Optimal disturbance rejection for PI controller with constraints on relative delay margin.

Area of Science:

• Process Control Engineering
• Robust Control Theory
• System Stability Analysis

Background:

• Performance optimization with robustness constraints is a common challenge in process control.
• Conventional robustness indices, like maximum sensitivity, present analytical difficulties.
• Simpler robust analysis methods are needed for effective controller design.

Purpose of the Study:

• Introduce the relative delay margin as a more accessible robustness measure.
• Demonstrate its utility in designing optimal proportional-integral (PI) controllers for first-order-plus-dead-time (FOPDT) models.
• Provide a simpler procedure for stability analysis and robustness assessment.

Main Methods:

• Derive PI controller parameters analytically using phase margin and gain crossover frequency.
• Obtain the PI controller stability region using a simplified procedure.
• Formulate and solve an optimal disturbance rejection problem with relative delay margin constraints.

Main Results:

• The relative delay margin simplifies robust analysis and controller design.
• A new, simpler method for determining the PI controller stability region is presented.
• The proposed methodology, utilizing relative delay margin, shows superior performance in disturbance rejection compared to existing PI tuning rules.
• Relative delay margin contours are easier to sketch than those using maximum sensitivity.

Conclusions:

• The relative delay margin is a promising and effective measure for robustness analysis and controller design.
• This approach simplifies complex robust control problems, especially for FOPDT systems.
• The proposed PI controller tuning offers improved performance and robustness, applicable to advanced control strategies.