Nonlinear Hamiltonian modelling of magnetic shape memory alloy based actuators

This paper proposes an application of the Lagrangian formalism and its Hamiltonian extension to design, model and control a mechatronic system using Magnetic Shape Memory Alloys. In this aim, an original dynamical modelling of a Magnetic Shape Memory Alloy based actuator is presented. Energy-based techniques are used to obtain a coherent modelling of the magnetical, mechanical and thermodynamic phenomena. The Lagrangian formalism, well suited in such a case, is introduced and used to take into account the dynamical effects. Hamilton equations are deduced and used for the computation of the theoretical behaviour of this actuator. These numerical simulations are compared with some experimental measurements permitting the validation of the proposed modelling. Beyond the work presented here, these results will be used to design an energy shaping nonlinear control well-adapted for a strongly nonlinear active material.