Reduced-order Smith predictor for state feedback control with guaranteed stability

TL;DR

This paper introduces a reduced-order Smith predictor for state feedback control that guarantees stability through Lyapunov-based conditions, simplifying implementation with a dynamic controller approach.

Contribution

It proposes a novel dynamic controller implementation of the Smith predictor with stability guarantees using LMIs, improving upon traditional integral approximation methods.

Findings

Stability conditions derived via Lyapunov functionals and LMIs.

Demonstrated effectiveness through three literature-based examples.

Enhanced control law implementation with reduced complexity.

Abstract

This article deals with the implementation of the Smith Predictor for state feedback control in state space representation. The desired control law, obtained using partial differential equations and backstepping control, contains an integral term that has to be approximated for implementation. In this article, we propose a new way to implement this control law using a dynamic controller. The control law is composed of a state feedback term and a dynamic term that approaches the integral term that has to be estimated for implementation. Using a Lyapunov functional, we provide sufficient conditions, in terms of a linear matrix inequality, to guarantee that the closed-loop system is stable when the proposed control law is applied. We use three examples, taken from the literature, to show the benefits of the proposed approach.