Simplifying Bode's maximum available feedback design

Bode's method for obtaining 'maximum obtainable feedback' is a good example of a nontrivial feedback system design technique, but it is largely overlooked. This paper shows how the associated mathematics can be simplified and linear elements used in its implementation, so as to make it accessible for teaching to undergraduates.

Achieving or exceeding maximum available feedback

A feedback system for control or electronics should have high loop gain, so that its output is close to its desired state, and the effects of changes in the system and of disturbances are minimised. Bode proposed a method for single loop feedback systems to obtain the maximum available feedback, defined as the largest possible loop gain over a bandwidth pertinent to the system, with appropriate gain and phase margins. The method uses asymptotic approximations, and this paper describes some novel adjustments to the asymptotes, so that the final system often exceeds the maximum available feedback. The implementation of the method requires the cascading of a series of lead-lag element. This paper describes a new way to determine how many elements should be used.

Maximum induced subgraph of a recursive circulant

The recursive circulant RC(2(n), 4) enjoys several attractive topological properties. Let max_epsilon(G) (m) denote the maximum number of edges in a subgraph of graph G induced by m nodes. In this paper, we show that max_epsilon(RC(2n,4))(m) = Sigma(i)(r)=(0)(p(i)/2 + i)2(Pi), where p(0) > p(1) > ... > p(r) are nonnegative integers defined by m = Sigma(i)(r)=(0)2(Pi). We then apply this formula to find the bisection width of RC(2(n), 4). The conclusion shows that, as n-dimensional cube, RC(2(n), 4) enjoys a linear bisection width. (c) 2005 Elsevier B.V. All rights reserved.

Building integration photovoltaic module with reference to Ghana: using triple junction amorphous silicon

This paper assesses the potential for using building integrated photovoltaic (BIPV) roof shingles made from triple-junction amorphous silicon (3a-Si) for electrification and as a roofing material in tropical countries, such as Accra, Ghana. A model roof was constructed using triple-junction amorphous (3a-Si) PV on one section and conventional roofing tiles on the other. The performance of the PV module and tiles were measured, over a range of ambient temperatures and solar irradiance. PVSyst (a computer design software) was used to determine the most appropriate angle of tilt. It was observed that 3a-Si performs well in conditions such as Accra, because it is insensitive to high temperatures. Building integration gives security benefits, and reduces construction costs and embodied energy, compared to freestanding PV systems. Again, it serves as a means of protection from salt spray from the oceans and works well even when shaded. However, compared to conventional roofing materials, 3a-Si would increase the indoor temperature by 1-2 °C depending on the surface area of the roof covered with the PV modules. The results presented in this research enhance the understanding of varying factors involved in the selection of an appropriate method of PV installation to offset the short falls of the conventional roofing material in Ghana.

The evolution of maximum body size of terrestrial mammals

The extinction of dinosaurs at the Cretaceous/Paleogene (K/Pg) boundary was the seminal event that opened the door for the subsequent diversification of terrestrial mammals. Our compilation of maximum body size at the ordinal level by sub-epoch shows a near-exponential increase after the K/Pg. On each continent, the maximum size of mammals leveled off after 40 million years ago and thereafter remained approximately constant. There was remarkable congruence in the rate, trajectory, and upper limit across continents, orders, and trophic guilds, despite differences in geological and climatic history, turnover of lineages, and ecological variation. Our analysis suggests that although the primary driver for the evolution of giant mammals was diversification to fill ecological niches, environmental temperature and land area may have ultimately constrained the maximum size achieved.

Improved process topology for membrane distillation

In membrane distillation in a conventional membrane module, the enthalpies of vaporisation and condensation are supplied and removed by changes in the temperatures of the feed and permeate streams, respectively. Less than 5% of the feed can be distilled in a single pass, because the potential changes in the enthalpies of the liquid streams are much smaller than the enthalpy of vaporisation. Furthermore, the driving force for mass transfer reduces as the feed stream temperature and vapour pressure fall during distillation. These restrictions can be avoided if the enthalpy of vaporisation is uncoupled from the heat capacities of the feed and permeate streams. A specified distillation can then be effected continuously in a single module. Calculations are presented which estimate the performance of a flat plate unit in which the enthalpy of distillation is supplied and removed by the condensing and boiling of thermal fluids in separate circuits, and the imposed temperature difference is independent of position. Because the mass flux through the membrane is dependent on vapour pressure, membrane distillation is suited to applications with a high membrane temperature. The maximum mass flux in the proposed module geometry is predicted to be 30 kg/m2 per h at atmospheric pressure when the membrane temperature is 65°C. Operation at higher membrane temperatures is predicted to raise the mass flux, for example to 85 kg/m2 per h at a membrane temperature of 100°C. This would require pressurisation to 20 bar to prevent boiling at the heating plate of the feed channel. Pre-pressurisation of the membrane pores and control of the dissolved gas concentrations in the feed and the recyled permeate should be investigated as a means to achieve high temperature membrane distillation without pore penetration and wetting.

Advances in module design for membrane distillation

This review looks at the work carried out over the past 15 years on membrane distillation and reports the conditions utilized for research. The process is still used mainly at the laboratory scale, but a few pilot plants have been built across the world, mostly for desalination and the production of potable water. Studies into membrane distillation have been concerned with the effect of mass transfer, heat transfer, and stirring rate, but the most important effect that has to be considered with this process is temperature polarization. A section on temperature polarization and the effect of boundary layers is included in this review.

Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture

The objective of this paper is to reconsider the Maximum Entropy Production conjecture (MEP) in the context of a very simple two-dimensional zonal-vertical climate model able to represent the total material entropy production due at the same time to both horizontal and vertical heat fluxes. MEP is applied first to a simple four-box model of climate which accounts for both horizontal and vertical material heat fluxes. It is shown that, under condition of fixed insolation, a MEP solution is found with reasonably realistic temperature and heat fluxes, thus generalising results from independent two-box horizontal or vertical models. It is also shown that the meridional and the vertical entropy production terms are independently involved in the maximisation and thus MEP can be applied to each subsystem with fixed boundary conditions. We then extend the four-box model by increasing its resolution, and compare it with GCM output. A MEP solution is found which is fairly realistic as far as the horizontal large scale organisation of the climate is concerned whereas the vertical structure looks to be unrealistic and presents seriously unstable features. This study suggest that the thermal meridional structure of the atmosphere is predicted fairly well by MEP once the insolation is given but the vertical structure of the atmosphere cannot be predicted satisfactorily by MEP unless constraints are imposed to represent the determination of longwave absorption by water vapour and clouds as a function of the state of the climate. Furthermore an order-of-magnitude estimate of contributions to the material entropy production due to horizontal and vertical processes within the climate system is provided by using two different methods. In both cases we found that approximately 40 mW m−2 K−1 of material entropy production is due to vertical heat transport and 5–7 mW m−2 K−1 to horizontal heat transport