Fractional-Order Robust Control Design under parametric uncertain approach.

Area of Science:

• Control Engineering
• System Dynamics
• Applied Mathematics

Background:

• Linear time-invariant uncertain systems require advanced control strategies for optimal performance.
• Traditional robust control methods may not fully address the complexities of fractional-order dynamics and parametric uncertainty.
• Enhancing transient and steady-state responses in closed-loop systems remains a key challenge.

Purpose of the Study:

• To develop and validate a novel Fractional-Order Robust Control (FORC) methodology.
• To improve the performance and robustness of uncertain linear time-invariant systems, including fractional-order ones.
• To facilitate the digital implementation and hardware deployment of advanced fractional-order controllers.

Main Methods:

• Combining fractional-order control theory with robust control under parametric uncertainty.
• Utilizing a novel formulation of inequalities-based design for linear programming optimization.
• Employing impulse response invariant discretization of fractional-order differentiators (IRID-FOD) for digital implementation.
• Applying Hankel's reduction order method for hardware suitability.

Main Results:

• Designed fractional-order controllers guarantee desired transient and steady-state performance.
• The FORC methodology demonstrates improved and robust performance compared to classical robust control.
• Experimental validation on a thermal system confirms the effectiveness of the proposed approach.

Conclusions:

• The FORC methodology offers a significant advancement in controlling uncertain systems with fractional dynamics.
• The proposed design and discretization techniques enable practical digital implementation of robust fractional-order controllers.
• FORC provides superior performance and robustness, validated through experimental assessments.