Efeito de Sensores Dinâmicos de Primeira Ordem no Controle H-infinito de Sistemas Contínuos

Abstract

This work investigates H-infinite controller design for a fourth-order linear plant subject to disturbances, emphasizing the influence of first-order sensor dynamics. The theoretical framework relies on the Bounded Real Lemma and the LMI formulation obtained via the change of variables, enabling convex synthesis of state-feedback gains that guarantee asymptotic stability. The main contribution contrasts gains synthesized under the ideal assumption of direct state feedback with their practical implementation when control is applied to filtered measurements. This discrepancy is analyzed by forming the augmented system that explicitly includes sensor dynamics, deriving and studying the augmented characteristic polynomial, and checking stabilizability and LMI feasibility on the augmented model. Numerical synthesis and algebraic checks performed in Python, together with closed-loop simulations in Xcos/Scilab, show that controllers designed without accounting for sensor dynamics can destabilize the implemented system. The practical outcome is clear: when control acts on filtered outputs, controller synthesis must include the sensor model or be complemented by a state observer; proper scaling and numerical regularization are essential for reliable results.