Fractional-Order Robust Control Design under parametric uncertain approach

Abstract

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.