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

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.

Robust Output Regulation of the Linearized Boussinesq Equations with Boundary Control and Observation

“…Examples of output tracking without robustness and based on state feedback have been considered in [1]. Additionally, robust output tracking for a simplified room model with only temperature dynamics and in-domain control and observation has been studied in [22]. Finally, addition of the actuator dynamics for classes of linear systems has previously been considered in [10,8,25].…”