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Analytical fractional PID controller design based on Bode's ideal transfer function plus time delay.

Erhan Yumuk1, Müjde Güzelkaya1, İbrahim Eksin1

  • 1Istanbul Technical University, Department of Control and Automation Engineering, Maslak, 34469, Istanbul, Turkey.

ISA Transactions
|February 11, 2019
PubMed
Summary

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A new fractional order PID controller with a fractional filter improves control for higher-order processes. This method offers superior performance in frequency and time domains compared to existing techniques.

Area of Science:

  • Control Systems Engineering
  • Applied Mathematics

Background:

  • Higher-order processes often present significant control challenges.
  • Traditional PID controllers may struggle with complex system dynamics and time delays.

Purpose of the Study:

  • To propose a novel fractional order PID controller cascaded with a fractional filter for enhanced control of higher-order processes.
  • To develop an analytical design methodology for determining controller parameters based on frequency domain specifications.

Main Methods:

  • Representing higher-order system transfer functions using reduced fractional order plus time delay models.
  • Employing a unity feedback reference model with Bode's ideal loop transfer function and fractional order time delay.
  • Deriving empirical formulas for time domain characteristics from frequency domain specifications and model time delay.
Keywords:
Bode’s ideal loop transfer functionFractional order PID controllersFrequency domain designReduced fractional order modelsTime delay

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Main Results:

  • The proposed fractional order PID controller demonstrates significantly improved performance over existing methodologies.
  • Accurate empirical formulas for time domain characteristics were derived and validated through simulations.
  • The controller exhibits excellent iso-damping, noise attenuation, and load disturbance suppression capabilities.

Conclusions:

  • The proposed fractional order PID controller cascaded with a fractional filter is an effective solution for controlling higher-order processes.
  • The analytical design methodology provides a systematic approach to achieving desired frequency and time domain specifications.
  • This approach offers a robust and high-performing alternative to conventional control strategies.