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Robust adaptive sliding mode control for uncertain systems with unknown time-varying delay input.

Anouar Benamor1, Hassani Messaoud1

  • 1Laboratory of Automatic Signal and Image Processing, National School of Engineers of Monastir, University of Monastir, 5019, Tunisia.

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Summary

This study introduces robust adaptive sliding mode control (RASMC) for uncertain discrete systems with unknown delays. The novel control law estimates uncertainties, ensuring system stability and performance.

Keywords:
Adaptive controlLMIRobust controlSliding mode controlUncertain discrete-time systemUnknown delayVarying delay

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Area of Science:

  • Control Systems Engineering
  • Applied Mathematics
  • Robotics

Background:

  • Discrete systems with uncertainties and time-varying delays present significant control challenges.
  • Existing robust sliding mode control (RSMC) methods often require knowledge of uncertainty bounds.

Purpose of the Study:

  • To develop a robust adaptive sliding mode control (RASMC) law for uncertain discrete systems with unknown time-varying delays.
  • To address systems where the upper bound of uncertainty is unknown.

Main Methods:

  • Derivation of a new sliding surface using Linear Matrix Inequalities (LMIs).
  • Proposal of a novel Robust Sliding Mode Control (RSMC) assuming known uncertainty bounds.
  • Development of a Robust Adaptive Sliding Mode Control (RASMC) by estimating unknown uncertainty bounds.

Main Results:

  • The proposed RASMC law effectively estimates unknown uncertainty bounds.
  • The control law ensures convergence to zero on the sliding surface.
  • Simulations on an uncertain numerical system demonstrated good performance and comparative advantages.

Conclusions:

  • The developed RASMC provides a robust and effective control solution for uncertain discrete systems with unknown time-varying delays.
  • Validation on physical systems (PT326 process trainer, two-tank hydraulic system) confirms the practical applicability and efficiency of the proposed control approach.