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An integer order approximation method based on stability boundary locus for fractional order derivative/integrator

Furkan Nur Deniz1, Baris Baykant Alagoz1, Nusret Tan1

  • 1Inonu University, Department of Electrical and Electronics Engineering, Turkey.

ISA Transactions
|February 16, 2016
PubMed
Summary
This summary is machine-generated.

This study presents an integer order approximation method for fractional order operators in control systems. The stability boundary locus (SBL) fitting ensures stability preservation in approximate models.

Keywords:
Fractional order control systemFractional order operatorsInteger order approximationStability boundary locus

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Area of Science:

  • Control Systems Engineering
  • Numerical Methods
  • Systems Approximation

Background:

  • Fractional order calculus offers advanced modeling capabilities for complex systems.
  • Numerical implementation of fractional order operators in control systems presents challenges.
  • Stability analysis is crucial for feedback control system design.

Purpose of the Study:

  • To introduce an integer order approximation method for fractional order derivative/integrator operators.
  • To ensure stability preservation in the numerical implementation of fractional order control systems.
  • To provide a straightforward method for approximating fractional order systems with integer order models.

Main Methods:

  • The proposed method involves fitting the stability boundary locus (SBL) of fractional order operators with SBL of integer order transfer functions.
  • Matching SBL curves in a limited frequency range allows for accurate approximation.
  • The method is validated through illustrative examples and comparison with existing approximation techniques.

Main Results:

  • The SBL fitting method effectively approximates fractional order operators and systems using integer order models.
  • The proposed approach successfully preserves the stability of the approximated models.
  • Performance is demonstrated through examples, including the approximation of fractional order PID controllers.

Conclusions:

  • The stability boundary locus fitting method provides a robust and effective way to obtain integer order approximations of fractional order systems.
  • This method facilitates the numerical implementation of fractional order control strategies by ensuring stability.
  • The approach is applicable to various control applications, including fractional order PID controllers.