1,201 research outputs found
Output-input stability and minimum-phase nonlinear systems
This paper introduces and studies the notion of output-input stability, which
represents a variant of the minimum-phase property for general smooth nonlinear
control systems. The definition of output-input stability does not rely on a
particular choice of coordinates in which the system takes a normal form or on
the computation of zero dynamics. In the spirit of the ``input-to-state
stability'' philosophy, it requires the state and the input of the system to be
bounded by a suitable function of the output and derivatives of the output,
modulo a decaying term depending on initial conditions. The class of
output-input stable systems thus defined includes all affine systems in global
normal form whose internal dynamics are input-to-state stable and also all
left-invertible linear systems whose transmission zeros have negative real
parts. As an application, we explain how the new concept enables one to develop
a natural extension to nonlinear systems of a basic result from linear adaptive
control.Comment: Revised version, to appear in IEEE Transactions on Automatic Control.
See related work in http://www.math.rutgers.edu/~sontag and
http://black.csl.uiuc.edu/~liberzo
On turbulent entrainment and dissipation in dilute polymer solutions
We present a comparative experimental study of a turbulent flow developing in clear water and dilute polymer solutions (25 and 50 wppm polyethylene oxide). The flow is forced by a planar grid that oscillates vertically with stroke S and frequency f in a square container of initially still fluid. Two-component velocity fields are measured in a vertical plane passing through the center of the tank by using time resolved particle image velocimetry. After the forcing is initiated, a turbulent layer develops that is separated from the initially irrotational fluid by a sharp interface, the so-called turbulent/nonturbulent interface (TNTI). The turbulent region grows in time through entrainment of surrounding fluid until the fluid in the whole container is in turbulent motion. From the comparison of the experiments in clear water and polymer solutions we conclude: (i) Polymer additives modify the large scale shape of the TNTI. (ii) Both, in water and in the polymer solution the mean depth of the turbulent layer, H(t), follows the theoretical prediction for Newtonian fluids H(t)∞√Kt, where K∞S^2f is the “grid action.” (iii) We find a larger grid action for dilute polymer solutions than for water. As a consequence, the turbulent kinetic energy of the flow increases and the rate of energy input becomes higher. (iv) The entrainment rate β=v_e/v_(rms) (where v_e=dH/dt is the interface propagation velocity and v_(rms) is the root mean square of the vertical velocity) is lower for polymers (β_p≈0.7) than for water (β_w≈0.8). The measured values for β are in good agreement with similarity arguments, from which we estimate that in our experiment about 28% of the input energy is dissipated by polymers
Viscous tilting and production of vorticity in homogeneous turbulence
Viscous depletion of vorticity is an essential and well known property of turbulent flows, balancing, in the mean, the net vorticity production associated with the vortex stretching mechanism. In this letter, we, however, demonstrate that viscous effects are not restricted to a mere destruction process, but play a more complex role in vorticity dynamics that is as important as vortex stretching. Based on the results from three dimensional particle tracking velocimetry experiments and direct numerical simulation of homogeneous and quasi-isotropic turbulence, we show that the viscous term in the vorticity equation can also locally induce production of vorticity and changes of the orientation of the vorticity vector (viscous tilting)
Small scale aspects of flows in proximity of the turbulent/non-turbulent interface
The work reported below is a first of its kind study of the properties of
turbulent flow without strong mean shear in a Newtonian fluid in proximity of
the turbulent/non-turbulent interface, with emphasis on the small scale
aspects. The main tools used are a three-dimensional particle tracking system
(3D-PTV) allowing to measure and follow in a Lagrangian manner the field of
velocity derivatives and direct numerical simulations (DNS). The comparison of
flow properties in the turbulent (A), intermediate (B) and non-turbulent (C)
regions in the proximity of the interface allows for direct observation of the
key physical processes underlying the entrainment phenomenon. The differences
between small scale strain and enstrophy are striking and point to the definite
scenario of turbulent entrainment via the viscous forces originating in strain.Comment: 4 pages, 4 figures, Phys. Fluid
Passification-based adaptive control with quantized measurements
We propose and analyze passification-based adaptive controller for linear uncertain systems with quantized measurements. Since the effect of the quantization error is similar to the effect of a disturbance, the adaptation law with σ-modification is used. To ensure convergence to a smaller set, the parameters of the adaptation law are being switched during the evolution of the system and a dynamic quantizer is used. It is proved that if the quantization error is small enough then the proposed controller ensures convergence of the state of a hyper-minimum-phase system to an arbitrarily small vicinity of the origin. Applicability of the proposed controller to polytopic-type uncertain systems and its efficiency is demonstrated by the example of yaw angle control of a flying vehicle
Adaptive control of passifiable linear systems with quantized measurements and bounded disturbances
We consider a linear uncertain system with an unknown bounded disturbance under a passification-based adaptive controller with quantized measurements. First, we derive conditions ensuring ultimate boundedness of the system. Then we develop a switching procedure for an adaptive controller with a dynamic quantizer that ensures convergence to a smaller set. The size of the limit set is defined by the disturbance bound. Finally, we demonstrate applicability of the proposed controller to polytopic-type uncertain systems and its efficiency by the example of a yaw angle control of a flying vehicle
Switched Control of Electron Nuclear Spin Systems
In this article, we study control of electron-nuclear spin dynamics at
magnetic field strengths where the Larmor frequency of the nucleus is
comparable to the hyperfine coupling strength. The quantization axis for the
nuclear spin differs from the static B_0 field direction and depends on the
state of the electron spin. The quantization axis can be switched by flipping
the state of electron spin, allowing for universal control on nuclear spin
states. We show that by performing a sequence of flips (each followed by a
suitable delay), we can perform any desired rotation on the nuclear spins,
which can also be conditioned on the state of the electron spin. These
operations, combined with electron spin rotations can be used to synthesize any
unitary transformation on the coupled electron-nuclear spin system. We discuss
how these methods can be used for design of experiments for transfer of
polarization from the electron to the nuclear spins
On the estimation of time dependent lift of a European Starling during flapping
We study the role of unsteady lift in the context of flapping wings in birds'
flight. Both aerodynamicists and biologists attempt to address this subject,
yet it seems that the contribution of the unsteady lift still holds many open
questions. The current study deals with the estimation of unsteady aerodynamic
forces on a freely flying bird through analysis of wingbeat kinematics and near
wake flow measurements using time resolved particle image velocimetry. The
aerodynamic forces are obtained through unsteady thin airfoil theory and lift
calculation using the momentum equation for viscous flows. The unsteady lift is
comprised of circulatory and non-circulatory components. Both are presented
over wingbeat cycles. Using long sampling data, several wingbeat cycles have
been analyzed in order to cover the downstroke and upstroke phases. It appears
that the lift varies over the wingbeat cycle emphasizing its contribution to
the total lift and its role in power estimations. It is suggested that the
circulatory lift component cannot assumed to be negligible and should be
considered when estimating lift or power of birds in flapping motion
A Lagrangian investigation of the small-scale features of turbulent entrainment through particle tracking and direct numerical simulation
We report an analysis of small-scale enstrophy ω2 and rate of strain s2 dynamics in the proximity of the turbulent/non-turbulent interface in a flow without strong mean shear. The techniques used are three-dimensional particle tracking (3D-PTV), allowing the field of velocity derivatives to be measured and followed in a Lagrangian manner, and direct numerical simulations (DNS). In both experiment and simulation the Taylor-microscale Reynolds number is Reλ = 50. The results are based on the Lagrangian viewpoint with the main focus on flow particle tracers crossing the turbulent/non-turbulent interface. This approach allowed a direct investigation of the key physical processes underlying the entrainment phenomenon and revealed the role of small-scale non-local, inviscid and viscous processes. We found that the entrainment mechanism is initiated by self-amplification of s2 through the combined effect of strain production and pressure--strain interaction. This process is followed by a sharp change of ω2 induced mostly by production due to viscous effects. The influence of inviscid production is initially small but gradually increasing, whereas viscous production changes abruptly towards the destruction of ω2. Finally, shortly after the crossing of the turbulent/non-turbulent interface, production and dissipation of both enstrophy and strain reach a balance. The characteristic time scale of the described processes is the Kolmogorov time scale, τη. Locally, the characteristic velocity of the fluid relative to the turbulent/non-turbulent interface is the Kolmogorov velocity, u
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