Optimal robust fractional order PI^λD controller synthesis for first order plus time delay systems.

Area of Science:

• Control Engineering
• Automation Systems
• Process Control

Background:

• First-order plus time-delay (FOPTD) processes are common in industrial applications.
• Existing control methods often struggle to balance robustness and optimal dynamic performance.
• Fractional order (FO) control offers potential for improved system regulation.

Purpose of the Study:

• To develop a systematic tuning procedure for an optimal robust fractional order PIλD (FOPIλD) controller.
• To enhance control performance for FOPTD processes by integrating frequency-domain and time-domain specifications.
• To demonstrate the superiority of the proposed FOPIλD controller over existing methods.

Main Methods:

• A practical tuning procedure combining frequency-domain (FD) specifications (phase margin, gain crossover frequency, flat phase constraint) and time-domain (TD) specifications (integral of time multiplied absolute error - JITAE).
• Synthesis scheme to obtain and visualize feasible regions for FD specifications (ωgc and PM) in 3D plots.
• Extensive simulations on delay-dominant, lag-dominant, and high-order systems with a zero.

Main Results:

• The proposed FOPIλD controller achieves optimal robust performance by balancing stability, robustness to gain variations, and dynamic response.
• Visualized feasible regions provide valuable prior knowledge for controller design.
• Simulations show significant performance improvements of the FOPIλD controller compared to FOPI, FOPID (Ziegler-Nichols, fractional filter), and SIMC-PI controllers.

Conclusions:

• The proposed tuning procedure offers a practical and systematic approach to designing optimal robust FOPIλD controllers for FOPTD processes.
• The FOPIλD controller demonstrates superior performance, particularly for challenging systems like those with significant time delays.
• This work provides a robust and efficient control solution for a wide range of industrial processes.