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

TL;DR

This paper develops a low-dimensional internal model based controller for robustly tracking temperature and velocity outputs in a 2D room model governed by linearized Boussinesq equations, integrating PDE and ODE dynamics.

Contribution

It introduces a novel controller design for a coupled PDE-ODE system with finite-dimensional actuation and sensing, ensuring robustness in output regulation.

Findings

Controller successfully tracks temperature and velocity outputs.

Numerical example demonstrates effectiveness of the control strategy.

Robustness of the approach is validated through simulations.

Abstract

We study temperature and velocity output tracking problem for a two-dimensional room model with the fluid dynamics governed by the linearized translated Boussinesq equations. Additionally, the room model includes finite-dimensional models for actuation and sensing dynamics, thus the complete model dynamics are governed by an ODE-PDE-ODE system. As the main result, we design a low-dimensional internal model based controller for robust output racking of the room model. Efficiency of the controller is demonstrated through a numerical example of velocity and temperature tracking.