Finite differences on staggered grids preserving the port-Hamiltonian structure with application to an acoustic duct

Trenchant, Vincent; Ramírez, Héctor; Gorrec, Yann Le; Kotyczka, Paul

doi:10.1016/j.jcp.2018.06.051

Cited by 45 publications

(24 citation statements)

References 28 publications

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“…In this particular case, the constitutive relations needed for system (10) to be well-defined are given by (15), and then directly included in (18). In Sections 3.2 and 3.3, it will be shown that PFEM leads directly to a finite-dimensional pHs of the form (1) with…”

Section: Hyperbolic Systemsmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Approximation of Port-Hamiltonian Systems for Hyperbolic or Parabolic PDEs with Boundary Control

Brugnoli¹,

Haine²,

Serhani³

et al. 2021

JAMP

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We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of infinite-dimensional port-Hamiltonian systems (pHs) for which the Partitioned Finite Element Method (PFEM) straightforwardly applies. The proposed strategy is applied to abstract multidimensional linear hyperbolic and parabolic systems of PDEs. Then we show that instructional model problems based on the wave equation, Mindlin equation and heat equation fit within this unified framework. Secondly, we introduce the ongoing project SCRIMP (Simulation and Control of Interactions in Multi-Physics) developed for the numerical simulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCS open-source computing platform for the finite element spatial discretization. Finally, we illustrate how to solve the considered model problems within this framework by carefully explaining the methodology. As additional support, companion interactive Jupyter notebooks are available.

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Section: Hyperbolic Systemsmentioning

confidence: 99%

“…Unfortunately, this method seems to be limited to the one-dimensional case. A finite difference method with staggered grids was developed in [15] for two-dimensional domains, but complex geometries are then difficult to tackle. Weak formulations leading to Galerkin numerical approximations began to be explored in the past few years.…”

Section: Introductionmentioning

confidence: 99%

Numerical Approximation of Port-Hamiltonian Systems for Hyperbolic or Parabolic PDEs with Boundary Control

Brugnoli¹,

Haine²,

Serhani³

et al. 2021

JAMP

View full text Add to dashboard Cite

show abstract

“…The discritization method used in this paper is the mixed finite element method used to preserve the port-Hamiltonian structure such that we can use passivity-based control using the discretized finite dimensional system (15). We can also use other structure-preserving methods to discretize the system (12), such as the pseudo-spectral method [22], the finite difference method on a staggered grid [23], and the finite volume structure-preserving discretization method [24].…”

Section: The Ipmc Actuator Modelmentioning

confidence: 99%

Port-Hamiltonian Modeling and IDA-PBC Control of an IPMC-Actuated Flexible Beam

Zhou

Hu³

et al. 2021

Actuators

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In this paper, the infinite-dimensional port-Hamiltonian modelling and control problem of a flexible beam actuated using ionic polymer metal composite (IPMC) actuators is investigated. The port-Hamiltonian framework is used to propose an interconnected control model of the mechanical flexible beam and the IPMC actuator. The mechanical flexible dynamic is modelled as a Timoshenko beam, and the electric dynamics of the IPMCs are considered in the model. Furthermore, a passivity-based control-strategy is used to obtain the desired configuration of the proposed interconnected system, and the closed-loop stability is analyzed using the early lumped approach. Lastly, numerical simulations and experimental results are presented to validate the proposed model and the effectiveness of the proposed control law.

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“…Formally,the control design concerns the solution of PDEs, leading to the study of existence and decay of classical solutions of hyperbolic systems, using for instance a Riemann invariants approach [18], [19] or operator theory [20]. Alternatives to control design approaches based on models described by PDEs are early lumping approaches [21], in which the PDEs are spatially approximated by a set of ordinary differential equations (ODEs). The advantage of working with ODEs is that simpler control design techniques can be used although at the expense of possibly losing the physical interpretation of the model and the parameters.…”

Section: Symbolmentioning

confidence: 99%

Port-Hamiltonian Modeling and Control of a Micro-Channel Experimental Plant

2020

Self Cite

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We present a port-Hamiltonian system (PHS) model based on the interconnection between basic hydraulic elements equivalent to electrical components such as capacitors, inductors, and resistors to represent the dynamics of a water micro-channel experimental plant. We compare the fluid-structured interconnected PHS model with the data obtained from a micro-channel experimental plant. We then implement a controller using the total hydraulic-mechanical energy as a local Lyapunov function. Finally, we apply an integral action controller (IAC) to correct for modeling errors and load disturbances. The IAC is easy to design given the proposed interconnected model. INDEX TERMS Fluid-structured interconnected system, Micro-channel model identification, Local Lyapunov function, Integral Action Controller.

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Finite differences on staggered grids preserving the port-Hamiltonian structure with application to an acoustic duct

Cited by 45 publications

References 28 publications

Numerical Approximation of Port-Hamiltonian Systems for Hyperbolic or Parabolic PDEs with Boundary Control

Numerical Approximation of Port-Hamiltonian Systems for Hyperbolic or Parabolic PDEs with Boundary Control

Port-Hamiltonian Modeling and IDA-PBC Control of an IPMC-Actuated Flexible Beam

Port-Hamiltonian Modeling and Control of a Micro-Channel Experimental Plant

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