Systemidentifikation und Reglersynthese für örtlich verteilte Prozesse durch adaptive Takagi-Sugeno Fuzzy Systeme am Beispiel des Raumklimaverhaltens

ine wichtige Aufgabe der ""präventiven Konservierung"" ist die Stabilisierung des Raumklimas, insbesondere der relativen Luftfeuchte. Die betreffenden Raumklimagrößen unterliegen dabei einer signifikanten örtlichen Verteilung, die im Rahmen der Raumklimaregelung berücksichtigt werden muss. Durch Nutzung von Sensornetzwerken und Verwendung mobiler Aktuatoren kann das Raumklima als örtlich verteilter Prozess betrachtet werden. Bei den resultierenden Modellgleichungen handelt es sich um nichtlineare partielle Differentialgleichungssysteme, welche im Allgemeinen numerisch iterativ gelöst werden müssen, was mit erheblichem Rechen- und Zeitaufwand verbunden ist. In der vorliegenden Arbeit wird daher ein zweistufiger Ansatz zur Modellreduktion für örtlich verteilte nichtlineare Prozesse vorgestellt. Zunächst wird mit Hilfe von Finiten-Differenzen Methoden eine örtliche Diskretisierung durchgeführt. Anschließend wird die Theorie der Takagi-Sugeno Fuzzy Systeme auf die nichtlinearen Gleichungssysteme übertragen. Das Verfahren wird zunächst theoretisch eingeführt und im Anschluss auf das Raumklimaverhalten übertragen.

One of the most important and challenging goals of preventive conservation is the protecting of cultural assets from unfavorable climate conditions during storage and exhibition. The longevity of these assets is best ensured by keeping the relative humidity within a suitable range. Modern approaches for modelling and controlling view indoor air conditions as lumped parameter systems, an assumption which has led to unsatisfying results for preventive conservation purposes. A long run of indoor climate measurements thus carried out for the current research, yielded the insight that some important physical values, especially relative humidity, are significantly influenced by spatial distribution. This insight led to the focus in this thesis on modelling and control of nonlinear distributed parameter systems. Since the calculation of spatial distributed systems is imperative for the preservation of cultural assets, it is advantageous to be able to accomplish these calculations quickly. A common approach to such calculations has been to first formulate a general flow problem and then solve it with Computation Fluid Dynamics (CFD). However, because a flow problem is described by a set of nonlinear partial differential equations, only numerical solutions can usually be found, e.g. in CFD. This is desirable in the sense that these numerical solutions are very detailed, but they are not widely used for controller synthesis because the process of arriving at them is very time consuming and complicated.For this reason, a reduced approach capable of simplifying controller design without neglecting the spatial distribution is developed in this thesis. First of all, a spatial discretization is performed via finite-difference methods. The set of partial differential equations is thus reduced to a set of ordinary differential equations. Subsequently, the derived nonlinear equations are approximated by a Takagi-Sugeno Fuzzy approach. In contrast to lumped parameter systems, there is a need for model reduction in distributed parameter systems, where the number of subsystems would otherwise increase exponentially. As shown in the following, this model reduction is accomplished through introducing the Hadamard-Product. Methods for controller design are then given, as well as system identification approaches. For the examined case of controlling indoor air conditions, system identification methods proved mandatory, since there is no way of deriving model parameters in real world applications. After these theoretical approaches are elucidated, they are applied to the indoor air conditions and compared to the afore-mentioned currently used methods. It is thus demonstrated that spatial distributed systems are far more beneficial for preventive conservation and can be simplified while improving accuracy for the purpose of controlling indoor climate conditions and related applications.