Calculation of robustly relatively stabilizing PID controllers for linear time-invariant systems with unstructured...

Area of Science:

• Control Systems Engineering
• Robust Control Theory
• System Identification

Background:

• Proportional-Integral-Derivative (PID) controllers are widely used in industrial control systems.
• Designing PID controllers for systems with unstructured uncertainty remains a challenge.
• Robust stability and robust relative stability are critical performance metrics.

Purpose of the Study:

• To develop a method for calculating all robustly relatively stabilizing PID controllers for Linear Time-Invariant (LTI) systems with unstructured uncertainty.
• To visualize the regions of robustly stabilizing and robustly relatively stabilizing PID controllers in the P-I-D parameter space.
• To demonstrate the practical applicability of the proposed method through simulations and experimental validation.

Main Methods:

• The method involves plotting an envelope of P-I-D parameter combinations that satisfy robust stability conditions.
• Robust stability and relative stability conditions are formulated using the H_∞ norm.
• The technique is applied to LTI systems with unstructured multiplicative and additive uncertainty.

Main Results:

• The study successfully obtains regions of robustly stabilizing and robustly relatively stabilizing PID controllers in the P-I-D parameter space.
• The method is demonstrated on a controlled plant model with different types of unstructured uncertainty.
• The technique's effectiveness is verified on a real hot-air tunnel laboratory model.

Conclusions:

• The presented method provides a comprehensive approach to designing robust PID controllers for uncertain LTI systems.
• The graphical representation of controller parameter regions aids in selecting suitable PID controllers.
• The validation on a physical system confirms the practical utility of the developed technique for robust controller design.