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CATEGORIES:Applied and Computational Analysis
SUMMARY:A variational approach for modelling and simulatin
g electrical circuits - Sina Ober-Bloebaum (Univer
sity of Paderborn)
DTSTART;TZID=Europe/London:20101118T150000
DTEND;TZID=Europe/London:20101118T160000
UID:TALK25370AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/25370
DESCRIPTION:Variational integrators are based on a discrete va
riational formulation of the underlying system\, e
.g. based on a discrete version of Hamilton's prin
ciple for conservative mechanical systems. The res
ulting integrators are symplectic and momentum pre
serving and have an excellent long-time energy beh
avior.\nSo far\, variational integrators have been
mainly developed and used for a wide variety of m
echanical systems.\nHowever\, considering real-lif
e systems\, these are in general not of purely mec
hanical character.\nIn fact\, more and more system
s become multidisciplinary in the sense\, that not
only mechanical parts\, but also electrical and s
oftware subsystems are involved\, resulting into a
mechatronic systems. Since the integration of the
se systems with a unified simulation tool is desir
able\, the aim is to extend the applicability of v
ariational integrators to mechatronic system.\n\nI
n this talk\, we develop a variational integrator
for the simulation of electrical circuits as first
step towards a unified simulation of electro-mech
anical systems.\nWhen considering the dynamics of
an electrical circuit\, one is faced with three sp
ecial situations that lead to a special treatment
within the variational formulation and thus the co
nstruction of appropriate variational integrators:
1. The system involves external (control) forcing
through external (controlled) voltage sources. 2.
The system in constrained via the Kirchhoff curre
nt (KCL) and voltage laws (KVL). 3. The Lagrangian
is degenerate.\n\nA comparison of a variational i
ntegrator based on the discrete constrained Lagran
ge-d'Alembert-Pontryagin principle with a simple B
DF method (which is usually the method of choice f
or the simulation of electrical circuits) shows th
at even for simple LCR circuits a better energy be
havior can be observed for the variational integra
tor\,\nwhereas the BDF method (non-symplectic) fai
ls in capturing the energy preservation (LC circui
ts) or\, in the presence of resistors (LCR circuit
s)\,\nthe correct energy decay. In addition\, from
numerical experiments we observe that using a var
iational integrator\, also the current frequencies
are much\nbetter preserved than for standard Rung
e-Kutta or BDF schemes without taking adaptive tim
e stepping into account.\n\nThis is joint work wit
h Jerry Marsden\, Houman Owhadi and Molei Tao from
CalTech.\n
LOCATION:MR14\, CMS
CONTACT:
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