6,660 research outputs found
Geometric control of particle manipulation in a two-dimensional fluid
Manipulation of particles suspended in fluids is crucial for many applications, such as precision machining, chemical processes, bio-engineering, and self-feeding of microorganisms. In this paper, we study the problem of particle manipulation by cyclic fluid boundary excitations from a geometric-control viewpoint. We focus on the simplified problem of manipulating a single particle by generating controlled cyclic motion of a circular rigid body in a two-dimensional perfect fluid. We show that the drift in the particle location after one cyclic motion of the body can be interpreted as the geometric phase of a connection induced by the system's hydrodynamics. We then formulate the problem as a control system, and derive a geometric criterion for its nonlinear controllability. Moreover, by exploiting the geometric structure of the system, we explicitly construct a feedback-based gait that results in attraction of the particle towards the rigid body. We argue that our gait is robust and model-independent, and demonstrate it in both perfect fluid and Stokes fluid
Ball on a beam: stabilization under saturated input control with large basin of attraction
This article is devoted to the stabilization of two underactuated planar
systems, the well-known straight beam-and-ball system and an original circular
beam-and-ball system. The feedback control for each system is designed, using
the Jordan form of its model, linearized near the unstable equilibrium. The
limits on the voltage, fed to the motor, are taken into account explicitly. The
straight beam-and-ball system has one unstable mode in the motion near the
equilibrium point. The proposed control law ensures that the basin of
attraction coincides with the controllability domain. The circular
beam-and-ball system has two unstable modes near the equilibrium point.
Therefore, this device, never considered in the past, is much more difficult to
control than the straight beam-and-ball system. The main contribution is to
propose a simple new control law, which ensures by adjusting its gain
parameters that the basin of attraction arbitrarily can approach the
controllability domain for the linear case. For both nonlinear systems,
simulation results are presented to illustrate the efficiency of the designed
nonlinear control laws and to determine the basin of attraction
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
Systems control theory applied to natural and synthetic musical sounds
Systems control theory is a far developped field which helps to study stability, estimation and control of dynamical systems. The physical behaviour of musical instruments, once described by dynamical systems, can then be controlled and numerically simulated for many purposes.
The aim of this paper is twofold: first, to provide the theoretical background on linear system theory, both in continuous and discrete time, mainly in the case of a finite number of degrees of freedom ; second, to give illustrative examples on wind instruments, such as the vocal tract represented as a waveguide, and a sliding flute
On the Construction of Safe Controllable Regions for Affine Systems with Applications to Robotics
This paper studies the problem of constructing in-block controllable (IBC)
regions for affine systems. That is, we are concerned with constructing regions
in the state space of affine systems such that all the states in the interior
of the region are mutually accessible through the region's interior by applying
uniformly bounded inputs. We first show that existing results for checking
in-block controllability on given polytopic regions cannot be easily extended
to address the question of constructing IBC regions. We then explore the
geometry of the problem to provide a computationally efficient algorithm for
constructing IBC regions. We also prove the soundness of the algorithm. We then
use the proposed algorithm to construct safe speed profiles for different
robotic systems, including fully-actuated robots, ground robots modeled as
unicycles with acceleration limits, and unmanned aerial vehicles (UAVs).
Finally, we present several experimental results on UAVs to verify the
effectiveness of the proposed algorithm. For instance, we use the proposed
algorithm for real-time collision avoidance for UAVs.Comment: 17 pages, 18 figures, under review for publication in Automatic
Quantum control of molecular rotation
The angular momentum of molecules, or, equivalently, their rotation in
three-dimensional space, is ideally suited for quantum control. Molecular
angular momentum is naturally quantized, time evolution is governed by a
well-known Hamiltonian with only a few accurately known parameters, and
transitions between rotational levels can be driven by external fields from
various parts of the electromagnetic spectrum. Control over the rotational
motion can be exerted in one-, two- and many-body scenarios, thereby allowing
to probe Anderson localization, target stereoselectivity of bimolecular
reactions, or encode quantum information, to name just a few examples. The
corresponding approaches to quantum control are pursued within separate, and
typically disjoint, subfields of physics, including ultrafast science, cold
collisions, ultracold gases, quantum information science, and condensed matter
physics. It is the purpose of this review to present the various control
phenomena, which all rely on the same underlying physics, within a unified
framework. To this end, we recall the Hamiltonian for free rotations, assuming
the rigid rotor approximation to be valid, and summarize the different ways for
a rotor to interact with external electromagnetic fields. These interactions
can be exploited for control --- from achieving alignment, orientation, or
laser cooling in a one-body framework, steering bimolecular collisions, or
realizing a quantum computer or quantum simulator in the many-body setting.Comment: 52 pages, 11 figures, 607 reference
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