Manuel Gräber

Nonlinear Model Predictive Control of a Vapor Compression Cycle based on First Principle Models

Abstract Vapor compression cycles are broadly used for air-conditioning, refrigeration and heat-pump applications and are responsible for a large part of primary energy consumptions. Increasing availability of electrical actuators leads to a high number of possible control inputs of vapor compression cycles. Due to their highly nonlinear behavior and strong cross coupling of inputs and outputs modeling and control of this systems is a nontrivial task. Classical control design methods based on linear plant models seem not to be able to achieve the best possible control in terms of energy efficiency and disturbances rejection. In this contribution we present a Nonlinear Model Predictive Control scheme for vapor compression cycles, which takes nonlinearities and cross coupling explicitly into account. First principle models are used to formulate a system of Ordinary Differential Equations (ODE) describing the dynamic behavior of the underlying process. Inside these models a new highly efficient method for refrigerant fluid properties computation based on bicubic spline interpolation is used. Based on the derived ODE an Optimal Control Problem is formulated and solved by a fast Direct Multiple Shooting algorithm. Finally a Nonlinear Model Predictive Control (NMPC) scheme with a sampling rate of only 0.5 s is derived. Simulation experiments show the ability of the method to immediately react to disturbances and at the same time keeping the system at the most energy efficient working point.

Optimization of an Unconventional Environmental Control System Architecture

The Environmental Control System is a relevant element of any conventional or More Electric Aircraft (MEA). It is either the key consumer of pneumatic power or draws a substantial load from the electric power system. The objective of this paper is to present a tool for the design of Environmental Control Systems and to apply it to an unconventional system. The approach is based on a recently proposed methodology, which is improved with respect to flexibility and ease-of-use. Furthermore, modeling and simulation of vapor compression cycles is discussed, which are candidate technological solutions for More Electric Aircraft cncepts. A steady-state moving boundary method is presented to model heat exchangers for such applications. Finally, the resulting design environment is applied to optimization of an unconventional ECS architecture and exemplary results are presented.

A Limiter for Preventing Singularity in Simplified Finite Volume Methods

Abstract System simulation with equation based and object-oriented modelling languages has become an important tool for system and control design of vapour compression cycles. A common approach of modelling one-phase and two-phase fluid flow is 1-D spatial discretisation according to the Finite Volume Method. In order to avoid stiff systems and to speed up simulation, pressure loss and momentum balance are usually handled in a simplified way. There exist different approaches. But all approaches suffer from one drawback. There are points where the resulting set of equations is not solvable and simulation fails. In this contribution the solvability problem is analysed in detail. It is shown that these problems are closely connected to fluid properties. Based on this result a modelling approach is suggested to avoid singularities.

Verbrauchsbestimmung von Kälteund Wärmepumpenkreisläufen durch hochdynamische Verdichtermessungen gekoppelt mit Echtzeitsimulationen

Der Verdichter in Kalte- oder Warmepumpenkreislaufen ist haufig der groste energetische Nebenverbraucher in Fahrzeugen. Die Bestimmung des genauen Anteils am Kraftstoffverbrauch ist allerdings schwierig, da dieser von zahlreichen Randbedingungen abhangt. Bedingt durch die langsame Dynamik der thermischen Speicher in einem Fahrzeug genugt es nicht, ausschlieslich stationare Betriebspunkte zu betrachten. Um realistische Aussagen zum Kraftstoffmehrverbrauch durch den Verdichter zu treffen, ist die Berucksichtigung des transienten Verhaltens des Gesamtsystems wichtig. Hierzu kann mit der im Folgenden vorgestellten Methode ein wichtiger Beitrag geleistet werden.