Stephen Duncan

Control of temperature profile for a spray deposition process

Spray forming is a novel method of rapidly manufacturing tools and dies for stamping and injection operations. The process sprays molten tool steel from a set of arc spray guns onto a ceramic former to build up a thick steel shell. The volumetric contraction that occurs as the steel cools is offset by a volumetric expansion taking place within the sprayed steel, which allows the dimensional accurate tools to be produced. To ensure that the required phase transformation takes place, the temperature of the steel is regulated during spraying. The sprayed metal acts both as a source of mass and a source of heat and by adjusting the rate at which metal is sprayed, the surface temperature profile over the surface of the steel shell can be controlled. The temperature profile is measured using a thermal imaging camera and regulated by adjusting the rate at which the guns spray the steel. Because the temperature is regulated by adjusting the feed rate to an actuator that is moving over the surface, this is an example of mobile control, which is a class of distributed parameter control. The paper describes the design of a time-varying H/sub 2/ controller for the process and presents results from the implementation of the controller on the spray forming process.

Infant mortality and famine: a study in historical epidemiology in northern England.

OBJECTIVE--To examine whether periodic variations in annual infant mortality were associated with malnutrition and the poor quality of the food supply available to the community. DESIGN--Retrospective study of historical epidemiology of infant mortality by time series analysis and family reconstitution of parish registers of burials and baptisms. SETTING--Penrith, Cumbria, England, 1557-1812. SUBJECTS--A total of 17,500 births during 1557-1812. RESULTS--This community in the Eden Valley, Cumbria, close to the Scottish borders, was living under marginal conditions with high mortality and low fertility. Clear oscillations in infant mortality synchronise with the oscillations in the wheat price index which is regarded as a measure of the availability of food to the community, and to pregnant and nursing mothers in particular. Input-output analysis showed that the relationship between the wheat price index (input) and infant mortality (output) was highly significant (p < 0.001). Events during the famine of 1623 have been analysed in detail: high wheat prices during pregnancy caused subsequent severe infant mortality but did not have indirect effects on the subsequent mortality of the surviving children over the age of 1 year. Non-stationary oscillations in neonatal and post neonatal mortality were strongly coherent (p < 0.001) with the wheat price index throughout the period. CONCLUSIONS--Infant mortality is particularly sensitive to famine and also to the quality of the food supply available to pregnant and nursing mothers. The lags between neonatal and post-neonatal mortalities and wheat prices, together with the analysis of the famine of 1623, support the hypothesis that neonatal mortality was related to malnutrition in pregnancy whereas post-neonatal mortality was primarily directly dependent on exogenous causes in the first year of life.

Low-order mathematical modelling of electric double layer supercapacitors using spectral methods

Abstract This work investigates two physics-based models that simulate the non-linear partial differential algebraic equations describing an electric double layer supercapacitor. In one model the linear dependence between electrolyte concentration and conductivity is accounted for, while in the other model it is not. A spectral element method is used to discretise the model equations and it is found that the error convergence rate with respect to the number of elements is faster compared to a finite difference method. The increased accuracy of the spectral element approach means that, for a similar level of solution accuracy, the model simulation computing time is approximately 50% of that of the finite difference method. This suggests that the spectral element model could be used for control and state estimation purposes. For a typical supercapacitor charging profile, the numerical solutions from both models closely match experimental voltage and current data. However, when the electrolyte is dilute or where there is a long charging time, a noticeable difference between the numerical solutions of the two models is observed. Electrical impedance spectroscopy simulations show that the capacitance of the two models rapidly decreases when the frequency of the perturbation current exceeds an upper threshold.

Using economic Model Predictive Control to design sustainable policies for mitigating climate change

Reducing greenhouse gas emissions is now an important and pressing matter. Systems control theory, and in particular feedback control, can contribute to the design of policies that achieve sustainable levels of emissions of CO2 (and other greenhouse gases) while minimizing the impact on the economy, and at the same time explicitly addressing the high levels of uncertainty associated with predictions of future emissions. In this paper, preliminary results are described for an approach where economic Model Predictive Control (MPC) is applied to a Regional dynamic Integrated model of Climate and the Economy (RICE model) as a test bed to design savings rates and global carbon tax for greenhouse gas emissions. Using feedback control, the policies are updated on the basis of the observed emissions, rather than on the predicted level of emissions. The basic structure and principle of the RICE model is firstly introduced and some key equations are described. The idea of introducing feedback control is then explained and economic MPC is applied to design policies for CO2 emissions. Simulation results are presented to demonstrate the effectiveness of the proposed method for two different scenarios. Feedback control design provides a degree of robustness against disturbances and model uncertainties, which is illustrated through a simulation study with two particular types of uncertainties. The results obtained in this paper illustrate the strength of the proposed design approach and form the basis for future research on using systems control theory to design optimal sustainable policies.

Processing data from scanning gauges on industrial web processes

This paper considers the processing of data collected by scanning gauges from industrial web processes such as metal rolling, coating, paper making and plastic film extrusion. It describes a method based upon the generalised sampling theorem for reconstructing two-dimensional variations in material properties from scanned data. The approach does not require any knowledge of the process apart from the bandwidth of the variations in the machine direction.

Optimal Robot Path for Minimizing Thermal Variations in a Spray Deposition Process

This paper describes a method for determining the optimal robot path that minimizes thermal variations over a surface during a spray deposition process, where the deposited material is hotter than the surface. An analytical expression is formed for the amplitude of the thermal modes of the surface temperature profile. This expression is then used to determine the optimal robot velocity, scan angle, and start position. Experimental results from a metal spray deposition process are used to confirm the analysis

Multivariable disturbance modelling for web processes

This paper considers suitable disturbance models for use in the design of control systems for web forming processes. It suggests a practical disturbance representation and, using spectral factorization, presents a multivariable aggregated model of the disturbance. The paper compares generalized minimum variance (GMV) controllers designed using uncorrelated and correlated disturbance models and demonstrates the improvement in performance of a multivariable GMV controller which is designed to accommodate the cross direction correlation in the disturbance compared to the GMV controller that is commonly used in practice, which is based on a model that ignores the effects of correlated disturbances.

Human population dynamics

Time-series analysis of parish register series can be used to study human population dynamics at three different levels: (i) The metapopulation of preindustrial rural England. A short wavelength, exogenous oscillation in the burials series of 404 parishes can be detected which, it is suggested, was driven by a cycle of malnutrition associated with wheat prices. (ii) Individual populations, where long-term endogenous oscillations in baptisms and burials of wavelength 30-32 years or 43-44 years can be detected. Their characteristics and causes are explored and elucidated by matrix modelling. (iii) The separate neonatal, post-neonatal, child and adult mortalities in an individual population each show an exogenous short wavelength oscillation and a model is presented to show how these cycles were driven by an oscillation in grain prices and how they interacted. Together, they formed the feedback in a saturated, density-dependent population which was fundamental in controlling the characteristics of the longer wavelength endogenous oscillations in the population dynamics described above.

Dynamic modeling of cross-directional actuators: implications for control

Actuators that bend slice lips are commonly used in cross-directional (CD) control systems for paper making and plastic film extrusion. A dynamic model of these actuators is developed, which is used to investigate their spatial modes and dynamic responses. The model shows that both the shape and the amplitude of the spatial response depend upon the stiffness of the slice lip. The design of most practical CD control systems is simplified by assuming that the spatial and dynamic responses are separable in the sense that each of the spatial modes has the same dynamics. The validity of this assumption is examined and it is shown that subject to conditions that are likely to be satisfied in practice, the responses can be taken as separable. The model is verified using data from plastic film extrusion line and the consequences of separability for the design of CD control systems are discussed.

Modelling the dynamics of scarlet fever epidemics in the 19th century

Annual deaths from scarlet fever in Liverpool, UK during 1848–1900 have been used as a model system for studying the historical dynamics of the epidemics. Mathematical models are developed which include the growth of the population and the death rate from scarlet fever. Time-series analysis of the results shows that there were two distinct phases to the disease (i) 1848–1880: regular epidemics (wavelength = 3.7 years) consistent with the system being driven by an oscillation in the transmission coefficient (δβ) at its resonant frequency, probably associated with dry conditions in winter (ii) 1880–1900: an undriven SEIR system with a falling endemic level and decaying epidemics. This period was associated with improved nutritive levels. There is also evidence from time-series analysis that raised wheat prices in pregnancy caused increased susceptibility in the subsequent children. The pattern of epidemics and the demographic characteristics of the population can be replicated in the modelling which provides insights into the detailed epidemiology of scarlet fever in this community in the 19th century.