We present a control design for semilinear and quasilinear 2 × 2 hyperbolic partial differential equations with the control input at one boundary and a nonlinear ordinary differential equation coupled to the other. The controller can be designed to asymptotically stabilize the system at an equilibrium or relative to a reference signal. Two related but different controllers for semilinear and general quasilinear systems are presented and the additional challenges in quasilinear systems are discussed. Moreover, we present an observer that estimates the distributed PDE state and the unmeasured ODE state from measurements at the actuated boundary only, which can be used to also solve the output feedback control problem.

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In this paper, we present an output feedback controller for systems consisting of n 2 × 2 semilinear hyperbolic systems in series interconnection where actuation and sensing are restricted to one boundary. The output-feedback control law consists of a state-feedback controller combined with an observer. The control and estimation laws are based on the dynamics on the characteristic lines of the hyperbolic system, and achieve stabilization of the origin or tracking at one location, and full state estimation, respectively, globally and in minimum time. We demonstrate the controller performance in a numerical example, and apply the controller to a relevant disturbance rejection problem in oil well drilling.

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Summary Heave induces pressure oscillations when drilling offshore from floating rigs. A time-domain model is proposed to analyze and predict such pressure oscillations. The model considers the coupled dynamics of the mud and the drillstring, Herschel-Bulkley-type rheology, and realistic geometries. A computationally efficient method to evaluate friction as a nonlinear function of the mud-flow rate and drillstring velocity is discussed. In a simulation study, we illustrate several nonlinear phenomena that have important practical implications but were not included in previous, simpler models. In particular, muds with a yield point can increase the pressure amplitudes significantly, and severe downhole-pressure oscillations are not detectable from topside measurements in many cases.