Dynamical analysis and observer-based boundary optimal control of a counterflow heat exchanger

Abstract In this paper, we are interested in the dynamical analysis and boundary optimal control of counterflow heat exchanger in the case where the dynamics is described by hyperbolic partial differential equations. This topic is addressed by describing the dynamical model of the heat exchanger in an infinite-dimensional state-space, with bounded control and observation operators. First, we review the well-posedness problem and some fundamental properties relating to control theory, such as positivity, stability, reachability, stabilization and observability. These properties are complemented by spectral and pseudospectral analyses. Next, in the view of some results relating to the linear quadratic-optimal control of hyperbolic systems to which the model considered in this paper belongs, we introduce a certain state transformation that allows to put the abstract system in the lower triangular form so as to guarantee the uniqueness of solution of the operator Riccati equation. Finally, the design of an observer-based optimal control law coupled with an integral action is considered. The results are illustrated by means of numerical simulations for the set point tracking, and show the interest of the control approach proposed in this paper.