Robust Output Tracking for a Room Temperature Model with Distributed Control and Observation

TL;DR

This paper develops a finite-dimensional controller for robust temperature regulation in a room modeled by coupled Navier-Stokes and advection-diffusion equations, using model reduction and finite element methods.

Contribution

It introduces a low-order controller based on model reduction for robust output regulation of a coupled PDE system with distributed control and observation.

Findings

Reduced-order controller performs comparably to full model controller.

Model reduction enhances computational efficiency.

Controller effectively manages disturbances on boundary.

Abstract

We consider robust output regulation of a partial differential equation model describing temperature evolution in a room. More precisely, we examine a two-dimensional room model with the velocity field and temperature evolution governed by the incompressible steady state Navier-Stokes and advection-diffusion equations, respectively, which coupled together form a simplification of the Boussinesq equations. We assume that the control and observation operators of our system are distributed, whereas the disturbance acts on a part of the boundary of the system. We solve the robust output regulation problem using a finite-dimensional low-order controller, which is constructed using model reduction on a finite element approximation of the model. Through numerical simulations, we compare performance of the reduced-order controller to that of the controller without model reduction as well as to performance of a low-gain robust controller.