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Power mapping-based stability analysis and order adjustment control for fractional-order multiple delayed systems.

Qingbin Gao1, Jiazhi Cai1, Yifan Liu1

  • 1School of Mechanical Engineering and Automation, Harbin Institute of Technology (Shenzhen), Shenzhen, China.

ISA Transactions
|March 9, 2023
PubMed
Summary

This study enhances delay robustness in fractional-order systems using order adjustment control. This method offers greater control flexibility and improved stability for complex systems.

Keywords:
Dixon resultant theoryFractional-order systemsMultiple delaysPower mappingStability analysis

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Area of Science:

  • Control Theory
  • Systems Engineering
  • Applied Mathematics

Background:

  • Fractional-order systems with multiple delays present challenges in stability analysis.
  • Evaluating delay robustness is crucial for practical applications of these systems.

Purpose of the Study:

  • To investigate the asymptotic stability and delay robustness of fractional-order multiple delayed systems.
  • To develop a method for enhancing control flexibility and stability.

Main Methods:

  • Establishing a spectral connection between original and transformed fractional-order systems.
  • Applying the Cluster Treatment of Characteristic Roots paradigm.
  • Utilizing a Dixon resultant-based frequency sweeping framework for stability mapping.

Main Results:

  • A complete stability map was generated.
  • Order adjustment control was shown to significantly improve control flexibility.
  • Unlimited possibilities for enhancing delay robustness were identified.

Conclusions:

  • The proposed methods provide effective tools for analyzing and improving the stability of fractional-order delayed systems.
  • Order adjustment control is a promising strategy for robust system design.
  • The study addresses practical implementation by considering integer-order approximations.