Efficient method for time-domain simulation of the linear feedback systems containing fractional order controllers.

Area of Science:

• Control Systems Engineering
• Applied Mathematics
• System Simulation

Background:

• Time-domain simulation of linear output-feedback systems with fractional-order controllers often uses integer-order approximations.
• Existing approximation methods may compromise internal stability and lack precise error quantification.

Purpose of the Study:

• To propose an efficient time-domain simulation method for fractional-order systems.
• To address the drawbacks of internal instability and unknown approximation error in current approaches.

Main Methods:

• Approximating fractional-order controllers with integer-order transfer functions, potentially including a delay term.
• Ensuring internal stability of the closed-loop system during approximation.
• Developing formulas for estimating and correcting simulation errors under specific input conditions.

Main Results:

• The proposed method guarantees internal stability of the feedback system.
• The approximate controller is shown to be effectively realizable.
• Formulas for simulation error estimation and correction are presented.

Conclusions:

• The developed method offers a robust and accurate approach for time-domain simulation of fractional-order control systems.
• It overcomes key limitations of existing approximation techniques, enhancing simulation reliability.