Robust PID Controllers With Measurement Filters for Arbitrary-Order Uncertain Time-Delay Systems

Abstract

This paper presents a new methodology for the design of PID controllers based on linear matrix inequalities (LMIs). The proposed method can be applied to arbitrary-order SISO time-delay systems. The core of the approach relies on an innovative state-space control architecture that enables the integration of arbitrary-order systems with PI/PID controllers combined with different measurement noise filters, or alternatively, with a pure PI controller. The methodology allows the consideration of multiple design objectives, including disturbance rejection, reference tracking, measurement noise attenuation, the imposition of an exponential decay rate, the guarantee of positive PID controller gains, and robustness margins in the frequency domain, by imposing upper bounds on the ${\mathscr {H}}_{\infty }$ norm of the main sensitivity functions. Moreover, the approach explicitly accounts for parametric uncertainties. For validation, numerical examples were carried out ranging from low-order to higher-order models, combining different controller structures and multiple objectives simultaneously. The results were compared with recent and relevant methods from the literature, demonstrating the effectiveness and superiority of the proposed methodology.