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Area of Science:

  • Control Theory
  • Fractional Calculus
  • Nonlinear Systems

Background:

  • Active Disturbance Rejection Control (ADRC) is effective for systems with uncertainties.
  • Fractional-order systems present unique modeling and control challenges.
  • Existing ADRC methods may require complex adaptations for fractional-order dynamics.

Purpose of the Study:

  • To adapt the Active Disturbance Rejection Control (ADRC) method for commensurate fractional-order systems.
  • To develop a simplified ADRC approach for handling unmodeled dynamics, external disturbances, and parameter uncertainty.
  • To validate the proposed control strategy through numerical analysis and experimental implementation.

Main Methods:

  • Developed a fractional-order ADRC with a single active cancellation mechanism.
  • Simplified the system dynamics to an appropriate commensurate fractional order.
  • Designed a linear observer-based controller to estimate the unified disturbance.
  • Performed numerical stability analysis to determine error bounds.
  • Conducted experimental validation using approximate analog implementations.

Main Results:

  • The proposed fractional-order ADRC effectively estimates and cancels lumped disturbances.
  • Numerical analysis provided quantifiable tracking and estimate error bounds.
  • The control strategy demonstrated successful experimental validation in both linear and nonlinear fractional-order systems.
  • The observer-based controller design offers practical guidelines for parameter configuration.

Conclusions:

  • The adapted fractional-order ADRC offers a simplified and effective control solution for systems with unmodeled dynamics and disturbances.
  • The observer-based design ensures stability and provides accurate disturbance estimation.
  • Experimental results confirm the robustness and applicability of the proposed method in real-world fractional-order control scenarios.