Fractional-Order Robust Control Design under parametric uncertain approach

• Published in: ISA transactions Vol. 153; pp. 420 - 432
• Main Authors: Martins-Gomes, Marcus C., de C. Ayres Junior, Florindo A., da Costa Junior, Carlos T., de Bessa, Iury V., da S. Farias, Nei Junior, de Medeiros, Renan L.P., Silva, Luiz E.S., de Lucena Júnior, Vicente F.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.10.2024
• Subjects: Fractional-order control; Parametric uncertainty; Robust control; Robustness performance; Thermal system; Robust control; Fractional-order control; Parametric uncertainty; Thermal system; Robustness performance
• ISSN: 0019-0578; 1879-2022; 1879-2022
• DOI: 10.1016/j.isatra.2024.07.023

This paper presents a novel methodology that combines fractional-order control theory with robust control under a parametric uncertainty approach to enhance the performance of linear time-invariant uncertain systems with integer or fractional order, referred to as Fractional-Order Robust Control (FORC). In contrast to traditional approaches, the proposed methodology introduces a novel formulation of inequalities-based design, thus expanding the potential for discovering improved solutions through linear programming optimization. As a result, fractional order controllers are designed to guarantee desired transient and steady-state performance in a closed-loop system. To enable the digital implementation of the designed controller, an impulse response invariant discretization of fractional-order differentiators (IRID-FOD) is employed to approximate the fractional-order controllers to an integer-order transfer function. Additionally, Hankel’s reduction order method is applied, thus making it suitable for hardware deployment. Experimental tests carried out in a thermal system and the assessment results, based on time-domain responses and robustness analysis supported by performance indices and set value analysis in a thermal system test-bed, demonstrate the improved and robust performance of the proposed FORC methodology compared to classical robust control under parametric uncertainty. •New method for fractional controllers using Interval poles, improving performance.•Sets region to sweep frequency based on settling time and stability region of α.•Reduces conservativeness, allowing stability changes for flexible performance.•Ensures target with chosen fractional-order controller based on desired actions.