Boundary observer design for hyperbolic PDE ODE cascade systems
The paper presents an observer design for a class of hyperbolic PDE ODE cascade systems with a boundary measurement. The cascade systems consist of coupled PDEs, featuring one rightward and one leftward convecting first order transport PDEs, and a set of ODEs, which enter the PDEs through the left boundary of the systems. The design, which is based on the Volterra integral transformation, relies only on a single sensor at the right boundary of the system. The observer consists of a copy of the plant plus output injection terms both in the PDEs and the ODEs. The observer is constructed in a collocated setup, which means both sensing and actuation are located at the same boundary. The observer gains are computed analytically by solving Goursat type PDEs in terms of Bessel function of the first kind. The observer design is tested against a field scale flow loop test experiment in Stavanger by Statoil Oil Company. The results show that the observer converges to the actual values and that the design can be used as a process monitoring tool in oil well drilling.
Autom.