474 research outputs found
Root locii for systems defined on Hilbert spaces
The root locus is an important tool for analysing the stability and time
constants of linear finite-dimensional systems as a parameter, often the gain,
is varied. However, many systems are modelled by partial differential equations
or delay equations. These systems evolve on an infinite-dimensional space and
their transfer functions are not rational. In this paper a rigorous definition
of the root locus for infinite-dimensional systems is given and it is shown
that the root locus is well-defined for a large class of infinite-dimensional
systems. As for finite-dimensional systems, any limit point of a branch of the
root locus is a zero. However, the asymptotic behaviour can be quite different
from that for finite-dimensional systems. This point is illustrated with a
number of examples. It is shown that the familiar pole-zero interlacing
property for collocated systems with a Hermitian state matrix extends to
infinite-dimensional systems with self-adjoint generator. This interlacing
property is also shown to hold for collocated systems with a skew-adjoint
generator
Cayley graphs of order kp are hamiltonian for k < 48
We provide a computer-assisted proof that if G is any finite group of order
kp, where k < 48 and p is prime, then every connected Cayley graph on G is
hamiltonian (unless kp = 2). As part of the proof, it is verified that every
connected Cayley graph of order less than 48 is either hamiltonian connected or
hamiltonian laceable (or has valence less than three).Comment: 16 pages. GAP source code is available in the ancillary file
-semigroups for hyperbolic partial differential equations on a one-dimensional spatial domain
Hyperbolic partial differential equations on a one-dimensional spatial domain
are studied. This class of systems includes models of beams and waves as well
as the transport equation and networks of non-homogeneous transmission lines.
The main result of this paper is a simple test for -semigroup generation
in terms of the boundary conditions. The result is illustrated with several
examples
Efficient electrochemical model for lithium-ion cells
Lithium-ion batteries are used to store energy in electric vehicles. Physical
models based on electro-chemistry accurately predict the cell dynamics, in
particular the state of charge. However, these models are nonlinear partial
differential equations coupled to algebraic equations, and they are
computationally intensive. Furthermore, a variable solid-state diffusivity
model is recommended for cells with a lithium ion phosphate positive electrode
to provide more accuracy. This variable structure adds more complexities to the
model. However, a low-order model is required to represent the lithium-ion
cells' dynamics for real-time applications. In this paper, a simplification of
the electrochemical equations with variable solid-state diffusivity that
preserves the key cells' dynamics is derived. The simplified model is
transformed into a numerically efficient fully dynamical form. It is proved
that the simplified model is well-posed and can be approximated by a low-order
finite-dimensional model. Simulations are very quick and show good agreement
with experimental data
Zero Dynamics for Port-Hamiltonian Systems
The zero dynamics of infinite-dimensional systems can be difficult to
characterize. The zero dynamics of boundary control systems are particularly
problematic. In this paper the zero dynamics of port-Hamiltonian systems are
studied. A complete characterization of the zero dynamics for a
port-Hamiltonian systems with invertible feedthrough as another
port-Hamiltonian system on the same state space is given. It is shown that the
zero dynamics for any port-Hamiltonian system with commensurate wave speeds are
well-defined, and are also a port-Hamiltonian system. Examples include wave
equations with uniform wave speed on a network. A constructive procedure for
calculation of the zero dynamics, that can be used for very large system order,
is provided.Comment: 17 page
- …