Modeling of a Fluid-structure coupled system using port-Hamiltonian formulation

Abstract The interactions between fluid and structural dynamics are an important subject of study in several engineering applications. In airplanes, for example, these coupled vibrations can lead to structural fatigue, noise and even instability. At ISAE, we have an experimental device that consists of a cantilevered plate with a fluid tank near the free tip. This device is being used for model validation and active control studies. This work uses the port-Hamiltonian systems formulation for modeling this experimental device. Structural dynamics and fluid dynamics are independently modeled as infinite-dimensional systems. The plate is approximated as a beam. Shallow water equations are used for representing the fluid in the moving tank. The global system is coupled and spatial discretization of the infinite-dimensional systems using mixed finite-element method allows to obtain a finite-dimensional system that is still Hamiltonian.

[1]  Denis Matignon,et al.  A class of damping models preserving eigenspaces for linear conservative port-Hamiltonian systems , 2013, Eur. J. Control.

[2]  Hans Zwart,et al.  Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces , 2012 .

[3]  Kirsten Morris,et al.  Strong stabilization of piezoelectric beams with magnetic effects , 2013, 52nd IEEE Conference on Decision and Control.

[4]  Dewey H. Hodges,et al.  Introduction to Structural Dynamics and Aeroelasticity , 2002 .

[5]  Pierre Rouchon,et al.  Dynamics and solutions to some control problems for water-tank systems , 2002, IEEE Trans. Autom. Control..

[6]  van der Arjan Schaft,et al.  On the Hamiltonian Formulation of Nonholonomic Mechanical Systems , 1994 .

[7]  Laurent Lefèvre,et al.  Control by interconnection and energy shaping methods of port Hamiltonian models - Application to the shallow water equations , 2009, ECC.

[8]  Denis Arzelier,et al.  Modeling of a coupled fluid-structure system excited by piezoelectric actuators , 2014, 2014 IEEE/ASME International Conference on Advanced Intelligent Mechatronics.

[9]  Bernhard Maschke,et al.  Port Hamiltonian System in Descriptor Form for Balanced Reduction: Application to a Nanotweezer , 2014 .

[10]  Volker Mehrmann,et al.  Differential-Algebraic Equations: Analysis and Numerical Solution , 2006 .

[11]  Arjan van der Schaft,et al.  Hamiltonian discretization of boundary control systems , 2004, Autom..

[12]  Alessandro Macchelli,et al.  An Algorithm to Discretize One-Dimensional Distributed Port Hamiltonian Systems , 2007 .

[13]  Boussad Hamroun.  Approche hamiltonienne à ports pour la modélisation, la réduction et la commande des systèmes non linéaires à paramètres distribués : application aux écoulements à surface libre , 2009 .

[14]  Stefano Stramigioli,et al.  Modeling and Control of Complex Physical Systems - The Port-Hamiltonian Approach , 2014 .

[15]  Laurent Lefèvre,et al.  Pseudo-spectral methods for the spatial symplectic reduction of open systems of conservation laws , 2012, J. Comput. Phys..

[16]  Jacquelien M. A. Scherpen,et al.  Port-Hamiltonian Modeling of a Nonlinear Timoshenko Beam with Piezo Actuation , 2014, SIAM J. Control. Optim..