Modelling and control of systems with flow

In practice, feedback control design consists of three steps: modelling, model reduction and controller design for the reduced model. Systems with flow are often complicated, and there is yet no standard algorithm that integrates these steps. In this thesis we make a modest effort by considering two applications: climate control for food storage, and UV disinfection of fluids. The goal is twofold. First, the aim is to come to a controller design that is practically relevant. The controller has to easy implementable and of high quality. Second, we try to retain as much physical information from the system as possible. The advantage of a controller that contains physical information lies in the time saving when designing the system and the controller simultaneously. For the food storage room a realistic but relatively simple model is derived. This model is validated and calibrated by experimental results. The factors that stand in the way of standard model reduction and controller design, are air flow and the input that is not continuous, but switches between two values. Via a combination of standard model reduction techniques (Pad\'{e} approximation, linearization, timescale decomposition) the system is reduced to a first order linear system with the switching time as input. For this, a simple and high quality controller is designed. The controller is tested successfully on the basic model. The system dynamics is parameterized by the physical properties of the system, which can give great numerical advantages for the system design. For a UV disinfection reactor a realistic basic model is derived. The factors that stand in the way of standard model reduction and controller design, are flow, nonlinear input, and the extremely large state space that is needed for an accurate discretisation. Via a combination of standard model reduction techniques (Pad\'{e} approximation, linearization, input/output balancing) the system is reduced to a first order linear system. For this, a simple and high quality controller is designed. The controller is tested successfully on the basic model. A drawback is that the input/output balancing does not retain any physical system information. Further, the model describes a very specific case. As an alternative, a modelling technique is designed that uses the measured residence time distribution. The advantage here is that the resulting model is linear and suited for practical controller design. Moreover, the model is automatically calibrated to the experimental data that it is based on. The drawback is that the model does not hold any physical system information.