Discrete-time modeling and analysis of a class of linear thermodynamic distributed parameter systems

Significant contributions have been made in continuous-time thermodynamic modeling, analysis, control, and estimation of distributed parameter systems. Compared with continuous-time works, research on discrete-time approaches is relatively limited. This contribution studies discrete-time modeling and analysis of a class of linear thermodynamic distributed parameter systems described by coupled hyperbolic partial differential equations (PDE) that can describe various applications in practice. Based on the Cayley-Tustin time discretization approach, the continuous-time infinite-dimensional model is converted to a discrete-time infinite dimensional model, where no spatial discretization or model order reduction is performed. We show that under this transformation, an approximation of the total internal entropy production is preserved, and the difference between the supply rates of the continuous- and discrete-time systems converges to zero as the time discretization interval tends to zero. Finally, the proposed analysis is illustrated through a counter-current heat exchanger with two state variables.