Frequency Domain Characterization Of Sliding Mode Control Of An Inverter Used In DSTATCOM Application

In this paper, the commonly used switching schemes for sliding mode control of power converters is analyzed and designed in the frequency domain. Particular application of a distribution static compensator (DSTATCOM) in voltage control mode is investigated in a power distribution system. Tsypkin's method and describing function is used to obtain the switching conditions for the two-level and three-level voltage source inverters. Magnitude conditions of carrier signals are developed for robust switching of the inverter under carrier-based modulation scheme of sliding mode control. The existence of border collision bifurcation is identified to avoid the complex switching states of the inverter. The load bus voltage of an unbalanced three-phase nonstiff radial distribution system is controlled using the proposed carrier-based design. The results are validated using PSCAD/EMTDC simulation studies and through a scaled laboratory model of DSTATCOM that is developed for experimental verification

Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.

Describing ocular aberrations with wavefront vergence maps

A common optometric problem is to specify the eye’s ocular aberrations in terms of Zernike coefficients and to reduce that specification to a prescription for the optimum sphero-cylindrical correcting lens. The typical approach is first to reconstruct wavefront phase errors from measurements of wavefront slopes obtained by a wavefront aberrometer. This paper applies a new method to this clinical problem that does not require wavefront reconstruction. Instead, we base our analysis of axial wavefront vergence as inferred directly from wavefront slopes. The result is a wavefront vergence map that is similar to the axial power maps in corneal topography and hence has a potential to be favoured by clinicians. We use our new set of orthogonal Zernike slope polynomials to systematically analyse details of the vergence map analogous to Zernike analysis of wavefront maps. The result is a vector of slope coefficients that describe fundamental aberration components. Three different methods for reducing slope coefficients to a spherocylindrical prescription in power vector forms are compared and contrasted. When the original wavefront contains only second order aberrations, the vergence map is a function of meridian only and the power vectors from all three methods are identical. The differences in the methods begin to appear as we include higher order aberrations, in which case the wavefront vergence map is more complicated. Finally, we discuss the advantages and limitations of vergence map representation of ocular aberrations.

An exploration of young students' ability to generalise function tasks

The Early Years Generalising Project involves Australian students, Years 1-4 (age 5-9), and explores how the students grasp and express generalisations. This paper focuses on the data collected from clinical interviews with Year 3 and 4 cohorts in an investigative study focusing on the identifications, prediction and justification of function rules. It reports on students' attempts to generalise from function machine contexts, describing the various ways students express generalisation and highlighting the different levels of justification given by students. Finally, we conjecture that there are a set of stages in the expression and justification of generalisations that assist students to reach generality within tasks.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

Smoothing a Discrete Hazard Function for the Number of Patients Colonized with Methicillin-Resistance Staphylococcus Aureus in an Intensive Care Unit

A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.