### Abstract

Original language | English |
---|---|

Title of host publication | Modeling and Control of Complex Physical Systems : the Port-Hamiltonian Approach |

Editors | V. Duindam, A. Macchelli, S. Stramigioli, H. Bruyninckx |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 273-318 |

ISBN (Print) | 978-3-642-03195-3 |

DOIs | |

Publication status | Published - 2009 |

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*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

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

TY - CHAP

T1 - Control of finite-dimensional port-Hamiltonian systems

AU - Garcia Canseco, E.

AU - Ortega, R.

AU - Pasumarthy, R.

AU - Schaft, van der, A.J.

PY - 2009

Y1 - 2009

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.

U2 - 10.1007/978-3-642-03196-0_5

DO - 10.1007/978-3-642-03196-0_5

M3 - Chapter

SN - 978-3-642-03195-3

SP - 273

EP - 318

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

A2 - Duindam, V.

A2 - Macchelli, A.

A2 - Stramigioli, S.

A2 - Bruyninckx, H.

PB - Springer

CY - Berlin

ER -