Piezoelectric beam with distributed control ports: a power-preserving discretization using weak formulation.**The contribution of the authors has been done within the context of the French National Research Agency sponsored project HAMECMOPSYS. Further information is available at http://www.hamecmopsys.ens2m.fr/

Flávio Luiz Cardoso-Ribeiro, Denis Matignon, Valérie Pommier-Budinger
2016 IFAC-PapersOnLine  
OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is a publisher-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID: 16131 Any correspondence concerning this service should be sent to the repository Abstract: A model reduction method for infinite-dimensional port-Hamiltonian systems with distributed ports is presented. The method is applied to the Euler-Bernoulli equation with
more » ... iezoelectric patches. The voltage is considered as an external input of the system. This gives rise to an unbounded input operator. A weak formulation is used to overcome this difficulty. It also allows defining a discretization method which leads to a finite-dimensional port-Hamiltonian system; the energy flow of the original system is preserved. Numerical results are compared to experimental ones to validate the method. Further work should use this model to couple the approximated equations with a more complex system, and to design active control laws. Abstract: A model reduction method for infinite-dimensional port-Hamiltonian systems with distributed ports is presented. The method is applied to the Euler-Bernoulli equation with piezoelectric patches. The voltage is considered as an external input of the system. This gives rise to an unbounded input operator. A weak formulation is used to overcome this difficulty. It also allows defining a discretization method which leads to a finite-dimensional port-Hamiltonian system; the energy flow of the original system is preserved. Numerical results are compared to experimental ones to validate the method. Further work should use this model to couple the approximated equations with a more complex system, and to design active control laws. Abstract: A model reduction method for infinite-dimensional port-Hamiltonian systems with distributed ports is presented. The method is applied to the Euler-Bernoulli equation with piezoelectric patches. The voltage is considered as an external input of the system. This gives rise to an unbounded input operator. A weak formulation is used to overcome this difficulty. It also allows defining a discretization method which leads to a finite-dimensional port-Hamiltonian system; the energy flow of the original system is preserved. Numerical results are compared to experimental ones to validate the method. Further work should use this model to couple the approximated equations with a more complex system, and to design active control laws. Abstract: A model reduction method for infinite-dimensional port-Hamiltonian systems with distributed ports is presented. The method is applied to the Euler-Bernoulli equation with piezoelectric patches. The voltage is considered as an external input of the system. This gives rise to an unbounded input operator. A weak formulation is used to overcome this difficulty. It also allows defining a discretization method which leads to a finite-dimensional port-Hamiltonian system; the energy flow of the original system is preserved. Numerical results are compared to experimental ones to validate the method. Further work should use this model to couple the approximated equations with a more complex system, and to design active control laws.
doi:10.1016/j.ifacol.2016.07.456 fatcat:nfkv6v5r7zaklkeeemkiesfpoi