244 research outputs found
Nonlinear Analysis of an Improved Swing Equation
In this paper, we investigate the properties of an improved swing equation
model for synchronous generators. This model is derived by omitting the main
simplifying assumption of the conventional swing equation, and requires a novel
analysis for the stability and frequency regulation. We consider two scenarios.
First we study the case that a synchronous generator is connected to a constant
load. Second, we inspect the case of the single machine connected to an
infinite bus. Simulations verify the results
Equivalence of switching linear systems by bisimulation
A general notion of hybrid bisimulation is proposed for the class of switching linear systems. Connections between the notions of bisimulation-based equivalence, state-space equivalence, algebraic and inputâoutput equivalence are investigated. An algebraic characterization of hybrid bisimulation and an algorithmic procedure converging in a finite number of steps to the maximal hybrid bisimulation are derived. Hybrid state space reduction is performed by hybrid bisimulation between the hybrid system and itself. By specializing the results obtained on bisimulation, also characterizations of simulation and abstraction are derived. Connections between observability, bisimulation-based reduction and simulation-based abstraction are studied.\ud
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Nonholonomic systems with symmetry allowing a conformally symplectic reduction
Non-holonomic mechanical systems can be described by a degenerate
almost-Poisson structure (dropping the Jacobi identity) in the constrained
space. If enough symmetries transversal to the constraints are present, the
system reduces to a nondegenerate almost-Poisson structure on a ``compressed''
space. Here we show, in the simplest non-holonomic systems, that in favorable
circumnstances the compressed system is conformally symplectic, although the
``non-compressed'' constrained system never admits a Jacobi structure (in the
sense of Marle et al.).Comment: 8 pages. A slight edition of the version to appear in Proceedings of
HAMSYS 200
Bond graphs in model matching control
Bond graphs are primarily used in the network modeling of lumped parameter physical systems, but controller design with this graphical technique is relatively unexplored. It is shown that bond graphs can be used as a tool for certain model matching control designs. Some basic facts on the nonlinear model matching problem are recalled. The model matching problem is then associated with a particular disturbance decoupling problem, and it is demonstrated that bicausal assignment methods for bond graphs can be applied to solve the disturbance decoupling problem as to meet the model matching objective. The adopted bond graph approach is presented through a detailed example, which shows that the obtained controller induces port-Hamiltonian error dynamics. As a result, the closed loop system has an associated standard bond graph representation, thereby rendering energy shaping and damping injection possible from within a graphical context
Making big steps in trajectories
We consider the solution of initial value problems within the context of
hybrid systems and emphasise the use of high precision approximations (in
software for exact real arithmetic). We propose a novel algorithm for the
computation of trajectories up to the area where discontinuous jumps appear,
applicable for holomorphic flow functions. Examples with a prototypical
implementation illustrate that the algorithm might provide results with higher
precision than well-known ODE solvers at a similar computation time
On local linearization of control systems
We consider the problem of topological linearization of smooth (C infinity or
real analytic) control systems, i.e. of their local equivalence to a linear
controllable system via point-wise transformations on the state and the control
(static feedback transformations) that are topological but not necessarily
differentiable. We prove that local topological linearization implies local
smooth linearization, at generic points. At arbitrary points, it implies local
conjugation to a linear system via a homeomorphism that induces a smooth
diffeomorphism on the state variables, and, except at "strongly" singular
points, this homeomorphism can be chosen to be a smooth mapping (the inverse
map needs not be smooth). Deciding whether the same is true at "strongly"
singular points is tantamount to solve an intriguing open question in
differential topology
Variational and Geometric Structures of Discrete Dirac Mechanics
In this paper, we develop the theoretical foundations of discrete Dirac
mechanics, that is, discrete mechanics of degenerate Lagrangian/Hamiltonian
systems with constraints. We first construct discrete analogues of Tulczyjew's
triple and induced Dirac structures by considering the geometry of symplectic
maps and their associated generating functions. We demonstrate that this
framework provides a means of deriving discrete Lagrange-Dirac and nonholonomic
Hamiltonian systems. In particular, this yields nonholonomic Lagrangian and
Hamiltonian integrators. We also introduce discrete
Lagrange-d'Alembert-Pontryagin and Hamilton-d'Alembert variational principles,
which provide an alternative derivation of the same set of integration
algorithms. The paper provides a unified treatment of discrete Lagrangian and
Hamiltonian mechanics in the more general setting of discrete Dirac mechanics,
as well as a generalization of symplectic and Poisson integrators to the
broader category of Dirac integrators.Comment: 26 pages; published online in Foundations of Computational
Mathematics (2011
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