199,492 research outputs found
Port-Hamiltonian formulation and structure-preserving discretization of hyperelastic strings
Port-Hamiltonian (PH) systems provide a framework for modeling, analysis and
control of complex dynamical systems, where the complexity might result from
multi-physical couplings, non-trivial domains and diverse nonlinearities. A
major benefit of the PH representation is the explicit formulation of power
interfaces, so-called ports, which allow for a power-preserving interconnection
of subsystems to compose flexible multibody systems in a modular way. In this
work, we present a PH representation of geometrically exact strings with
nonlinear material behaviour. Furthermore, using structure-preserving
discretization techniques a corresponding finite-dimensional PH state space
model is developed. Applying mixed finite elements, the semi-discrete model
retains the PH structure and the ports (pairs of velocities and forces) on the
discrete level. Moreover, discrete derivatives are used in order to obtain an
energy-consistent time-stepping method. The numerical properties of the newly
devised model are investigated in a representative example. The developed PH
state space model can be used for structure-preserving simulation and model
order reduction as well as feedforward and feedback control design.Comment: Submitted as a proceeding to the ECCOMAS Thematic Conference on
Multibody Dynamics 202
Dynamic iteration and model order reduction for magneto-quasistatic systems
Our world today is becoming increasingly complex, and technical devices are getting ever smaller and more powerful. The high density of electronic components together with high clock frequencies leads to unwanted side-effects like crosstalk, delayed signals and substrate noise, which are no longer negligible in chip design and can only insufficiently be represented by simple lumped circuit models. As a result, different physical phenomena have to be taken into consideration since they have an increasing influence on the
signal propagation in integrated circuits. Computer-based simulation methods play thereby a key role. The modelling and analysis of complex multi-physics problems typically leads to coupled systems of partial differential equations and differential-algebraic equations (DAEs). Dynamic iteration and model order reduction are two numerical tools for efficient and fast simulation of coupled systems.
Formodelling of low frequency electromagnetic field, we use magneto-quasistatic (MQS) systems which can be considered as an approximation to Maxwells equations. A spatial discretization by using the finite element method leads to a DAE system. We analyze the structural and physical
properties of this system and develop passivity-preserving model reduction methods. A special block structure of the MQS model is exploited to to improve the performance of the model reduction algorithms
Structured backward errors for eigenvalues of linear port-Hamiltonian descriptor systems
When computing the eigenstructure of matrix pencils associated with the
passivity analysis of perturbed port-Hamiltonian descriptor system using a
structured generalized eigenvalue method, one should make sure that the
computed spectrum satisfies the symmetries that corresponds to this structure
and the underlying physical system. We perform a backward error analysis and
show that for matrix pencils associated with port-Hamiltonian descriptor
systems and a given computed eigenstructure with the correct symmetry structure
there always exists a nearby port-Hamiltonian descriptor system with exactly
that eigenstructure. We also derive bounds for how near this system is and show
that the stability radius of the system plays a role in that bound
Structure-preserving model reduction of physical network systems by clustering
In this paper, we establish a method for model order reduction of a certain
class of physical network systems. The proposed method is based on clustering
of the vertices of the underlying graph, and yields a reduced order model
within the same class. To capture the physical properties of the network, we
allow for weights associated to both the edges as well as the vertices of the
graph. We extend the notion of almost equitable partitions to this class of
graphs. Consequently, an explicit model reduction error expression in the sense
of H2-norm is provided for clustering arising from almost equitable partitions.
Finally the method is extended to second-order systems
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