Sensor location in a controlled thermal fluid

We investigate different criteria for locating sensors for the state estimation in a controlled thermal fluid modeled by the Boussinesq equations. This paper focuses on the linearized Boussinesq equation. We combine optimal sensor location with observer design to obtain a sensor placement. One way to locate sensors is to minimize the covariance of the estimation error. Another way is based on the geometric structure of the feedback functional gain. The controllers are finite dimensional and act on a portion of the boundary through Neumann/Robin boundary conditions. Dirichlet boundary conditions are imposed on the rest of the boundary. A lower order observer is constructed by using the LQG balanced truncation for the linearized controlled system. Computer simulations are presented to compare the effectiveness of different sensor locations.