22,055 research outputs found
The NATO III 5 MHz Distribution System
A high performance 5 MHz distribution system is described which has extremely low phase noise and jitter characteristics and provides multiple buffered outputs. The system is completely redundant with automatic switchover and is self-testing. Since the 5 MHz reference signals distributed by the NATO III distribution system are used for up-conversion and multiplicative functions, a high degree of phase stability and isolation between outputs is necessary. Unique circuit design and packaging concepts insure that the isolation between outputs is sufficient to quarantee a phase perturbation of less than 0.0016 deg when other outputs are open circuited, short circuited or terminated in 50 ohms. Circuit design techniques include high isolation cascode amplifiers. Negative feedback stabilizes system gain and minimizes circuit phase noise contributions. Balanced lines, in lieu of single ended coaxial transmission media, minimize pickup
Control and stabilization of systems with homoclinic orbits
In this paper we consider the control of two physical systems, the near wall region of a turbulent boundary layer and the rigid body, using techniques from the theory of nonlinear dynamical systems. Both these systems have saddle points linked by heteroclinic orbits. In the fluid system we show how the structure of the phase space can be used to keep the system near an (unstable) saddle. For the rigid body system we discuss passage along the orbit as a possible control manouver, and show how the Energy-Casimir method can be used to analyze stabilization of the system about the saddles
Ordered and disordered dynamics in monolayers of rolling particles
We consider the ordered and disordered dynamics for monolayers of rolling
self-interacting particles with an offset center of mass and a non-isotropic
inertia tensor. The rolling constraint is considered as a simplified model of a
very strong, but rapidly decaying bond with the surface, preventing application
of the standard tools of statistical mechanics. We show the existence and
nonlinear stability of ordered lattice states, as well as disturbance
propagation through and chaotic vibrations of these states. We also investigate
the dynamics of disordered gas states and show that there is a surprising and
robust linear connection between distributions of angular and linear velocity
for both lattice and gas states, allowing to define the concept of temperature
Finite Controllability of Infinite-Dimensional Quantum Systems
Quantum phenomena of interest in connection with applications to computation
and communication almost always involve generating specific transfers between
eigenstates, and their linear superpositions. For some quantum systems, such as
spin systems, the quantum evolution equation (the Schr\"{o}dinger equation) is
finite-dimensional and old results on controllability of systems defined on on
Lie groups and quotient spaces provide most of what is needed insofar as
controllability of non-dissipative systems is concerned. However, in an
infinite-dimensional setting, controlling the evolution of quantum systems
often presents difficulties, both conceptual and technical. In this paper we
present a systematic approach to a class of such problems for which it is
possible to avoid some of the technical issues. In particular, we analyze
controllability for infinite-dimensional bilinear systems under assumptions
that make controllability possible using trajectories lying in a nested family
of pre-defined subspaces. This result, which we call the Finite Controllability
Theorem, provides a set of sufficient conditions for controllability in an
infinite-dimensional setting. We consider specific physical systems that are of
interest for quantum computing, and provide insights into the types of quantum
operations (gates) that may be developed.Comment: This is a much improved version of the paper first submitted to the
arxiv in 2006 that has been under review since 2005. A shortened version of
this paper has been conditionally accepted for publication in IEEE
Transactions in Automatic Control (2009
A variational problem on Stiefel manifolds
In their paper on discrete analogues of some classical systems such as the
rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced
their analysis in the general context of flows on Stiefel manifolds. We
consider here a general class of continuous time, quadratic cost, optimal
control problems on Stiefel manifolds, which in the extreme dimensions again
yield these classical physical geodesic flows. We have already shown that this
optimal control setting gives a new symmetric representation of the rigid body
flow and in this paper we extend this representation to the geodesic flow on
the ellipsoid and the more general Stiefel manifold case. The metric we choose
on the Stiefel manifolds is the same as that used in the symmetric
representation of the rigid body flow and that used by Moser and Veselov. In
the extreme cases of the ellipsoid and the rigid body, the geodesic flows are
known to be integrable. We obtain the extremal flows using both variational and
optimal control approaches and elucidate the structure of the flows on general
Stiefel manifolds.Comment: 30 page
Discrete Hamilton-Jacobi Theory
We develop a discrete analogue of Hamilton-Jacobi theory in the framework of
discrete Hamiltonian mechanics. The resulting discrete Hamilton-Jacobi equation
is discrete only in time. We describe a discrete analogue of Jacobi's solution
and also prove a discrete version of the geometric Hamilton-Jacobi theorem. The
theory applied to discrete linear Hamiltonian systems yields the discrete
Riccati equation as a special case of the discrete Hamilton-Jacobi equation. We
also apply the theory to discrete optimal control problems, and recover some
well-known results, such as the Bellman equation (discrete-time HJB equation)
of dynamic programming and its relation to the costate variable in the
Pontryagin maximum principle. This relationship between the discrete
Hamilton-Jacobi equation and Bellman equation is exploited to derive a
generalized form of the Bellman equation that has controls at internal stages.Comment: 26 pages, 2 figure
Physical Dissipation and the Method of Controlled Lagrangians
We describe the effect of physical dissipation on stability of
equilibria which have been stabilized, in the absence of damping,
using the method of controlled Lagrangians. This method
applies to a class of underactuated mechanical systems including
“balance” systems such as the pendulum on a cart. Since
the method involves modifying a system’s kinetic energy metric
through feedback, the effect of dissipation is obscured.
In particular, it is not generally true that damping makes a
feedback-stabilized equilibrium asymptotically stable. Damping
in the unactuated directions does tend to enhance stability,
however damping in the controlled directions must be “reversed”
through feedback. In this paper, we suggest a choice
of feedback dissipation to locally exponentially stabilize a class
of controlled Lagrangian systems
Dissipation and Controlled Euler-Poincaré Systems
The method of controlled Lagrangians is a technique for stabilizing underactuated mechanical systems which involves modifying a system’s energy and dynamic structure through feedback. These modifications can obscure the effect of physical dissipation in the closed-loop. For example,
generic damping can destabilize an equilibrium which is closed-loop stable for a conservative system model. In this paper, we consider the effect of damping on Euler-Poincaré (special reduced Lagrangian) systems which have been stabilized about an equilibrium using the method of controlled Lagrangians. We describe a choice of feed-back dissipation which asymptotically stabilizes a sub-class of controlled Euler-Poincaré systems subject to physical damping. As an example, we consider intermediate axis rotation of a damped rigid body with a single internal rotor
Preparation and detection of magnetic quantum phases in optical superlattices
We describe a novel approach to prepare, detect and characterize magnetic
quantum phases in ultra-cold spinor atoms loaded in optical superlattices. Our
technique makes use of singlet-triplet spin manipulations in an array of
isolated double well potentials in analogy to recently demonstrated quantum
control in semiconductor quantum dots. We also discuss the many-body
singlet-triplet spin dynamics arising from coherent coupling between nearest
neighbor double wells and derive an effective description for such system. We
use it to study the generation of complex magnetic states by adiabatic and
non-equilibrium dynamics.Comment: 5 pages, 2 Figures, reference adde
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