Robust Output Regulation of Thermal Fluid Flows

In this thesis, we consider control of fluids from the perspective of mathematical systems theory by studying mathematical models which describe evolution of velocity and temperature of fluids. The models consist of at least one partial differential equation and in some cases also include ordinary differential equations and can be used to describe temperature and velocity properties related to for example heating, ventilation and air conditioning (HVAC). Our goal is to design automatic controllers that are based on properties of the fluid models and ensure that, given time, certain measured temperature or velocity quantities of the model behave as desired.

Throughout this thesis we focus on practical implementability of the proposed controller designs, since that cannot be taken as granted especially for models including partial differential equations. We design error feedback controllers, based on the so-called internal model principle, for robust output regulation of linear and nonlinear thermal fluid flow models and illustrate the controllers’ performance using numerical simulations. The error feedback controllers operate based on measurements of fluid temperature or velocity at some parts of the spatial domain, and robustness means that the controllers reject disturbances and tolerate model uncertainties in addition to forcing the measured quantity to a desired sinusoidal trajectory given time.

The main contribution of this thesis comes from our focus on robust output regulation using error feedback controllers. For the considered thermal fluid flow models, the existing control solutions focus on the problem of stabilization or use state feedback controllers. That is, the controllers of this thesis have the advantages of error feedback compared to state feedback and robustness of the achieved output regulation.