Robustness of controllers designed using Galerkin type approximations

One of the difficulties in designing controllers for infinite-dimensional systems arises from attempting to calculate a state for the system. It is shown that Galerkin type approximations can be used to design controllers which will perform as designed when implemented on the original infinite-dimensional system. No assumptions, other than those typically employed in numerical analysis, are made on the approximating scheme

Convergence of controllers designed using state space methods

The convergence of finite dimensional controllers for infinite dimensional systems designed using approximations is examined. Stable coprime factorization theory is used to show that under the standard assumptions of uniform stabilizability/detectability, the controllers stabilize the original system for large enough model order. The controllers converge uniformly to an infinite dimensional controller, as does the closed loop response

Modeling an elastic beam with piezoelectric patches by including magnetic effects

Models for piezoelectric beams using Euler-Bernoulli small displacement theory predict the dynamics of slender beams at the low frequency accurately but are insufficient for beams vibrating at high frequencies or beams with low length-to-width aspect ratios. A more thorough model that includes the effects of rotational inertia and shear strain, Mindlin-Timoshenko small displacement theory, is needed to predict the dynamics more accurately for these cases. Moreover, existing models ignore the magnetic effects since the magnetic effects are relatively small. However, it was shown recently \cite{O-M1} that these effects can substantially change the controllability and stabilizability properties of even a single piezoelectric beam. In this paper, we use a variational approach to derive models that include magnetic effects for an elastic beam with two piezoelectric patches actuated by different voltage sources. Both Euler-Bernoulli and Mindlin-Timoshenko small displacement theories are considered. Due to the magnetic effects, the equations are quite different from the standard equations.Comment: 3 figures. 2014 American Control Conference Proceeding

Computer program to generate attitude error equations for a gimballed platform

Computer program for solving attitude error equations related to gimballed platform is described. Program generates matrix elements of attitude error equations when initial matrices and trigonometric identities have been defined. Program is written for IBM 360 computer

An evaluation of linear acoustic theory for a hovering rotor

Linear acoustic calculations are compared with previously reported data for a small-scale hovering rotor operated at high tip Mach numbers. A detailed calculated description of the distributions of blade surface pressure and shear stress due to skin friction is presented. The noise due to skin friction and loading, in the rotor disk plane, is small compared to thickness noise. The basic conclusions of Boxwell et al about the importance of nonlinear effects are upheld. Some approximations involved in the current theories for the inclusion of nonlinear effects are discussed. Using a model nonlinear problem, it is shown that to use the acoustic analogy, good knowledge of the flowfield is required

Heterostructure solar cells

The performance of gallium arsenide solar cells grown on Ge substrates is discussed. In some cases the substrate was thinned to reduce overall cell weight with good ruggedness. The conversion efficiency of 2 by 2 cm cells under AMO reached 17.1 percent with a cell thickness of 6 mils. The work described forms the basis for future cascade cell structures, where similar interconnecting problems between the top cell and the bottom cell must be solved. Applications of the GaAs/Ge solar cell in space and the expected payoffs are discussed

Orbits and origins of the young stars in the central parsec of the galaxy

We present new proper motions from the 10 m Keck telescopes for a puzzling population of massive, young stars located within a parsec of the supermassive black hole at the Galactic Center. Our proper motion measurements have uncertainties of only 0.07 mas yr^(−1) (3 km s^(−1) ), which is ≳7 times better than previous proper motion measurements for these stars, and enables us to measure accelerations as low as 0.2 mas yr^(−2) (7 km s^(−1) yr^(−1) ). These measurements, along with stellar line-of-sight velocities from the literature, constrain the true orbit of each individual star and allow us to directly test the hypothesis that the massive stars reside in two stellar disks as has been previously proposed. Analysis of the stellar orbits reveals only one disk of young stars using a method that is capable of detecting disks containing at least 7 stars. The detected disk contains 50% (38 of 73) of the young stars, is inclined by ~115° from the plane of the sky, and is oriented at a position angle of ∼100° East of North. The on-disk and off-disk populations have similar K-band luminosity functions and radial distributions that decrease at larger radii as ∝ r^(−2). The disk has an out-of-the-disk velocity dispersion of 28±6 km s^(−1) , which corresponds to a half-opening angle of 7°±2° , and several candidate disk members have eccentricities greater than 0.2. Our findings suggest that the young stars may have formed in situ but in a more complex geometry than a simple thin circular disk

Moving from rational to irrational modelling: predicting alcohol consumption

Traditional health behaviour models (eg. Theory of Planned Behaviour) rest on the assumption that behaviour is the result of a deliberate, rational decision-making process. These 'rational' models however fail to account for the situational influences of behaviour. Thus, the ability to explain spontaneous, irrational behaviour such as binge drinking is limited. A more appropriate theoretical framework has been outlined by Gibbons and Gerrard. The Prototype Willingness Model (PWM) accepts that behaviour is not always rational and may be influenced by a number of situational factors. Through the inclusion of an 'irrational' pathway to behaviour, the PWM has had success predicting health risk behaviours such as binge drinking, which are more likely to be subject to situational influences. The current study aimed to compare the Theory of Planned Behaviour (TPB) and the Prototype Willingness Model's (PWM) ability to predict alcohol consumption within an adult sporting sample (M= 30.15 years, SD= 12.48 years). Participants completed either a paper- or web- based anonymous questionnaire. The total sample (N= 319) included males and females from team and individual oriented sports. Sport type comparisons highlight the contrast between the social nature of team sports and individual sports where social pressures to consume alcohol may not be as prominent. Overall, team sports people's quantity of alcohol consumption was significantly greater than individual sports people's. Multiple Regression Analyses (MRAs) were conducted to examine the TPB and PWMs ability to predict team and individual sports people's quantity of alcohol consumption. As expected, the results suggest that the prototype was more salient for team sports people where hazardous alcohol consumption and prototype perceptions were significantly positively associated. The current study has highlighted the association between prototype perceptions hazardous alcohol consumption. Risk behaviour goes beyond the scope of rational forethought, thus the frameworks we employ must also acknowledge this. The important aspect of the PWM is that it provides a more enriched model upon which interventions can be based. It goes beyond the TPB by including social mechanisms that influence behaviour. Future research should now focus on manipulating prototype perceptions in an attempt to reduce hazardous alcohol consumption