Control of finite-dimensional port-Hamiltonian systems

E. Garcia Canseco, R. Ortega, R. Pasumarthy, A.J. Schaft, van der

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

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Abstract

We discuss in this chapter a number of approaches to exploit the modelstructure of port-Hamiltonian systems for control purposes. Actually, the formulationof physical control systems as port-Hamiltonian systems may lead in somecases to a re-thinking of standard control paradigms. Indeed, it opens up the way toformulate control problems in a way that is different and perhaps broader than usual.For example, formulating physical systems as port-Hamiltonian systems naturallyleads to the consideration of impedance control problems, where the behavior ofthe system at the interaction port is sought to be shaped by the addition of a controllersystem, and it suggests energy-transfer strategies, where the energy is soughtto be transferred from one part the system to another. Furthermore, it naturally leadsto the investigation of a particular type of dynamic controllers, namely those thatcan be also represented as port-Hamiltonian systems and that are attached to thegiven plant system in the same way as a physical system is interconnected to anotherphysical system. As an application of this strategy of control by interconnectionwithin the port-Hamiltonian setting we consider the problem of (asymptotic)stabilization of a desired equilibrium by shaping the Hamiltonian into a Lyapunovfunction for this equilibrium. From a mathematical point of view we will show thatthe mathematical formalism of port-Hamiltonian systems provides various usefultechniques, ranging from Casimir functions, Lyapunov function generation, shapingof the Dirac structure by composition, and the possibility to combine finitedimensionaland infinite-dimensional systems.
Original languageEnglish
Title of host publicationModeling and Control of Complex Physical Systems : the Port-Hamiltonian Approach
EditorsV. Duindam, A. Macchelli, S. Stramigioli, H. Bruyninckx
Place of PublicationBerlin
PublisherSpringer
Pages273-318
ISBN (Print)978-3-642-03195-3
DOIs
Publication statusPublished - 2009

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Hamiltonians
Lyapunov functions
Energy transfer
Stabilization
Control systems
Controllers
Chemical analysis

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Garcia Canseco, E., Ortega, R., Pasumarthy, R., & Schaft, van der, A. J. (2009). Control of finite-dimensional port-Hamiltonian systems. In V. Duindam, A. Macchelli, S. Stramigioli, & H. Bruyninckx (Eds.), Modeling and Control of Complex Physical Systems : the Port-Hamiltonian Approach (pp. 273-318). Berlin: Springer. https://doi.org/10.1007/978-3-642-03196-0_5
Garcia Canseco, E. ; Ortega, R. ; Pasumarthy, R. ; Schaft, van der, A.J. / Control of finite-dimensional port-Hamiltonian systems. Modeling and Control of Complex Physical Systems : the Port-Hamiltonian Approach. editor / V. Duindam ; A. Macchelli ; S. Stramigioli ; H. Bruyninckx. Berlin : Springer, 2009. pp. 273-318
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Garcia Canseco, E, Ortega, R, Pasumarthy, R & Schaft, van der, AJ 2009, Control of finite-dimensional port-Hamiltonian systems. in V Duindam, A Macchelli, S Stramigioli & H Bruyninckx (eds), Modeling and Control of Complex Physical Systems : the Port-Hamiltonian Approach. Springer, Berlin, pp. 273-318. https://doi.org/10.1007/978-3-642-03196-0_5

Control of finite-dimensional port-Hamiltonian systems. / Garcia Canseco, E.; Ortega, R.; Pasumarthy, R.; Schaft, van der, A.J.

Modeling and Control of Complex Physical Systems : the Port-Hamiltonian Approach. ed. / V. Duindam; A. Macchelli; S. Stramigioli; H. Bruyninckx. Berlin : Springer, 2009. p. 273-318.

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

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T1 - Control of finite-dimensional port-Hamiltonian systems

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N2 - We discuss in this chapter a number of approaches to exploit the modelstructure of port-Hamiltonian systems for control purposes. Actually, the formulationof physical control systems as port-Hamiltonian systems may lead in somecases to a re-thinking of standard control paradigms. Indeed, it opens up the way toformulate control problems in a way that is different and perhaps broader than usual.For example, formulating physical systems as port-Hamiltonian systems naturallyleads to the consideration of impedance control problems, where the behavior ofthe system at the interaction port is sought to be shaped by the addition of a controllersystem, and it suggests energy-transfer strategies, where the energy is soughtto be transferred from one part the system to another. Furthermore, it naturally leadsto the investigation of a particular type of dynamic controllers, namely those thatcan be also represented as port-Hamiltonian systems and that are attached to thegiven plant system in the same way as a physical system is interconnected to anotherphysical system. As an application of this strategy of control by interconnectionwithin the port-Hamiltonian setting we consider the problem of (asymptotic)stabilization of a desired equilibrium by shaping the Hamiltonian into a Lyapunovfunction for this equilibrium. From a mathematical point of view we will show thatthe mathematical formalism of port-Hamiltonian systems provides various usefultechniques, ranging from Casimir functions, Lyapunov function generation, shapingof the Dirac structure by composition, and the possibility to combine finitedimensionaland infinite-dimensional systems.

AB - We discuss in this chapter a number of approaches to exploit the modelstructure of port-Hamiltonian systems for control purposes. Actually, the formulationof physical control systems as port-Hamiltonian systems may lead in somecases to a re-thinking of standard control paradigms. Indeed, it opens up the way toformulate control problems in a way that is different and perhaps broader than usual.For example, formulating physical systems as port-Hamiltonian systems naturallyleads to the consideration of impedance control problems, where the behavior ofthe system at the interaction port is sought to be shaped by the addition of a controllersystem, and it suggests energy-transfer strategies, where the energy is soughtto be transferred from one part the system to another. Furthermore, it naturally leadsto the investigation of a particular type of dynamic controllers, namely those thatcan be also represented as port-Hamiltonian systems and that are attached to thegiven plant system in the same way as a physical system is interconnected to anotherphysical system. As an application of this strategy of control by interconnectionwithin the port-Hamiltonian setting we consider the problem of (asymptotic)stabilization of a desired equilibrium by shaping the Hamiltonian into a Lyapunovfunction for this equilibrium. From a mathematical point of view we will show thatthe mathematical formalism of port-Hamiltonian systems provides various usefultechniques, ranging from Casimir functions, Lyapunov function generation, shapingof the Dirac structure by composition, and the possibility to combine finitedimensionaland infinite-dimensional systems.

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EP - 318

BT - Modeling and Control of Complex Physical Systems : the Port-Hamiltonian Approach

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A2 - Macchelli, A.

A2 - Stramigioli, S.

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PB - Springer

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ER -

Garcia Canseco E, Ortega R, Pasumarthy R, Schaft, van der AJ. Control of finite-dimensional port-Hamiltonian systems. In Duindam V, Macchelli A, Stramigioli S, Bruyninckx H, editors, Modeling and Control of Complex Physical Systems : the Port-Hamiltonian Approach. Berlin: Springer. 2009. p. 273-318 https://doi.org/10.1007/978-3-642-03196-0_5