Boundary Energy-Shaping Control of an Ideal Compressible Isentropic Fluid in 1-D. Issue 1 (July 2017)

• Record Type: Journal Article
• Authors: Macchelli, Alessandro; Le Gorrec, Yann; Ramírez, Héctor
• Is Part Of: IFAC-PapersOnLine. Volume 50:Issue 1(2017)
• Page Start: 5598
• Page End: 5603
• Publication Date: 2017-07
• Subjects: distributed port-Hamiltonian systems -- ideal compressible isentropic fluid -- boundary control -- energy-shaping control -- stability of PDEs; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2017.08.1105
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper illustrates a synthesis methodology of asymptotically stabilising, energy-based, boundary control laws for a large class of distributed port-Hamiltonian systems. The result is applied on a non-linear model of an ideal, compressible, isentropic fluid with one-dimensional spatial domain. The idea is to design at first 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 a new Hamiltonian with a minimum at the desired equilibrium. Then, under some assumptions on the existence of solutions and pre-compactness of trajectories, asymptotic stability is obtained via damping injection on the boundary. The result is a consequence of the La Salles Invariance Principle in infinite dimensions.