Closed loop model reduction applied to a tank reactor process

The subject of this article is the direct assessment of model simplification from a feedback control perspective. Normally, dynamic systems are simplified dimensionally and structurally from an open loop perspective. In spite of the intentions, the resulting models still often tend to be unnecessary complex for controller design and synthesis. Here, a four step method is proposed that incorporates a feedback controller, and makes use of the closed loop sensitivity functions to indicate significant impact on the closed loop behaviour from a performed model simplification. The method is applied to a first order reaction in an ideally stirred tank reactor with a cooling system. For this system a general and detailed model is derived. The model includes temperature dependent parameters such as specific heat capacities and densities. This reference model is locally unstable in most operating points, making open loop simplification impractical. The proposed closed loop simplification method makes it possible to evaluate which approximations of the system that can be justified.