Projeto de controle robusto de ordem fracionária para sistemas com incerteza paramétrica

Abstract

This research introduces a novel methodology that integrates fractional-order control theory with robust control techniques to address parametric uncertainty, aimed at enhancing the performance of linear time-invariant uncertain systems with integer or fractional orders, referred to as Fractional-Order Robust Control (FORC). Unlike traditional methods, this proposed approach offers a new formulation of inequalitiesbased design, broadening the scope for discovering improved solutions through linear programming optimization. Consequently, fractional-order controllers are tailored to ensure desired transient and steady-state performance in closed-loop systems. In order to facilitate the digital implementation of the designed controller, the impulse response invariant discretization of fractional-order differentiators (IRID-FOD) is used to approximate fractional-order controllers to integer-order transfer functions. Additionally, the Hankel reduction order method is applied, making the controllers suitable for hardware deployment. Experimental tests conducted on a thermal system, along with assessment results based on time-domain responses and robustness analysis supported by performance indices and set value analysis, demonstrate the enhanced and robust performance of the proposed FORC methodology compared to classical robust control under parametric uncertainty.