Mathematical modelling and optimal multivariable control of chemical processes

This work reports the developnent of a mathenatical model and distributed, multi variable computer-control for a pilot plant double-effect climbing-film evaporator. A distributed-parameter model of the plant has been developed and the time-domain model transformed into the Laplace domain. The model has been further transformed into an integral domain conforming to an algebraic ring of polynomials, to eliminate the transcendental terms which arise in the Laplace domain due to the distributed nature of the plant model. This has made possible the application of linear control theories to a set of linear-partial differential equations. The models obtained have well tracked the experimental results of the plant. A distributed-computer network has been interfaced with the plant to implement digital controllers in a hierarchical structure. A modern rnultivariable Wiener-Hopf controller has been applled to the plant model. The application has revealed a limitation condition that the plant matrix should be positive-definite along the infinite frequency axis. A new multi variable control theory has emerged fram this study, which avoids the above limitation. The controller has the structure of the modern Wiener-Hopf controller, but with a unique feature enabling a designer to specify the closed-loop poles in advance and to shape the sensitivity matrix as required. In this way, the method treats directly the interaction problems found in the chemical processes with good tracking and regulation performances. Though the ability of the analytical design methods to determine once and for all whether a given set of specifications can be met is one of its chief advantages over the conventional trial-and-error design procedures. However, one disadvantage that offsets to some degree the enormous advantages is the relatively complicated algebra that must be employed in working out all but the simplest problem. Mathematical algorithms and computer software have been developed to treat some of the mathematical operations defined over the integral domain, such as matrix fraction description, spectral factorization, the Bezout identity, and the general manipulation of polynomial matrices. Hence, the design problems of Wiener-Hopf type of controllers and other similar algebraic design methods can be easily solved.

A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA

Data Envelopment Analysis (DEA) is a nonparametric method for measuring the efficiency of a set of decision making units such as firms or public sector agencies, first introduced into the operational research and management science literature by Charnes, Cooper, and Rhodes (CCR) [Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429–444]. The original DEA models were applicable only to technologies characterized by positive inputs/outputs. In subsequent literature there have been various approaches to enable DEA to deal with negative data. In this paper, we propose a semi-oriented radial measure, which permits the presence of variables which can take both negative and positive values. The model is applied to data on a notional effluent processing system to compare the results with those yielded by two alternative methods for dealing with negative data in DEA: The modified slacks-based model suggested by Sharp et al. [Sharp, J.A., Liu, W.B., Meng, W., 2006. A modified slacks-based measure model for data envelopment analysis with ‘natural’ negative outputs and inputs. Journal of Operational Research Society 57 (11) 1–6] and the range directional model developed by Portela et al. [Portela, M.C.A.S., Thanassoulis, E., Simpson, G., 2004. A directional distance approach to deal with negative data in DEA: An application to bank branches. Journal of Operational Research Society 55 (10) 1111–1121]. A further example explores the advantages of using the new model.

A study of potential serum markers for a diagnosis of gram-positive and gram-negative bacterial sepsis

Sepsis continues to be a major cause of morbidity and mortality as it can readily lead tosevere sepsis, septic shock, multiple organ failure and death. The onset can be rapid and difficult to define clinically. Despite the numerous candidate markers proposed in the literature, to date a serum marker for sepsis has not been found. The aim of this study was to assay the serum of clinically diagnosed patients with eithera Gram-negative or Gram- positive bacterial sepsis for elevated levels of nine potentialmarkers of sepsis, using commercially produced enzyme linked immunosorbent assays(ELISA). The purpose was to find a test marker for sepsis that would be helpful toclinicians in cases of uncertain sepsis and consequently expose false positive BC'scaused by skin or environmental contaminants. Nine test markers were assayed including IL-6, IL-I 0, ILI2, TNF-α, lipopolysaccharide binding protein, procalcitonin, sE-selectin, sICAM -1 and a potential differential marker for Gram-positive sepsis- anti-lipid S antibody. A total of 445 patients were enrolled into this study from the Queen Elizabeth Hospital and Selly Oak Hospital (Birmingham). The results showed that all the markers were elevated in patients with sepsis and that patients with a Gram-negative sepsis consistently produced higher median/range serum levels than those with a Gram-positive sepsis. No single marker was able to identify all the septic patients. Combining two markers caused the sensitivities and specificities for a diagnosis of sepsis to increase to within a 90% to 100% range. By a process of elimination the markers that survived into the last phase were IL-6 with sICAM -1, and anti-lipid S IgG assays Defining cut-off levels for a diagnosis of sepsis became problematic and a semi-blind trial was devised to test the markers in the absence of both clinical details and positive blood cultures. Patients with pyrexia of unknown origin and negative BC were included in this phase (4). The results showed that IL-6 with sICAM-l are authentic markers of sepsis. There was 82% agreement between the test marker diagnosis and the clinical diagnosis for sepsis in patients with a Gram-positive BC and 78% agreement in cases of Gram-negative Be. In the PUO group the test markers identified 12 cases of sepsis and the clinical diagnosis 15. The markers were shown to differentiate between early sepsis and sepsis, inflammatory responses and infection. Anti-lipid S with IL-6 proved be a sensitive marker for Gram-positive infections/sepsis.