Application of an infinite-dimensional observer for drilling systems incorporating kick and loss detection

We apply a PDE observer to a hydraulic system to detect and quantify an in- or outflux. We show that the PDE model of the hydraulic system can be expressed as a 2×2 linear hyperbolic system of PDEs with spatially varying coefficients coupled with an ODE at the inlet boundary that models the in- or outflux. Using the method of backstepping, we design an observer which is exponentially stable at the origin in the ℒ²-norm while relying on measurements taken at the outlet boundary, only. Simulation results verify the validity of the observer.