Frequency frame approach on loop shaping of first order plus time delay systems using fractional order PI controller.

Area of Science:

• Control Systems Engineering
• Automation and Process Control
• Fractional Order Systems

Background:

• First order plus time delay (FOPTD) systems are common in industrial processes.
• Designing effective controllers for FOPTD systems, especially with fractional order controllers, presents challenges in achieving stability and performance.
• Existing methods may not fully address the robustness requirements for these systems.

Purpose of the Study:

• To propose an analytical design method for fractional order proportional integral (FOPI) controllers specifically for FOPTD systems.
• To develop general computation equations for tuning FOPI controllers to meet desired frequency and phase properties.
• To introduce and utilize the concept of a
• frequency frame
• to enhance system robustness and stability.

Main Methods:

• Derivation of analytical design equations for FOPI controllers.
• Tuning controller parameters based on specified frequency and phase characteristics within the Bode plot.
• Application of the
• frequency frame
• concept to manipulate gain and phase crossover frequencies for improved robustness.

Main Results:

• The designed FOPI controllers ensure system stability for FOPTD systems.
• The proposed method positively impacts system performance and robustness.
• The
• frequency frame
• concept provides a quantifiable way to improve control system robustness by adjusting its boundaries.

Conclusions:

• The analytical design method offers a systematic approach to designing FOPI controllers for FOPTD systems.
• The
• frequency frame
• concept is a valuable tool for enhancing the robustness and stability of control systems.
• The method is validated through illustrative examples, demonstrating its practical applicability and advantages.