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Non-Predictive Model-Free Control of Nonlinear Systems with Unknown Input Time Delay.

Quanmin Zhu1, Jianhua Zhang2, Weicun Zhang3

  • 1School of Engineering, University of the West of England, Coldharbour Lane, Bristol BS16 1QY, UK.

Entropy (Basel, Switzerland)
|July 29, 2023
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Summary
This summary is machine-generated.

This study introduces a control framework for unknown dynamic systems with input delay. It offers a simple output feedback controller with stability analysis, ensuring reliable performance for linearizable nonlinear systems.

Keywords:
input delay systemslow complexity controllerlow gain controlnon-predictive and model-free controlstabilization

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Area of Science:

  • Control Systems Engineering
  • Dynamic Systems Analysis
  • Nonlinear Control Theory

Background:

  • Controlling unknown dynamic systems with input delays presents significant challenges.
  • Existing methods often require complex models or extensive computations.
  • A need exists for robust and computationally efficient control strategies.

Purpose of the Study:

  • To develop a general framework for controlling unknown dynamic systems with unknown input delay.
  • To design a concise output feedback control system with tunable stabilization and dynamic response.
  • To provide rigorous stability analysis methods for the proposed control system.

Main Methods:

  • Structuring a concise output feedback control system with low feedback gain for stabilization and high feedforward gain for steady-state error removal.
  • Proposing a gain/phase margin theorem for stability analysis based on feedback gain regulation.
  • Presenting a stability theorem using rational function approximation for time delays to handle transcendental characteristic equations.

Main Results:

  • The proposed control framework effectively manages unknown dynamic systems with unknown input delay.
  • Two distinct stability analysis methods yield coherent results, validating the control system's robustness.
  • The controller's low complexity simplifies implementation without sacrificing performance.
  • Applicability to linearizable nonlinear systems is demonstrated.

Conclusions:

  • The developed framework provides a practical and effective solution for controlling complex dynamic systems.
  • The proposed stability analysis methods offer reliable tools for system verification.
  • The controller's simplicity and performance make it suitable for various engineering applications.