Universal block diagram based modeling and simulation schemes for fractional-order control systems

Area of Science:

• Control Systems Engineering
• Computational Mathematics

Background:

• Fractional-order control systems offer enhanced performance but pose modeling challenges.
• Existing simulation methods can be complex and computationally intensive.

Purpose of the Study:

• To develop universal block diagram based schemes for modeling and simulating fractional-order control systems.
• To provide efficient methods for handling both zero and nonzero initial conditions.

Main Methods:

• Designed a fractional operator block in Simulink for fractional-order derivatives and integrals.
• Developed a compensation scheme using auxiliary signals for nonzero initial conditions.
• Proposed an integrator chain scheme to simplify modeling procedures.

Main Results:

• The proposed schemes effectively model fractional-order control systems with zero initial conditions.
• The integrator chain scheme simplifies modeling for nonzero initial conditions.
• Demonstrated efficiency and accuracy for various Caputo fractional-order ordinary differential equations (FODEs), including implicit forms.

Conclusions:

• The universal block diagram schemes are accurate and effective for simulating fractional-order control systems.
• These methods provide an efficient approach for handling complex FODEs with different initial conditions.