Boundary energy-shaping control of an isothermal tubular reactor

This paper illustrates a general synthesis methodology of asymptotic stabilizing, energy-based, boundary control laws that are applicable to a large class of distributed port-Hamiltonian systems. The methodological results are applied on a simplified model of an isothermal tubular reactor. Due to the presence of diffusion and convection, such example, even if relatively easy from a computational point of view, is not trivial. The idea here is to design a state feedback law able to perform the energy-shaping task, i.e. able to render the closed-loop system a port-Hamiltonian system with the same structure, but characterized by a new Hamiltonian with a unique and isolated minimum at the equilibrium. Asymptotic stability is then obtained via damping injection on the boundary and is a consequence of the LaSalle's Invariance Principle in infinite dimensions.