Digital PI-PD controller design for arbitrary order systems: Dominant pole placement approach

Area of Science:

• Control Systems Engineering
• Digital Control Theory

Background:

• Achieving precise transient response in complex systems, especially those with time delays, remains a challenge in control engineering.
• Existing methods for digital controller design may not universally address arbitrary order systems.

Purpose of the Study:

• To propose a novel digital PI-PD controller design methodology.
• To enable desired transient response in arbitrary order systems, including those with time delays, using dominant pole placement.

Main Methods:

• The design problem is reformulated as a digital PID controller design problem.
• Dominant pole locations are parameterized, and Chebyshev polynomials are used to ensure stability by placing other poles away from the dominant pair.
• PID controller parameters are transformed into PI-PD controller parameters by considering the closed-loop zero.

Main Results:

• The proposed method successfully designs digital PI-PD controllers for arbitrary order systems with and without time delays.
• Simulations on an example transfer function show comparable or superior performance to existing PID methods.
• Real-world implementation on a fan and plate laboratory system validates the method's effectiveness.

Conclusions:

• The presented digital PI-PD controller design method offers a robust solution for achieving desired transient responses in complex systems.
• The conversion to a PID design problem simplifies the controller synthesis for PI-PD controllers.
• The method's practical applicability is confirmed through experimental validation.