Finite-dimensional observer-based PI regulation control of a reaction-diffusion equation

TL;DR

This paper presents a boundary control method combining a finite-dimensional observer and a PI controller to achieve setpoint regulation of reaction-diffusion systems, including unstable plants, with explicit criteria for observer order.

Contribution

It introduces a novel boundary control strategy using a finite-dimensional observer coupled with a PI controller for reaction-diffusion equations, providing explicit criteria for observer order selection.

Findings

Achieves stabilization and regulation of reaction-diffusion systems.

Provides explicit criteria for observer order selection.

Applicable to systems with Dirichlet and Neumann boundary outputs.

Abstract

This paper investigates the output feedback setpoint regulation control of a reaction-diffusion equation by means of boundary control. The considered reaction-diffusion plant may be open-loop unstable. The proposed control strategy consists of the coupling of a finite-dimensional observer and a PI controller in order to achieve the boundary setpoint regulation control of various system outputs such as the Dirichlet and Neumann traces. In this context, it is shown that the order of the finite-dimensional observer can always be selected large enough, with explicit criterion, to achieve both the stabilization of the plant and the setpoint regulation of the system output.