Modeling, Realization, and Simulation of Thermo-Fluid Coupled Systems Using Singularly Perturbed Sliding Manifolds

A new approach based on sliding control is presented for modeling and simulation of thermo-fluid systems described by differential-algebraic equations (DAEs). The dynamics of thermo-fluid systems are often complicated by momentum interactions that occur on a time scale that is orders of magnitude faster than the time scale of interest. To address this problem the momentum equation is often modeled using algebraic steady state approximations. This will, in general, result in a model described by nonlinear DAEs for which few control methods are currently applicable. In this paper, the modeling problem is addressed using an approach that systematically constructs an explicit state space approximation of the DAEs. The state space model can in turn be used with existing control methods. This procedure, known as realization, is achieved by solving an associated nonlinear control problem by combining boundary layer sliding control with the singular perturbation method. The necessary criteria for key properties such as convergence are established. Further, the new approach is illustrated using a vapor compression cycle example. This demonstrates significant advantages over directly modeling momentum interactions.