6,913 research outputs found
Global Exponential Attitude Tracking Controls on SO(3)
This paper presents four types of tracking control systems for the attitude
dynamics of a rigid body. First, a smooth control system is constructed to
track a given desired attitude trajectory, while guaranteeing almost
semi-global exponential stability. It is extended to achieve global exponential
stability by using a hybrid control scheme based on multiple configuration
error functions. They are further extended to obtain robustness with respect to
a fixed disturbance using an integral term. The resulting robust, global
exponential stability for attitude tracking is the unique contribution of this
paper, and these are developed directly on the special orthogonal group to
avoid singularities of local coordinates, or ambiguities associated with
quaternions. The desirable features are illustrated by numerical examples
Modeling for Control of Symmetric Aerial Vehicles Subjected to Aerodynamic Forces
This paper participates in the development of a unified approach to the
control of aerial vehicles with extended flight envelopes. More precisely,
modeling for control purposes of a class of thrust-propelled aerial vehicles
subjected to lift and drag aerodynamic forces is addressed assuming a
rotational symmetry of the vehicle's shape about the thrust force axis. A
condition upon aerodynamic characteristics that allows one to recast the
control problem into the simpler case of a spherical vehicle is pointed out.
Beside showing how to adapt nonlinear controllers developed for this latter
case, the paper extends a previous work by the authors in two directions.
First, the 3D case is addressed whereas only motions in a single vertical plane
was considered. Secondly, the family of models of aerodynamic forces for which
the aforementioned transformation holds is enlarged.Comment: 7 pages, 4 figure
An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method
In this paper we propose a collocation method for solving some well-known
classes of Lane-Emden type equations which are nonlinear ordinary differential
equations on the semi-infinite domain. They are categorized as singular initial
value problems. The proposed approach is based on a Hermite function
collocation (HFC) method. To illustrate the reliability of the method, some
special cases of the equations are solved as test examples. The new method
reduces the solution of a problem to the solution of a system of algebraic
equations. Hermite functions have prefect properties that make them useful to
achieve this goal. We compare the present work with some well-known results and
show that the new method is efficient and applicable.Comment: 34 pages, 13 figures, Published in "Computer Physics Communications
Basins of attraction in a harmonically excited spherical bubble model
Basins of the periodic attractors of a harmonically excited single
spherical gas/vapour bubble were examined numerically. As cavitation
occurs in the low pressure level regions in engineering applications,
the ambient pressure was set slightly below the vapour pressure. In
this case the system is not strictly dissipative and the bubble can
grow infinitely for sufficiently high pressure amplitudes and/or
starting from large initial bubble radii, consequently, the stable
bubble motion is not guaranteed. For moderate excitation pressure
amplitudes the exact basins of attraction were determined via the
computation of the invariant manifolds of the unstable solutions. At
sufficiently large amplitudes transversal intersection of the
manifolds can take place, indicating the presence of a Smale horseshoe
map and the chaotic behaviour of system. The incidence of this kind of
chaotic motion was predicted by the small parameter perturbation
method of Melnikov
Closed-form estimates of the domain of attraction for nonlinear systems via fuzzy-polynomial models
In this work, the domain of attraction of the origin of
a nonlinear system is estimated in closed-form via level sets with
polynomial boundary, iteratively computed. In particular, the
domain of attraction is expanded from a previous estimate, such
as, for instance, a classical Lyapunov level set. With the use of
fuzzy-polynomial models, the domain-of-attraction analysis can
be carried out via sum of squares optimization and an iterative
algorithm. The result is a function wich bounds the domain of
attraction, free from the usual restriction of being positive and
decrescent in all the interior of its level sets
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