Explicit Output Feedback Stabilization of a Thermal Convection Loop by Continuous Backstepping and Singular Perturbations

An output feedback feedback boundary control law that stabilizes fluid flow in a 2D thermal convection loop is presented. The fluid is enclosed between two cylinders, heated from above and cooled from below, which makes its motion unstable for a large enough Rayleigh number. We consider a collocated setup, with actuation and measurements located at the outer boundary. Actuation is through rotation (direct velocity actuation) and heat flux (heating or cooling) of the outer cylinder, while measurements of friction and temperature are available at the same boundary. The design is based on a combination of singular perturbation theory and backstepping output feedback control design for parabolic PDEs. Stability is proved by Lyapunov method. Though only a linearized version of the plant is considered in the design, an extensive closed loop simulation study of the nonlinear model shows that the result holds for reasonably large initial conditions. A highly accurate approximation to the control and observer output injection kernels is found in closed form.