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SUMMARY:A variational approach for modelling and simulating electrical cir
 cuits - Sina Ober-Bloebaum (University of Paderborn)
DTSTART:20101118T150000Z
DTEND:20101118T160000Z
UID:TALK25370@talks.cam.ac.uk
CONTACT:6743
DESCRIPTION:Variational integrators are based on a discrete variational fo
 rmulation of the underlying system\, e.g. based on a discrete version of H
 amilton's principle for conservative mechanical systems. The resulting int
 egrators are symplectic and momentum preserving and have an excellent long
 -time energy behavior.\nSo far\, variational integrators have been mainly 
 developed and used for a wide variety of mechanical systems.\nHowever\, co
 nsidering real-life systems\, these are in general not of purely mechanica
 l character.\nIn fact\, more and more systems become multidisciplinary in 
 the sense\, that not only mechanical parts\, but also electrical and softw
 are subsystems are involved\, resulting into a mechatronic systems. Since 
 the integration of these systems with a unified simulation tool is desirab
 le\, the aim is to extend the applicability of variational integrators to 
 mechatronic system.\n\nIn this talk\, we develop a variational integrator 
 for the simulation of electrical circuits as first step towards a unified 
 simulation of electro-mechanical systems.\nWhen considering the dynamics o
 f an electrical circuit\, one is faced with three special situations that 
 lead to a special treatment within the variational formulation and thus th
 e construction of appropriate variational integrators: 1. The system invol
 ves external (control) forcing through external (controlled) voltage sourc
 es. 2. The system in constrained via the Kirchhoff current (KCL) and volta
 ge laws (KVL). 3. The Lagrangian is degenerate.\n\nA comparison of a varia
 tional integrator based on the discrete constrained Lagrange-d'Alembert-Po
 ntryagin principle with a simple BDF method (which is usually the method o
 f choice for the simulation of electrical circuits) shows that even for si
 mple LCR circuits a better energy behavior can be observed for the variati
 onal integrator\,\nwhereas the BDF method (non-symplectic) fails in captur
 ing the energy preservation (LC circuits) or\, in the presence of resistor
 s (LCR circuits)\,\nthe correct energy decay. In addition\, from numerical
  experiments we observe that using a variational integrator\, also the cur
 rent frequencies are much\nbetter preserved than for standard Runge-Kutta 
 or BDF schemes without taking adaptive time stepping into account.\n\nThis
  is joint work with Jerry Marsden\, Houman Owhadi and Molei Tao from CalTe
 ch.\n
LOCATION:MR14\, CMS
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