Structure preserving port-Hamiltonian discretization of a 1-D inflatable space reflector

In this paper we show how to spatially discretize a distributed port-Hamiltonian (pH) system, which describes the dynamics of an 1-D piezoelectric Euler-Bernoulli beam. Standard spatial discretization schemes for PDE systems have the disadvantage that they typically lead to a finite dimensional system which is not anymore in the pH form. So, there is a need for a spatial discretization scheme which preserves the structure of the system. The problem of spatially discretizing a pH system with constant Stokes-Dirac structures and quadratic energy functions was solved in the past. But here we consider a piezoelectric Euler-Bernouli with nonlinear deformation. So, the Stokes-Dirac structure and energy function of the system are also nonlinear, and this causes some additional problems.