Multi-variable port Hamiltonian model of piezoelectric material

Abstract

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Modeling for control of an inflatable space reflector, the nonlinear 1-D case

“…PORT-HAMILTONIAN MODELING OF AN PIEZOELECTRIC EULER-BERNOULLI BEAM In this section we want to introduce a pH model, see [1], [5], [4], [9], for a flexible piezoelectric beam, described in the nonlinear Euler-Bernoulli framework. We assume that a surface force is acting on the beam, e.g.…”

“…The result will be one pH model of a beam which represents the physics of the composite. Another way is to first define a pH model for every layer and then do the interconnection of the layers to achieve a pH model of the composite, see [4]. This approach has the disadvantage that the interconnection induces constraints to the system which cause unnecessary 2.…”

“…The approach we propose differs from [4], [9], because we derive a model which can represent nonlinear deformations of the beam. Additionally we derive the equations of motion by the generalized Hamiltonian's principle, see [8].…”

Port-Based Modeling of a Flexible Link

“…These objects describe the interconnection structure of the system, that is the way in which power flows within the system and between the system and its environment. The dynamics follows from the Stokes-Dirac structure combined with the constitutive equations, i.e., with the Hamiltonian (energy) function, [4], [5], [25], [26]. Besides the port Hamiltonian approach, what is quite unusual is the way in which the elastic behavior is described.…”

Port-based Modelling and Control of the Mindlin Plate

“…The equations of motion (9) can be re-written in terms of the energy and co-energy variables (12) and (13), so that the system (14) can be obtained. This system is the dpH formulation of the Mindlin model of an elastic plate.…”