Design of a Complex fractional Order PID controller for a First Order Plus Time Delay system

Area of Science:

• Control Systems Engineering
• Advanced Control Theory

Background:

• Real fractional Order PID (ROPID) controllers have limitations due to restricted parameter intervals.
• These limitations can prevent control systems from meeting precise design specifications.

Purpose of the Study:

• To introduce and analyze the Complex fractional Order PID (COPID) controller.
• To overcome the inherent limitations of ROPID controllers.
• To demonstrate the enhanced performance of COPID controllers in achieving accurate control system design.

Main Methods:

• Analysis and design of the COPID controller.
• Comparative design of both ROPID and COPID controllers for a First Order Plus Time Delay (FOPTD) system (low pressure flowing water circuit).
• Frequency domain design specifications including gain crossover frequency, phase margin, and robustness against gain variation were used.

Main Results:

• COPID controllers demonstrated superior accuracy in achieving design specifications compared to ROPID controllers, especially under rigorous conditions.
• The COPID controller successfully addressed the limitations of ROPID controllers in satisfying hard design specifications.
• Accurate achievement of frequency domain specifications was confirmed for the COPID controller.

Conclusions:

• The COPID controller, by incorporating complex orders, provides a more capable alternative to ROPID controllers.
• COPID controllers offer enhanced accuracy and robustness for control systems, particularly for challenging design requirements.
• The study validates the effectiveness of COPID controllers in achieving precise control system performance.