Boussad Hamroun

This paper proposes a method that combines LQG control design and structure preserving model reduction for the reduced order control of Infinite Dimensional Port Hamiltonian Systems (IDPHS). For that purpose the weighting operators used in LQG control design are chosen such that the resulting dynamic controller is passive and the closed-loop system equivalent to control by interconnection. The method of Petrov-Galerkin is then used to approximate the balanced realization of the IDPHS by a finite dimensional port Hamiltonian system and to provide the associated reduced order LQG controller. The main advantages of the proposed method are that, first, both control and reduction are driven by closed-loop performances and that, second, due to the passivity properties of the controller the closed-loop stability is guaranteed when the finite dimensional controller is applied to the infinite dimensional system.

Infinite-dimensional port-Hamiltonian representation of irreversible processes accounting for the thermal energy domain is presented. Two examples are studied: the transmission line and a non-isothermal reaction diffusion process. The proposed approach uses thermodynamic variables in order to define the infinite-dimensional interconnection structure linking the different phenomena. A presentation is given for one-dimensional spatial domain. For the transmission line, the Hamiltonian is the total energy and for the reaction diffusion process it is the enthalpy or the opposite of entropy.