Research study on stabilization and control modern sampled-data control theory

The methods of continuous and discrete describing function analysis were applied to predicting the existence of self-sustained oscillations in the single-axis model of the large space telescope system with nonlinear control moment gyroscope friction characteristics. It is shown that the stability equations may be solved by a numerical-iterative technique using the describing function analysis, instead of the usual graphical methods. The numerical method is found to be effective in leading to a convergent solution rapidly, with an appropriate guess of the initial condition

Research study on stabilization and control: Modern sampled-data control theory. Design of the large space telescope system

Conditions of self-sustained oscillations in a two-axis model of the nonlinear LST system are studied. The describing function of the CMG frictional nonlinearity of the LST system is used for the analysis, as well as continuous-data and discrete-data models of the simplified LST control system. A numerical-iterative method is described for the analysis of the two-axis system. Approximation methods and the direct plotting of the stability equation are implemented in the study. It is shown that although the dynamics of the two axes are identical, the amplitudes of self-sustained oscillations in the two axes may in principle be different. Analysis shows that the LST systems are of equal amplitudes but with 180-degree phase shift

Research study on stabilization and control modern sampled-data control theory. Design of the Large Space Telescope system

The numerical technique is applied to the prediction of self-sustained oscillations in a two-axis model of the nonlinear system with sampled data. The sampled-data two-axis LST system model, and its stability equation are analyzed along with the exact solution of the stability equation by numerical-iterative techniques

Spin gap behavior in Cu2_2Sc2_2Ge4_4O13_{13} by 45^{45}Sc nuclear magnetic resonance

We report the results of a $^{45}$Sc nuclear magnetic resonance (NMR) study on the quasi-one-dimensional compound Cu$_2$Sc$_2$Ge$_4$O$_{13}$ at temperatures between 4 and 300 K. This material has been a subject of current interest due to indications of spin gap behavior. The temperature-dependent NMR shift exhibits a character of low-dimensional magnetism with a negative broad maximum at $T_{max}$ $\simeq$ 170 K. Below $$, the NMR shifts and spin lattice relaxation rates clearly indicate activated responses, confirming the existence of a spin gap in Cu$_2$Sc$_2$Ge% $_4$O$_{13}$. The experimental NMR data can be well fitted to the spin dimer model, yielding a spin gap value of about 275 K which is close to the 25 meV peak found in the inelastic neutron scattering measurement. A detailed analysis further points out that the nearly isolated dimer picture is proper for the understanding of spin gap nature in Cu$_2$Sc$_2$Ge$_4$O$_{13}$.Comment: 4 pages, 6 figures, submitted to Phys. Rev.

Distance-two labelings of digraphs

For positive integers $j\ge k$, an $L(j,k)$-labeling of a digraph $D$ is a function $f$ from $V(D)$ into the set of nonnegative integers such that $|f(x)-f(y)|\ge j$ if $x$ is adjacent to $y$ in $D$ and $|f(x)-f(y)|\ge k$ if $x$ is of distant two to $y$ in $D$. Elements of the image of $f$ are called labels. The $L(j,k)$-labeling problem is to determine the $\vec{\lambda}_{j,k}$-number $\vec{\lambda}_{j,k}(D)$ of a digraph $D$, which is the minimum of the maximum label used in an $L(j,k)$-labeling of $D$. This paper studies $\vec{\lambda}_{j,k}$- numbers of digraphs. In particular, we determine $\vec{\lambda}_{j,k}$- numbers of digraphs whose longest dipath is of length at most 2, and $\vec{\lambda}_{j,k}$-numbers of ditrees having dipaths of length 4. We also give bounds for $\vec{\lambda}_{j,k}$-numbers of bipartite digraphs whose longest dipath is of length 3. Finally, we present a linear-time algorithm for determining $\vec{\lambda}_{j,1}$-numbers of ditrees whose longest dipath is of length 3.Comment: 12 pages; presented in SIAM Coference on Discrete Mathematics, June 13-16, 2004, Loews Vanderbilt Plaza Hotel, Nashville, TN, US

The Effect of Retro-Cueing on an ERP Marker of VSTM Maintenance

Previous research has found that Contralateral Delay Activity (CDA) is correlated with the number of items maintained in Visual Short Term Memory from one visual field (VF) (Vogel & Machizawa, 2004). CDA is usually elicited by a to-be-remembered array after a prospective cue (pro-cue) signalling the relevant side of the visual display, and is interpreted as a putative electrophysiological signature of WM maintenance. Attention can also be directed to the contents of VSTM, after the presentation of a visual array, using a retroactive cue (retro-cue) (Nobre, Griffin, & Rao, 2008). Because retro-cueing directs attention within a memory trace, potentially reducing the load of items to be maintained, we hypothesised that this would significantly attenuate the CDA. Participants were initially presented with a spatial pro-cue which reduced the number of to-be-remembered items to one side. After a delay, a memory array of either four (low load) or eight (high load) items was displayed. A retro-cue then cued participants to one location within the relevant VF, further reducing the load of to-be-remembered items; or provided no information, requiring participants to hold all items in the relevant VF. At the end of the trial, participants performed a same/different judgement on a test stimulus. Retro-cues significantly improved VSTM performance. Unexpectedly, the CDA was found to be abolished by the presentation of both spatially predictive and neutral cues, independently of the VSTM load participants had to maintain

Design of a digital controller for spinning flexible spacecraft

An approach to digital control system design is applied to the analysis and design of a practical onboard digital attitude control system for a class of spinning vehicles characterized by a rigid body and two connected flexible appendages. The approach used is to design a continuous-data control system that will provide a satisfactory system response. Then, using the digital redesign method, a digital controller with onboard digital computer is designed to provide a digital control system whose states are similar to those of the continuous system at sampling instants. The simplicity of application of this approach is indicated by example. The example, using spinning Skylab parameters, is used to substantiate the conclusions

Microscopic open channel boundary layer velocity measurement using a virtual image method

A method for velocity measurement is described which employs a microscope and high speed motion picture camera to record the motion of small tracer particles suspended in the flow. The procedure, termed the image method, involves particle illumination such that the particle itself and its virtual image created by reflection from a boundary both appear on the film. The boundary is then located equidistant from the two images. The plane of focus is oriented normal to the boundary giving a picture of the entire velocity profile normal to the boundary within the limits of the field of view. A frame by frame analysis of the particle motion can yield velocity profile and turbulence information. The image method was adapted to a small open channel. Considerable difficulty was encountered in illuminating the particles with sufficient intensity to impress their image on the film. Thus, quantitative data was not obtained. It was concluded that the lens system used to focus the light source was inadequate. However, the method has potential applications in velocity measurement near a boundary and flow visualization ' studies.U.S. Department of the InteriorU.S. Geological SurveyOpe