Classical controller design techniques for fractional order case.

Area of Science:

• Control Systems Engineering
• Applied Mathematics

Background:

• Fractional-order systems present unique challenges in classical controller design.
• Robust performance is crucial for control systems operating with uncertain parameters.

Purpose of the Study:

• To propose novel robust controller design methods for fractional-order interval transfer functions (FOITFs).
• To ensure robust performance specifications are met for fractional-order interval plants.
• To develop a classical PID controller design technique using fractional-order reference models.

Main Methods:

• Utilizing classical design methods with Bode envelopes of FOITFs for lag, lag-lead, and PI controllers.
• Employing an optimization technique based on a fractional-order reference model for PID controller design.
• Applying the least squares optimization method to obtain PID controller parameters.

Main Results:

• Successfully designed robust lag, lag-lead, and PI controllers for FOITFs.
• Demonstrated that the proposed controllers meet robust performance specifications for fractional-order interval plants.
• Obtained multiple stable PID controller parameter sets for the same plant using the optimization method.

Conclusions:

• The proposed classical controller design techniques are effective for fractional-order interval systems.
• The methods ensure robust performance and stability in the presence of plant uncertainty.
• The optimization approach provides a viable way to design stable PID controllers for fractional-order plants.