Multi-Scale Distributed Port-Hamiltonian Representation of Ionic Polymer-Metal Composite

Nishida, Gou; Takagi, Kentaro; Maschke, Bernhard; Zhang, Luo

doi:10.3182/20080706-5-kr-1001.00388

Cited by 12 publications

(13 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…∂ , f L ∂ ) and the space of effort variables: E r = R 2N +4 (e p , e q , e 0 ∂ , e L ∂ ) 11 . Inserting relations (31) - (34) into the definition of the canonical Hamiltonian operator (14), and evaluating the approximations at the collocation points z l , one compute the restriction of the exterior derivation and the Hamiltonian operator to the approximation spaces. This leads to the following matrix relations on the coefficients of the approximations:…”

Section: Polynomial Approximation and Discretization Of The Stokes-dimentioning

confidence: 99%

“…Consider now the bilinear product (18) and evaluate the associated symmetrized bilinear product, according to (2), using the polynomial approximations of the effort and flow variables (31), (32), (33) and (34). This leads to the following symmetric bilinear form on the product space of reduced effort and flow variables F r × E r :…”

Section: Restricted Bilinear Product and Stokes' Theoremmentioning

confidence: 99%

“…This modelling approach has proven to be fruitful for the modelling, simulation and control of many hyperbolic systems such as transmission lines models [19], beam equations [27] or shallow water equations [22]. Quite surprisingly it may also be applied to some parabolic examples such as transport phenomena in multi-scale adsorption columns [1], fuel cells [18] or Ionic Polymer-Metal Composites [34].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Pseudo-spectral methods for the spatial symplectic reduction of open systems of conservation laws

Moulla

Lefèvre

Maschke

2012

Journal of Computational Physics

View full text Add to dashboard Cite

International audienceA reduction method is presented for systems of conservation laws with boundary energy flow. It is stated as a generalized pseudo-spectral method which performs exact differentiation by using simultaneously several approximation spaces generated by polynomials bases and suitable choices of port-variables. The symplecticity of this spatial reduction method is proved when used for the reduction of both closed and open systems of conservation laws, for any choice of collocation points (i.e. for any polynomial bases). The symplecticity of some more usual collocation schemes is discussed and finally their accuracy on approximation of the spectrum, on the example of the ideal transmission line, is discussed in comparison with the suggested reduction scheme

show abstract

Section: Polynomial Approximation and Discretization Of The Stokes-dimentioning

confidence: 99%

Section: Restricted Bilinear Product and Stokes' Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Pseudo-spectral methods for the spatial symplectic reduction of open systems of conservation laws

Moulla

Lefèvre

Maschke

2012

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…Thirdly, we propose a compensation of dissipative energies to adjust the above methods based on conservation laws to actual systems with dissipation. Finally, we experiment with a soft actuator, an IPMC [9] to demonstrate the results of these methods.…”

Section: Introductionmentioning

confidence: 97%

Boundary detection of variational symmetry breaking using port-representation of conservation laws

Nishida

Sugiura

Yamakita

et al. 2009

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

Self Cite

View full text Add to dashboard Cite

“…This modelling approach has been applied successfully to many hyperbolic systems as varied as transmission line models [6], beam equations [7] or shallow water equations [8]. The approach has also been applied to parabolic models such as for heat and mass transport models in an adsorption column [9], for fuel cell models [10] or for ionic polymer-metal composites [11].…”

Section: Introductionmentioning

confidence: 99%

Geometric pseudospectral method for spatial integration of dynamical systems

Moulla

Lefèvre

Maschke

2011

Mathematical and Computer Modelling of Dynamical Systems

Self Cite

View full text Add to dashboard Cite

A reduction method that preserves geometric structure and energetic properties of non-linear distributed parameter systems is presented. It is stated as a general pseudospectral method using approximation spaces generated by polynomials bases. It applies to Hamiltonian formulations of distributed parameter systems that may be derived for hyperbolic systems (wave equation, beam model, shallow water model) as well as for parabolic ones (heat or diffusion equations, reaction-diffusion models). It is defined in order to preserve the geometric symplectic interconnection structure (Stokes-Dirac structure) of the infinite-dimensional model by performing exact differentiation and by a suitable choice of port variables. This leads to a reduced port-controlled Hamiltonian finite-dimensional system of ordinary differential equations. Moreover, the stored and dissipated power in the reduced model are approximations of the distributed ones. The method thus allows the direct use of thermodynamics phenomenological constitutive equations for the design of passivity-based or energy-shaping control techniques.

show abstract

Multi-Scale Distributed Port-Hamiltonian Representation of Ionic Polymer-Metal Composite

Cited by 12 publications

References 11 publications

Pseudo-spectral methods for the spatial symplectic reduction of open systems of conservation laws

Pseudo-spectral methods for the spatial symplectic reduction of open systems of conservation laws

Boundary detection of variational symmetry breaking using port-representation of conservation laws

Geometric pseudospectral method for spatial integration of dynamical systems

Contact Info

Product

Resources

About