From canonical Hamiltonian to Port-Hamiltonian modeling application to magnetic shape memory alloys actuators.

Nandish Calchand (1) , Arnaud Hubert (1) , Yann Le Gorrec (1) , Bernhard Maschke (2)

1 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)
2 LAGEP - Laboratoire d'automatique et de génie des procédés

This paper presents the modelling of an actuator based on Magnetic Shape Memory Alloys (MSMA). The actuation principle relies on the ability of the material to change its shape under the application of a magnetic field. Previous models proposed by authors were based on canonical (symplectic) Hamiltonian modeling and thermodynamics of irreversible processes. These models, though physically cogent, are non-minimal differential algebraic dynamical models and hence less adapted for control purposes.This paper therefore proposes a modified and systemoriented modeling procedure which lends itself naturally to a port-Hamiltonian model. The latter is found to be a minimal realization of the above whereby interconnection between subsystems is clearly visible. Using Lagrange multipliers, constraints which arise due to causality and interconnection are expressed. In the last section, Differential Algebraic Equations (DAE) resulting from previous models are reduced to Ordinary Differential Equations (ODE) and by using coordinate transformations, constraints are decoupled from the system input/output. The resulting model is well-suited for control.

Domaines: Micro et nanotechnologies/Microélectronique

Nandish Calchand, Arnaud Hubert, Yann Le Gorrec, Bernhard Maschke. From canonical Hamiltonian to Port-Hamiltonian modeling application to magnetic shape memory alloys actuators.. 4th Annual Dynamic Systems and Control Conference, DSCC'11., Oct 2011, Arlington, VA, United States. pp.1-8. ⟨hal-00720258⟩