Control of a thermal fluid heat exchanger with actuator dynamics

In this paper we consider the problems of modeling and control of counter-flow heat exchangers when one includes actuator dynamics as part of the model. Most models of heat exchangers assume zero axial conduction which is known to cause numerical problems and impacts control design. This paper extends earlier work where we now include full-flux terms and allow for actuator dynamics. Motivation for this paper comes from problems of design and control of vapor compression systems where the vapor compression cycle includes two heat exchangers, a compressor and an expansion valve. The control inputs to the condenser (heat exchanger one) are outputs of the the compressor and inputs to the evaporator (heat exchanger two) are outputs to the expansion valve. Thus, the dynamics of the compressor, motors and expansion valve are important when designing controllers for the heat exchangers. We focus on a simple heat exchanger model which includes actuator dynamics and use this model to evaluate the impact of including full-flux terms on controller design. We establish that as the axial conduction terms approach zero, one obtains convergence to the hyperbolic model with no axial conduction. In the case where the flux terms are dropped and the flow is zero, the resulting (degenerate) ODE control system is no longer stabailizble. Numerical examples are provided to illustrate the theoretical results.