The state feedback servo-regulator for countercurrent heat-exchanger system modelled by system of hyperbolic PDEs

The state feedback regulator problem for a network of countercurrent heat exchangers is considered in this article. The system is described by two sets of hyperbolic partial differential equations (PDEs) and the model is nonlinear with respect to the control input. To deal with the nonlinearity, the equilibrium temperature profile is calculated and utilized in the linearization of the original nonlinear system. Then, based on infinite-dimensional representation, the state feedback regulator problem (in particular the tracking problem) is considered, where the target is to design a controller that, while guaranteeing the stability of the closed-loop system, drives the controlled output to track a reference signal generated by an exosystem with its spectrum on the imaginary axis. Given the explicit expression of the transfer function, we provide sufficient conditions such that the resulting linearized system is causal and stable. Given that the controlled system is stable, we propose a simple and novel method to provide the stabilization feedback gain K, such that the controlled system tracks the reference signal. Finally, a numerical simulation illustrating the results is presented.