Optimal Control Prediction Method for Control Allocation

This paper proposes a novel prediction method for online optimal control allocation that extends the volume of moments achievable with the Moore-Penrose generalized inverse to the entire Attainable Moment Set. This method formulates the control allocation problem using selected basis vectors and associated gains which reduces the optimization problem dimensions and provides physical insight into the resulting optimal solutions. The proposed algorithm finds the entire family of unique optimal control solutions along the desired moment vector from the origin to the boundary of the Attainable Moment Set. Numerical results for the Moore-Penrose prediction method show that the unique minimal controls obtained yield the desired moment with near machine precision accuracy while maintaining control effectors within specified position limits. This method has been fully validated against the unique solution obtained on the boundary of the Attainable Moment Set using the Durham Direct Allocation method. Minimal control solutions obtained for moments in the interior of the Attainable Moment Set, similarly yield the desired moment to near machine precision while providing control solutions that are smaller (i.e. 2-norm) than solutions found with traditional control allocation algorithms (e.g. interior point methods) applied to the minimal control problem. Numerical simulations using a Matlab autocoded executable (MEX) for the representative real world problem of 3-moments with 20 individual control effectors and prescribed control position limits show a mean computation speed of approximately 125 Hz which is sufficient to enable real-time flight allocation

Affine Generalized Inverse for Optimal Control Allocation

This research is a follow on to the "Optimal Control Prediction Method for Control Allocation" paper in which the Prediction Method iterative algorithm was introduced. Previously, the Prediction Method was shown to provide optimal control allocation solutions over the entire Attainable Moment Set for the Moore-Penrose and the generalized (weighted) inverse. As an extension to the Prediction Method, this paper introduces a family of Moore Penrose Affine Generalized Inverses, applicable for all moments, which compute control allocation solutions using a constant matrix and fixed null-space vector. The Moore-Penrose Affine Generalized Inverse is proven to yield equivalent solutions to those of the Prediction Method and therefore is guaranteed to yield Moore-Penrose optimal control allocation solutions. While the Prediction Method is applicable for any moment along an a priori specified moment direction, the Affine Generalized Inverse is shown to yield optimal control allocation solutions in a neighborhood of the given moment which is not restricted to a specified moment direction. Furthermore, the Affine Generalized Inverse is shown to provide the time derivative of optimal control allocation solutions and to facilitate maintaining solutions within control effector rate limitations. The Moore-Penrose Affine Generalized Inverse is broadened to encompass any arbitrary (weighted) Affine Generalized Inverse. Finally, a method of creating a moment lookup table is outlined to utilize the Affine Generalized Inverse as an offline control allocation solution for all moments in the Attainable Moment Set

The Defamation Act 2013: What exactly is ‘a body that trades for profit’?

Clarifies the phrase ‘body that trades for profit’, and predicts how the courts are likely to interpret it. The article considers four particular types of non-human claimant, namely charities, housing associations, trade associations, and holding corporations. There remains some confusion over the likely implications of Parliament’s use in the Act of the phrase ‘a body that trades for profit’. There are several persuasive authorities from areas of law other than defamation suggesting that the courts should interpret the phrase ‘a body that trades for profit’ to mean 'a body that trades for the purpose of making profit for distribution to its members'

Opposing and following responses in sensorimotor speech control : why responses go both ways

When talking, speakers continuously monitor and use the auditory feedback of their own voice to control and inform speech production processes. When speakers are provided with auditory feedback that is perturbed in real time, most of them compensate for this by opposing the feedback perturbation. But some speakers follow the perturbation. In the current study, we investigated whether the state of the speech production system at perturbation onset may determine what type of response (opposing or following) is given. The results suggest that whether a perturbation-related response is opposing or following depends on ongoing fluctuations of the production system: It initially responds by doing the opposite of what it was doing. This effect and the non-trivial proportion of following responses suggest that current production models are inadequate: They need to account for why responses to unexpected sensory feedback depend on the production-system’s state at the time of perturbation

Analysis of NASA Common Research Model Dynamic Data

Recent NASA Common Research Model (CRM) tests at the Langley National Transonic Facility (NTF) and Ames 11-foot Transonic Wind Tunnel (11-foot TWT) have generated an experimental database for CFD code validation. The database consists of force and moment, surface pressures and wideband wing-root dynamic strain/wing Kulite data from continuous sweep pitch polars. The dynamic data sets, acquired at 12,800 Hz sampling rate, are analyzed in this study to evaluate CRM wing buffet onset and potential CRM wing flow separation

Effects of Active Sting Damping on Common Research Model Data Quality

Recent tests using the Common Research Model (CRM) at the Langley National Transonic Facility (NTF) and the Ames 11-foot Transonic Wind Tunnel (11' TWT) produced large sets of data that have been used to examine the effects of active damping on transonic tunnel aerodynamic data quality. In particular, large statistically significant sets of repeat data demonstrate that the active damping system had no apparent effect on drag, lift and pitching moment repeatability during warm testing conditions, while simultaneously enabling aerodynamic data to be obtained post stall. A small set of cryogenic (high Reynolds number) repeat data was obtained at the NTF and again showed a negligible effect on data repeatability. However, due to a degradation of control power in the active damping system cryogenically, the ability to obtain test data post-stall was not achieved during cryogenic testing. Additionally, comparisons of data repeatability between NTF and 11-ft TWT CRM data led to further (warm) testing at the NTF which demonstrated that for a modest increase in data sampling time, a 2-3 factor improvement in drag, and pitching moment repeatability was readily achieved not related with the active damping system

Singular solutions of a modified two-component Camassa-Holm equation

The Camassa-Holm equation (CH) is a well known integrable equation describing the velocity dynamics of shallow water waves. This equation exhibits spontaneous emergence of singular solutions (peakons) from smooth initial conditions. The CH equation has been recently extended to a two-component integrable system (CH2), which includes both velocity and density variables in the dynamics. Although possessing peakon solutions in the velocity, the CH2 equation does not admit singular solutions in the density profile. We modify the CH2 system to allow dependence on average density as well as pointwise density. The modified CH2 system (MCH2) does admit peakon solutions in velocity and average density. We analytically identify the steepening mechanism that allows the singular solutions to emerge from smooth spatially-confined initial data. Numerical results for MCH2 are given and compared with the pure CH2 case. These numerics show that the modification in MCH2 to introduce average density has little short-time effect on the emergent dynamical properties. However, an analytical and numerical study of pairwise peakon interactions for MCH2 shows a new asymptotic feature. Namely, besides the expected soliton scattering behavior seen in overtaking and head-on peakon collisions, MCH2 also allows the phase shift of the peakon collision to diverge in certain parameter regimes.Comment: 25 pages, 11 figure

Liquid drop splashing on smooth, rough and textured surfaces

Splashing occurs when a liquid drop hits a dry solid surface at high velocity. This paper reports experimental studies of how the splash depends on the roughness and the texture of the surfaces as well as the viscosity of the liquid. For smooth surfaces, there is a "corona" splash caused by the presence of air surrounding the drop. There are several regimes that occur as the velocity and liquid viscosity are varied. There is also a "prompt" splash that depends on the roughness and texture of the surfaces. A measurement of the size distribution of the ejected droplets is sensitive to the surface roughness. For a textured surface in which pillars are arranged in a square lattice, experiment shows that the splashing has a four-fold symmetry. The splash occurs predominantly along the diagonal directions. In this geometry, two factors affect splashing the most: the pillar height and spacing between pillars.Comment: 9 pages, 11 figure