Initial investigations of hybrid thermodynamic control systems with phase transitions

A systematic approach to the modelling of thermodynamic systems with phase transitions is presented. It is shown that the dynamics of these systems can be adequately represented within the regional hybrid systems framework. This means that the discrete state changes autonomously at fixed submanifold boundaries. Furthermore, we assume that in each single phase the system's dynamics can be described in terms of equilibrium thermodynamics. This allows for the application of well developed methods from contact geometry. The minimisation of entropy plays a central role in all processes involving energy transformation and storage. So for this class of systems, there is a natural optimal control problem, namely that where the increase of entropy is used as a criterion to be minimised. To illustrate these ideas a hybrid model of a simple thermodynamic system with a liquid-vapour phase transition is presented; the system-theoretic properties of this model are analysed and a hybrid optimal control problem is formulated.