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Implicit Euler discretization for chattering suppression in non-singular terminal sliding mode control.

Shanhai Jin1, Yuhan Wang1, Dejin Zhao1

  • 1School of Engineering, Yanbian University, Yanji 133002, Jilin, China.

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|November 22, 2025
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Summary
This summary is machine-generated.

This study introduces an implicit Euler discretization for non-singular terminal sliding mode control (NTSMC) to overcome numerical chattering. The method ensures finite-time convergence and improves accuracy in digital control systems.

Keywords:
Chattering suppressionFinite-time convergenceImplicit Euler discretizationNon-singular terminal sliding mode controlReal-time implementation

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Area of Science:

  • Control Engineering
  • Applied Mathematics
  • Digital Systems

Background:

  • Non-singular terminal sliding mode control (NTSMC) offers theoretical advantages but suffers from numerical chattering in digital implementations.
  • Chattering in NTSMC leads to excessive control signal oscillations and limits practical application.

Purpose of the Study:

  • To develop a novel discretization method for NTSMC that suppresses numerical chattering.
  • To preserve the finite-time convergence properties of NTSMC in a discrete-time setting.
  • To enhance the digital implementation feasibility of NTSMC.

Main Methods:

  • An implicit Euler discretization approach was employed, combined with polynomial reformulation and signum-projection equivalence.
  • Discrete Lyapunov analysis was used to rigorously prove finite-time convergence and first-order accuracy.
  • Comparative simulations and hardware experiments on a Permanent Magnet Synchronous Motor (PMSM) were conducted.

Main Results:

  • The proposed implicit Euler discretization effectively suppressed numerical chattering.
  • Finite-time convergence and first-order accuracy were mathematically established.
  • Hardware experiments demonstrated a 24-fold reduction in steady-state error and achieved 0.083° accuracy with a 6.35 μs computation time at 2 kHz control frequency.

Conclusions:

  • The implicit Euler discretization provides a viable solution for implementing NTSMC in digital systems.
  • The method offers superior performance compared to explicit discretization techniques, enabling larger sampling periods.
  • This advancement facilitates the practical application of NTSMC in high-performance động cơ control systems.