Beobachtung und Regelung hyperbolischer verteilt parametrischer Systeme am Beispiel einer Druckregelstrecke

In this thesis, methods for the observation and control of hyperbolic distributed parameter systems are considered, using the example of the pressure control of an engine test stand. The considered problem is essentially the pressure control in a pipe. The problem is described by a system of hyperbolic differential equations, where the state variables are position-dependent and time-dependent; in such a case, one speaks of a distributed parameter system (DPS). In order to provide an efficient numerical simulation of the system, the finite volume method (FVM) is used. Starting from the system description by means of an initial boundary value problem, an analysis of the system is carried out with the idea of writing it as an abstract initial value problem and using the operator's notation. It turns out that the considered system is a so-called Riesz spectral system, which considerably simplifies further analysis. The modal approximation of the system is calculated by means of the operator's notation and the analysis of the eigenvalues and eigenfunctions of the system. Using the FVM approximation and the modal approximation, a so-called early lumping controller and observer design is carried out. Two controller structures are designed: on the one hand, a linear state regulator with a square quality measure (LQ-regulator), which is expanded by an integral part and on the other hand an observer based control of the mean pressure in the pipe. The late lumping observer and controller design is also considered. In the chosen approach, the operator-Riccati equation has to be solved for both the late lumping controller design and the observer design for DPS. Various methods for solving the operator-Riccati equation are investigated. Finally, the designed controllers are validated and compared in simulation and in experiments.