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

Asymptotic stabilization of Euler-Poincaré mechanical systems

Stabilization of mechanical control systems by the method of controlled Lagrangians and matching is used to analyze asymptotic stabilization of systems whose underlying dynamics are governed by the Euler-Poincar´e equations. In particular, we analyze asymptotic stabilization of a satellite

Overview of the Chariton Valley switchgrass project: A part of the biomass power for rural development initiative

Investigation of renewable energy in Iowa is centering on the use of agricultural crops to generate electricity. Switchgrass, a native grass of Iowa, is one of the most promising biomass producers. Chariton Valley RC and D Inc., a USDA affiliated rural development organization based in southern Iowa and Alliant Power, a major Iowa energy company, are leading a statewide coalition of public and private interests to develop a sustainable biomass industry. Chariton Valley RC and D is working with local producers and the agricultural professionals to develop a biomass supply infrastructure. Alliant Power is working to develop the technology to convert agricultural crops to energy to serve as the basis for sustainable commercial energy production. Iowa State University and others are assessing the long-term potential of gasification for converting switchgrass to energy. Plans call for modifications to a 750 MW Alliant Power coal plant that will allow switchgrass to be co-fired with coal. A 5% co-fire rate would produce 35 MW of electrical power production and require 50,000 acres of dedicated biomass supply in southern Iowa. Growing biomass crops on erosive lands, then using them as a substitute fuel in coal-fired boilers can potentially reduce air pollution, greenhouse gas emissions, soil erosion and water pollution

Calibrating the relation of low-frequency radio continuum to star formation rate at 1 kpc scale with LOFAR

9 figures, 6 tables and 17 pages. This paper is part of the LOFAR surveys data release 1 and has been accepted for publication in a special edition of A&A that will appear in Feb 2019, volume 622. The catalogues and images from the data release will be publicly available on lofar-surveys.org upon publication of the journal. Reproduced with permission from Astronomy & Astrophysics. © 2018 ESO.Radio continuum (RC) emission in galaxies allows us to measure star formation rates (SFRs) unaffected by extinction due to dust, of which the low-frequency part is uncontaminated from thermal (free-free) emission. We calibrate the conversion from the spatially resolved 140 MHz RC emission to the SFR surface density ($\Sigma_{\rm SFR}$) at 1 kpc scale. We used recent observations of three galaxies (NGC 3184, 4736, and 5055) from the LOFAR Two-metre Sky Survey (LoTSS), and archival LOw-Frequency ARray (LOFAR) data of NGC 5194. Maps were created with the facet calibration technique and converted to radio $\Sigma_{\rm SFR}$ maps using the Condon relation. We compared these maps with hybrid $\Sigma_{\rm SFR}$ maps from a combination of GALEX far-ultraviolet and Spitzer 24 $\mu\rm m$ data using plots tracing the relation at $1.2\times 1.2$-kpc$^2$ resolution. The RC emission is smoothed with respect to the hybrid $\Sigma_{\rm SFR}$ owing to the transport of cosmic-ray electrons (CREs). This results in a sublinear relation $(\Sigma_{\rm SFR})_{\rm RC} \propto [(\Sigma_{\rm SFR})_{\rm hyb}]^{a}$, where $a=0.59\pm 0.13$ (140 MHz) and $a=0.75\pm 0.10$ (1365 MHz). Both relations have a scatter of $\sigma = 0.3~\rm dex$. If we restrict ourselves to areas of young CREs ($\alpha > -0.65$; $I_\nu \propto \nu^\alpha$), the relation becomes almost linear at both frequencies with $a\approx 0.9$ and a reduced scatter of $\sigma = 0.2~\rm dex$. We then simulate the effect of CRE transport by convolving the hybrid $\Sigma_{\rm SFR}$ maps with a Gaussian kernel until the RC-SFR relation is linearised; CRE transport lengths are $l=1$-5 kpc. Solving the CRE diffusion equation, we find diffusion coefficients of $D=(0.13$-$1.5) \times 10^{28} \rm cm^2\,s^{-1}$ at 1 GeV. A RC-SFR relation at $1.4$ GHz can be exploited to measure SFRs at redshift $z \approx 10$ using $140$ MHz observations.Peer reviewe