Modelling, interconnection and control of irreversible port Hamiltonian systems

Abstract: Originating in macroscopic mechanics, port Hamiltonian formulations were proposed and intensively used for the modular modelling and control of conservative and dissipative multiphysics systems for which the thermal domain does not need to be explicitly represented. Yet in many cutting-edge engineering applications, for example within the field of soft or micro-nano robotics, process control, material sciences, energy production etc … temperature plays a central role and needs to be explicitly taken into account. This class of systems is referred to as Irreversible Thermodynamic systems. Several attempts have been made to extend port Hamiltonian and Lagrangian formulations to Irreversible Thermodynamic systems. Among them, the Irreversible port Hamiltonian formulations, which consider the entropy as additional state variable, are particularly promising for their simplicity, their constructiveness and the amount of information they can encode.

In the first part of this talk we recall some definitions and properties of finite dimensional Irreversible port Hamiltonian systems. We show how this structure allows to cope with the first and second principles of Thermodynamics i.e. conservation of the internal energy and irreversible entropy creation. We then show how the interconnection of two controlled lrreversible port Hamiltonian Systems via thermal ports has to be state and co-state modulated in order to ensure the closed-loop lrreversible port Hamiltonian structure, satisfying the first and second laws of Thermodynamics. This modulation and closed loop invariants are then used to derive efficient controllers via energy shaping and entropy assignment. In the second part of this talk we present some recent extensions to boundary controlled distributed parameter systems defined on a 1D spatial domain and show, on the heat equation example, how similar energy shaping and entropy assignment techniques can be used for control design.

This talk is based on a joint work with Hector Ramirez and Bernhard Maschke.

mathematical physicsanalysis of PDEsdifferential geometrydynamical systemsfunctional analysisnumerical analysisoptimization and controlspectral theory

Audience: researchers in the discipline

Port-Hamiltonian Seminar

Series comments: Slides and recordings can be found here: uni-wuppertal.sciebo.de/s/CQfBsXr9iOI17ZY