Fractional-order PI plus D controller for second-order integrating plants: Stabilization and tuning method

Area of Science:

• Control Engineering
• Systems Theory
• Robotics

Background:

• Second-order integrating plants present control challenges due to inherent instability.
• Existing control strategies may offer limited stability regions and robustness.

Purpose of the Study:

• To propose a novel fractional-order PI plus D (PI^λ-D) controller structure.
• To enhance the stability region and robustness of second-order integrating systems.
• To develop a method for calculating optimal controller parameters.

Main Methods:

• Design of a feedback controller to strategically place integrating poles.
• Derivation of explicit formulae for the complex root boundary (CRB) with fractional integrators.
• Application of a stabilizing approach to constrain optimal controller parameter calculation.
• Validation through numerical simulations and hardware experiments on a quadrotor's altitude control system.

Main Results:

• The proposed PI^λ-D controller significantly improves the stability region of the control system.
• Explicit formulae for CRB enable precise calculation of optimal controller parameters.
• Numerical and experimental results demonstrate enhanced performance and robustness compared to existing methods.

Conclusions:

• The fractional-order PI^λ-D controller offers a superior approach for controlling second-order integrating plants.
• The method provides a systematic way to achieve robust and stable control.
• The quadrotor altitude control application validates the practical effectiveness of the proposed technique.