194 research outputs found
Differential flatness and absolute equivalence
In this paper we give a formulation of differential flatness-a concept originally introduced by Fliess, Levine, Martin, and Rouchon (1992)-in terms of absolute equivalence between exterior differential systems. Systems which are differentially flat have several useful properties which can be exploited to generate effective control strategies for nonlinear systems. The original definition of flatness was given in the context of differential algebra, and required that all mappings be meromorphic functions. Our formulation of flatness does not require any algebraic structure and allows one to use tools from exterior differential systems to help characterize differentially flat systems. In particular, we show that in the case of single input control systems (i.e., codimension 2 Pfaffian systems), a system is differentially flat if and only if it is feedback linearizable via static state feedback. However, in higher codimensions feedback linearizability and flatness are not equivalent: one must be careful with the role of time as well the use of prolongations which may not be realizable as dynamic feedbacks in a control setting. Applications of differential flatness to nonlinear control systems and open questions are also discussed
Differential Flatness and Absolute Equivalence
In this paper we give a formulation of differential flatness---a concept originally introduced by Fleiss, Levine, Martin, and Rouchon---in terms of absolute equivalence between exterior differential systems. Systems which are differentially flat have several useful properties which can be exploited to generate effective control strategies for nonlinear systems. The original definition of flatness was given in the context of differentiable algebra, and required that all mappings be meromorphic functions. Our formulation of flatness does not require any algebraic structure and allows one to use tools from exterior differential systems to help characterize differentially flat systems. In particular, we shown that in the case of single input control systems (i.e., codimension 2 Pfaffian systems), a system is differentially flat if and only if it is feedback linearizable via static state feedback. However, in higher codimensions feedback linearizability and flatness are *not* equivalent: one must be careful with the role of time as well the use of prolongations which may not be realizable as dynamic feedbacks in a control setting. Applications of differential flatness to nonlinear control systems and open questions will be discussed. Revised 14 Aug 9
Strong Modification of the Nonlinear Optical Response of Metallic Subwavelength Hole Arrays
The influence of hole shape on the nonlinear optical properties of metallic subwavelength hole arrays is investigated. It is found that the amount of second harmonics generated can be enhanced by changing the hole shape. In part this increase is a direct result of the effect of hole shape on the linear transmission properties. Remarkably, in addition to enhancements that follow directly from the linear properties of the array, we find a hot hole shape. For rectangular holes the effective nonlinear response is enhanced by more than 1 order of magnitude for one particular aspect ratio. This enhancement can be attributed to slow propagation of the fundamental wavelength through the holes which occurs close to the hole cutoff
Differential flatness and absolute equivalence
In this paper we give a formulation of differential flatness-a concept originally introduced by Fliess, Levine, Martin, and Rouchon (1992)-in terms of absolute equivalence between exterior differential systems. Systems which are differentially flat have several useful properties which can be exploited to generate effective control strategies for nonlinear systems. The original definition of flatness was given in the context of differential algebra, and required that all mappings be meromorphic functions. Our formulation of flatness does not require any algebraic structure and allows one to use tools from exterior differential systems to help characterize differentially flat systems. In particular, we show that in the case of single input control systems (i.e., codimension 2 Pfaffian systems), a system is differentially flat if and only if it is feedback linearizable via static state feedback. However, in higher codimensions feedback linearizability and flatness are not equivalent: one must be careful with the role of time as well the use of prolongations which may not be realizable as dynamic feedbacks in a control setting. Applications of differential flatness to nonlinear control systems and open questions are also discussed
Real Time Trajectory Generation for Differentially Flat Systems
This paper considers the problem of real time trajectory generation
and tracking for nonlinear control systems. We employ a two degree of
freedom approach that separates the nonlinear tracking problem into real
time trajectory generation followed by local (gain-scheduled)
stabilization. The central problem which we consider is how to generate, possibly
with some delay, a feasible state space and input trajectory in real
time from an output trajectory that is given online. We propose two
algorithms that solve the real time trajectory generation problem for
differentially flat systems with (possibly non-minimum phase) zero dynamics. One
is based on receding horizon point to point steering, the other allows
additional minimization of a cost function. Both algorithms explicitly address
the tradeoff between stability and performance and we prove convergence
of the algorithms for a reasonable class of output trajectories. To
illustrate the application of these techniques to physical systems, we present
experimental results using a vectored thrust flight control experiment built at
Caltech. A brief introduction to differentially flat systems and its
relationship with feedback linearization is also included
Mechanisms explaining the birthplace effect for male elite football players
Earlier research shows that wide regional variations exist in the success of athletes’ talent development but is divided with respect to the role of urbanity: both low and high urbanity have been identified as settings that contribute to the presence of talent hotspots. In this article, we intend to provide more insight into the role of urbanity in talent development in Dutch football. We used public data on the regional background of male elite players (N = 825) and combined this with public data on municipal characteristics from Statistics Netherlands and other sources: urbanity, football participation, instructional resources and population composition effects (migration background and income of inhabitants). Linear regression analysis showed that football participation, the proportion of non-western migrants and median income predict “talent yield”, i.e., the proportion of young people that reach an elite level in a municipality. Urbanity does not have an independent influence when the proportion of non-western migrants in the municipality is taken into account. The presence of instruc
Revisiting the Local Scaling Hypothesis in Stably Stratified Atmospheric Boundary Layer Turbulence: an Integration of Field and Laboratory Measurements with Large-eddy Simulations
The `local scaling' hypothesis, first introduced by Nieuwstadt two decades
ago, describes the turbulence structure of stable boundary layers in a very
succinct way and is an integral part of numerous local closure-based numerical
weather prediction models. However, the validity of this hypothesis under very
stable conditions is a subject of on-going debate. In this work, we attempt to
address this controversial issue by performing extensive analyses of turbulence
data from several field campaigns, wind-tunnel experiments and large-eddy
simulations. Wide range of stabilities, diverse field conditions and a
comprehensive set of turbulence statistics make this study distinct
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