Stabilizing regions of dominant pole placement for second order lead processes with time delay using filtered PID...

Area of Science:

• Control Engineering
• Systems Theory
• Applied Mathematics

Background:

• Time-delayed systems present significant control challenges.
• Traditional PID controller design often relies on approximations for time delays.
• Accurate discretization of continuous-time systems is crucial for digital implementation.

Purpose of the Study:

• To develop a novel filtered PID controller design method for second-order-plus-time-delay (SOPTDZ) systems.
• To avoid finite term approximations (e.g., Pade) in handling time delays.
• To provide an accurate discretization approach for both the system and the controller.

Main Methods:

• Pole-zero matching discretization for continuous-time SOPTDZ systems.
• Pole-zero matching for discretizing the filtered PID controller.
• Coefficient matching approach for deriving discrete-time controller analytical expressions.
• Particle Swarm Optimization (PSO) for approximating the stabilizable region.

Main Results:

• A unique filtered PID controller design based on dominant pole placement is presented.
• The method accurately converts transcendental time delay terms into finite poles.
• Analytical expressions for discrete-time controllers are derived for real and complex non-dominant poles.
• The approach is validated on stable, integrating, and unstable SOPTDZ systems.

Conclusions:

• The proposed method offers an effective way to design filtered PID controllers for SOPTDZ systems.
• Accurate discretization without approximations simplifies controller design and improves performance.
• The validated results demonstrate the method's robustness across various system types.