Port-based Modelling and Control of the Mindlin Plate

Macchelli, Alessandro; Melchiorri, Claudio; Bassi, L.

doi:10.1109/cdc.2005.1583120

Cited by 17 publications

(23 citation statements)

References 28 publications

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“…The PDE (1) can be used to model simple flexible 2D systems [10], or the dynamics of sound propagation in a rectangular cavity, [12]. For example, in the first case, p and (q x , q y ) represent the momenta and the strain, while v and (Γ x , Γ y ) the velocity and the stress.…”

Section: Rectangular Domainmentioning

confidence: 99%

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Boundary L<inf>2</inf>-gain stabilisation of a distributed Port-Hamiltonian system with rectangular domain

Macchelli

Gorrec

Ramírez

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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The main contribution of this paper is the development of a boundary control law for a class of distributed port-Hamiltonian systems with rectangular spatial domain that is able not only to shape the closed-loop Hamiltonian, but also to achieve a specific L2-gain between a pair of input and output signals of interest. The energy-shaping control action is based on the so-called control by interconnection and Casimir generation methodology (energy-Casimir method), here extended to deal with distributed port-Hamiltonian systems with 2D domain. On the other hand, the L2-gain property is obtained via damping injection by modulating a gain associated to a dissipative relation. Such approach takes inspiration from the Passivity Observer / Passivity Controller (PO / PC) technique originally developed for telemanipulation systems. Even if the proposed framework is quite abstract and general, possible target applications deal with the stabilisation of flexible structures, or with the stabilisation and attenuation of sound propagation in rectangular cavities.

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Section: Rectangular Domainmentioning

confidence: 99%

“…This topic is quite new, and few examples in literature can be found. Among them, the port-Hamiltonian model of 2D flexible structures is presented in [10], while in [11] a class of boundary control system associated to a n-D wave equation is discussed.…”

Section: Introductionmentioning

confidence: 99%

Boundary L<inf>2</inf>-gain stabilisation of a distributed Port-Hamiltonian system with rectangular domain

Macchelli

Gorrec

Ramírez

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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“…Especially mechanical systems with spatial domain of dimension greater than one can be analyzed in a straightforward manner in our setting, e.g. membranes [11], piezoelectricity [12] or the Mindlin plate (which is treated in [19] based on Stokes DiracStructures). This is not so straightforward in the approach based on Stokes-Dirac structures since in mechanical applications the strains (which are used as state variables) must satisfy compatibility conditions-this problem does not appear at all when the displacements and/or the deflections are the state variables.…”

Section: B System Structurementioning

confidence: 99%

On Casimir Functionals for Infinite-Dimensional Port-Hamiltonian Control Systems

Schöberl

Siuka

2013

IEEE Trans. Automat. Contr.

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We consider infinite-dimensional port-Hamiltonian systems with respect to control issues. In contrast to the well-established representation relying on Stokes-Dirac structures that are based on skew-adjoint differential operators and the use of energy variables, we employ a different port-Hamiltonian framework. Based on this system representation conditions for Casimir functionals will be derived where in this context the variational derivative plays an extraordinary role. Furthermore the coupling of finite-and infinite-dimensional systems will be analyzed in the spirit of the control by interconnection problem.

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“…Hier spielen die Randbedingungen eine entscheidende Rolle, wenn man Energietore am Rand definieren will, welche einen Leistungsfluss über den Rand ermöglichen. Regelungsmethoden basierend auf Feldtheorien erster Ordnung, vornehmlich im Hamilton'schen Szenario, findet man beispielsweise in [16,18] im Rahmen der Theorie der Jet-Mannigfaltigkeiten oder in einer Hamilton'schen Formulierung basierend auf einer Stokes-Dirac Struktur in [6][7][8].…”

Section: Introductionunclassified

Lagrange'sche und Hamilton'sche Beschreibung partieller Differentialgleichungen

Schöberl

Schlacher

2015

At - Automatisierungstechnik

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Zusammenfassung:In diesem Beitrag zeigen wir, dass für variationelle Feldtheorien erster Ordnung die partiellen Differentialgleichungen und die Randbedingungen anhand der Lagrange'schen Dichte eindeutig bestimmt werden können. Für Feldtheorien zweiter Ordnung schlagen wir ein Verfahren vor, welches es auch hier erlaubt (neben den PDEs) die Randbedingungen systematisch zu ermitteln. Dies erfolgt im Rahmen der Variationsformulierung mithilfe von Kontaktformen, welche als koordinatenfreie Variante der partiellen Integration verwendet werden. Ist man an einer evolutionären Darstellung der partiellen Differentialgleichungen interessiert, bietet sich eine Hamilton'sche Sichtweise an. In dieser Formulierung treten die Randbedingungen unter Umständen als Randtore in Erscheinung, was es erlaubt Leistungsflüsse über die Systemgrenzen zu analysieren. Auch in diesem Szenario ist es entscheidend die physikalisch korrekten Beziehungen am Rand zu gewinnen, was durch mehrfache partielle Integration nicht in eindeutiger Weise bewerkstelligbar ist. Zahlreiche Beispiele veranschaulichen die vorgestellten Methoden.Schlüsselwörter: Partielle Differentialgleichungen, Lagrange'sche Systeme, Hamilton'sche Systeme, Differentialgeometrie. Abstract:In this contribution we show that for variational systems of first-order the partial differential equations and the boundary conditions can be derived uniquely once a Lagrangian density has been specified. Furthermore, we suggest a procedure, such that also in the case of second-order field theories (besides the pdes) the boundary conditions can be derived in a straightforward manner. This will be performed by using so-called contact forms in a variational setting. An evolutionary description of the partial differential equations can be achieved in a Hamiltonian setting, and here the boundary conditions may act as boundary ports. This allows to introduce power flows over the boundary and it is of great interest to deal with the physically meaningful boundary conditions, which cannot be derived in a unique fashion by applying repeated integration by parts. Several examples highlight the suggested methods.

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Port-based Modelling and Control of the Mindlin Plate

Cited by 17 publications

References 28 publications

Boundary L<inf>2</inf>-gain stabilisation of a distributed Port-Hamiltonian system with rectangular domain

Boundary L<inf>2</inf>-gain stabilisation of a distributed Port-Hamiltonian system with rectangular domain

On Casimir Functionals for Infinite-Dimensional Port-Hamiltonian Control Systems

Lagrange'sche und Hamilton'sche Beschreibung partieller Differentialgleichungen

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