Boundary energy-shaping control of an isothermal tubular reactor. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Macchelli, Alessandro; Le Gorrec, Yann; Ramírez, Héctor
• Is Part Of: Mathematical and computer modelling of dynamical systems. Volume 23:Issue 1(2017)
• Page Start: 77
• Page End: 88
• Publication Date: 2017-01-02
• Subjects: Distributed port-Hamiltonian systems -- boundary control -- energy-shaping control -- stability of PDEs -- irreversible thermodynamics; Engineering -- Mathematical models -- Periodicals; Computer simulation -- Periodicals; 515.39
• DOI: 10.1080/13873954.2016.1232282
• Languages: English
• ISSNs: 1387-3954

Abstract

ABSTRACT: 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.