Abstract
We study a 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 cascade. As the main contribution, we design a low-dimensional internal model-based controller for robust output tracking of the room model. The controller’s performance is demonstrated through a numerical example.
Highlights
We consider fluid temperature and velocity control for a two-dimensional room model
The Boussinesq equations are a system of partial differential equations coupling the fluid flow dynamics given by the incompressible Navier–Stokes
We studied robust temperature and velocity output tracking of a two-dimensional room model with the fluid dynamics governed by the linearized Boussinesq equations
Summary
We consider fluid temperature and velocity control for a two-dimensional room model. In the model, behavior of the fluid within the room is described by the linearized Boussinesq equations. The controller is based on the internal model principle, see [17,19,35], and has several desirable properties It can be used in control of unstable systems, which is essential for this paper due to the fact that the linearized Boussinesq equations may be unstable [12] (depending on the room geometry and physical parameters). Robust output tracking for a simplified room model with only temperature dynamics and in-domain control and observation has been studied in [27]. 4, we present a numerical example of robust output tracking for the boundary controlled linearized Boussinesq equations with a mix of boundary and in-domain observations and including actuator and sensor dynamics. ·, · Ω and ·, · Γ denote the L2-inner product or duality pairing on the two-dimensional domain Ω and on the one-dimensional domain Γ , respectively
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
