Timm Strecker

Identification of unknown sinusoids in 2 × 2 linear hyperbolic PDEs

We investigate systems stated as 2 × 2 hyperbolic partial differential equations (PDEs) affected at one boundary by a biased signal containing unknown sinusoids. We design an observer estimating the sinusoids frequencies, bias, phases and amplitudes as well as the system states from sensing anti-collocated with the sinusoid. The theory is demonstrated in a simulation.

Rejecting heave-induced pressure oscillations in a semilinear hyperbolic well model

In this paper, we apply recent results on the output feedback control of 2×2 semilinear systems to the problem of rejecting heave-induced pressure oscillations in offshore drilling. The well is modeled as a transmission line with nonlinear friction, with both actuation and measurement restricted to one boundary. The heave motion is represented by disturbance terms entering both inside the domain and at the uncontrolled boundary. We construct an output feedback controller to track a reference pressure at one location in the well. The controller performance is demonstrated in simulations.

Rejecting Unknown Harmonic Disturbances in

In this paper, we solve the problem of rejecting a harmonic disturbance containing unknown frequencies and bias entering a linear hyperbolic system of 1-D partial differential equations at one boundary, using boundary sensing and actuation anticollocated with the disturbance. By combining a full state feedback controller with an adaptive observer that estimates system states and the disturbance’s bias, frequencies, amplitudes, and phases with exponential convergence, the effect of the disturbance is rejected exponentially fast. The theoretical results are applied to a relevant problem from the oil and gas industry, and the performance is demonstrated in a computer simulation.

2 \times 2

Abstract We consider the control and state estimation of a class of 2 × 2 semilinear hyperbolic systems with actuation and sensing collocated at one boundary. Our approach exploits the dynamics on the characteristic lines of the hyperbolic system. The control method using full-state feedback can be used for both stabilization of an equilibrium and tracking at an arbitrary point in the domain. The control objective is achieved globally in minimum time. A Lyapunov function is constructed to prove exponential convergence in the spatial supremum norm. For linear systems, the control input can be written explicitly as the inner product of kernels with the state, and turns out to be equivalent to the control input obtained from previously known backstepping methods. The observer achieves exact state estimation also in minimum time and, combined with the state-feedback controller, solves the output feedback control problem. The performance is demonstrated in a numerical example.