures the finite-time state convergence in the presence of network non-idealities. The efficacy of the proposed algorithm is examined through simulation results.


Discrete-time sliding mode control Networked Control System Disturbance estimation Communication delay Packet loss 


  1. 1.
    D. Shah, A. Mehta, Multirate output feedback based discrete-time sliding mode control for fractional delay compensation in NCSs, in IEEE Conference on Industrial Technology (ICIT-2017) (2017), pp. 848–853Google Scholar
  2. 2.
    D. Shah, A. Mehta “Discrete-Time Sliding Mode Control Using Thiran’s Delay Approximation for Networked Control System”, 43rd Annual Conference on Industrial Electronics (IECON-17), pp. 3025–3031, Nov. 2017Google Scholar
  3. 3.
    D. Shah, A.J. Mehta, Design of robust controller for networked control system, in Proceedings of IEEE International Conference on Computer, Communication and Control Technology, Sept. 2014, pp. 385–390Google Scholar
  4. 4.
    D. Shah, A. Mehta, Output feedback discrete-time networked sliding mode control, in IEEE Proceedings of Recent Advances in Sliding Modes (RASM) (2015), pp. 1–7Google Scholar
  5. 5.
    D. Shah, A. Mehta, Discrete-time sliding mode controller subject to real-time fractional delays and packet losses for networked control system. Int. J. Control Autom. Syst. (IJCAS) 15(6), 2690–2703 (Dec. 2017)Google Scholar
  6. 6.
    D. Shah, A. Mehta, Fractional delay compensated discrete-time SMC for networked control system. Digit. Commun. Netw. (DCN), Elsevier, 2(3), 385–390, Dec. 2016Google Scholar
  7. 7.
    A.J. Mehta, B. Bandyopadhyay, Multirate output feedback based stochastic sliding mode control. J. Dyn. Syst. Measur. Control 138(12), 124503(1-6) (2016)Google Scholar
  8. 8.
    A.J. Mehta, B. Bandyopadhyay, A. Inoue, Reduced-order observer design for servo system using duality to discrete-time sliding-surface design. IEEE Trans. Ind. Electron. 57(11), 3793–3800 (2010)CrossRefGoogle Scholar
  9. 9.
    J. Thiran, Recursive digital filters with maximally flat group delay. IEEE Trans. Circ. Theory 18(6), 659–664 (1971)MathSciNetCrossRefGoogle Scholar
  10. 10.
    L. Brown, L. Zhao, A test of Poisson’s Distribution. J. Stat. 64(3), 611–625 (2002)MathSciNetzbMATHGoogle Scholar
  11. 11.
    A. Bartoszewicz, P. Lesniewski, Reaching law approach to the sliding mode control of periodic review inventory systems. IEEE Trans. Autom. Sci. Eng. 11(3), 810–817 (2014)CrossRefGoogle Scholar
  12. 12.
    A. Bartoszewicz, Remarks on discrete-time variable structure control systems. IEEE Trans. Ind. Electron. 43(1), 235–238 (1996)MathSciNetGoogle Scholar
  13. 13.
    A. Bartoszewicz, Discrete-time variable structure control systems. IEEE Trans. Ind. Electron. 45(4), 633–637 (1996)CrossRefGoogle Scholar
  14. 14.
    J. Wu, T. Chen, Design of networked control systems with packet dropouts. IEEE Trans. Autom. Control 52(7), 1314–1319 (2007)MathSciNetCrossRefzbMATHGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Instrumentation and ControlSardar Vallabhbhai Patel Institute of TechnologyAnandIndia
  2. 2.Department of Electrical EngineeringInstitute of Infrastructure Technology Research and ManagementAhmedabadIndia

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