Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

Advanced controllers for building energy management systems. Advanced controllers based on traditional mathematical methods (MIMO P+I, state-space, adaptive solutions with constraints) and intelligent solutions (fuzzy logic and genetic algorithms) are investigated for humidifying, ventilating and air-conditioning applications.

This thesis presents the design and implementation of control strategies for building energy management systems (BEMS). The controllers considered include the multi PI-loop controllers, state-space designs, constrained input and output MIMO adaptive controllers, fuzzy logic solutions and genetic algorithm techniques. The control performances of the designs developed using the various methods based on aspects such as regulation errors squared, energy consumptions and the settling periods are investigated for different designs. The aim of the control strategy is to regulate the room temperature and the humidity to required comfort levels. In this study the building system under study is a 3 input/ 2 output system subject to external disturbances/effects. The three inputs are heating, cooling and humidification, and the 2 outputs are room air temperature and relative humidity. The external disturbances consist of climatic effects and other stochastic influences. The study is carried out within a simulation environment using the mathematical model of the test room at Loughborough University and the designed control solutions are verified through experimental trials using the full-scale BMS facility at the University of Bradford

System modelling and control

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Power System Simulation, Control and Optimization

This Special Issue “Power System Simulation, Control and Optimization” offers valuable insights into the most recent research developments in these topics. The analysis, operation, and control of power systems are increasingly complex tasks that require advanced simulation models to analyze and control the effects of transformations concerning electricity grids today: Massive integration of renewable energies, progressive implementation of electric vehicles, development of intelligent networks, and progressive evolution of the applications of artificial intelligence

Numerical issues and computational problems in algebraic control theory

The work of this thesis concerns computational issues arising from various fields of Algebraic Control Theory. Efficient algorithms covering the following classes of problems are developed. (i) Exterior Algebra Computations: For given matrices [Please see formulas inside thesis] algorithms achieving the computation of [Please see formulas inside thesis] are formulated. An algorithm for the evaluation of Plucker matrices is also proposed. Most of these algorithms are used in the development of a unifying numerical algorithm for the solution of the Determinantal Assignment Problem. (ii) Numerical Techniques for handling nonqeneric computations: Several numerical tools for the diagnosis of certain properties in an "almost sense", and the definition of procedures attaining the termination of algorithms are developed. (iii) Evaluation of the Greatest Common Divisor of polynomials: A new numerical algorithm for the evaluation of the greatest common divisor of any set of polynomials is formulated. (iv) Almost Zero Computations: Algorithms achieving the evaluation of the Prime almost zero of a polynomial set and the computation of the zero radius are given. Useful comments about the achievement of improved bounds for the zero-trapping region are also presented

Dynamic simulation of industrial grinding circuits : mineral liberation, advanced process control, and real-time optimisation

Étant donné que les minéraux apparaissent fréquemment dans des associations complexes dans la nature, la libération minérale est un aspect clé du traitement de minerais et celle-ci est accomplie par comminution. Cette opération est certainement l’une des plus importantes, mais aussi des plus coûteuses dans l’industrie. La réussite globale d’une usine dépend souvent de la performance du circuit de broyage car il existe un compromis pour atteindre la taille des particules libérant les minéraux ciblés afin d’obtenir des concentrés de haute pureté tout en ayant de faibles coûts d’opération, lesquels sont largement influencés par la consommation énergétique. Dans les années récentes, les entreprises ont été confrontées à des objectifs de performance plus exigeants, une concurrence accrue sur les marchés, et des réglementations environnementales et de sécurité plus strictes. D’autres défis supplémentaires sont inhérents aux circuits de broyage, par exemple les réponses non linéaires, le niveau élevé d’intercorrélation entre les variables et les recirculations de matière. Les problèmes ci-dessus soulignent la pertinence d’avoir des systèmes de contrôle et d’optimisation adéquats pour lesquels les praticiens profitent de plus en plus des approches basées sur des modèles pour y faire face de façon systématique. La modélisation et la simulation sont des outils puissants ayant des avantages significatifs tels que les faibles coûts, les temps requis pour réaliser des expériences relativement courts et la possibilité de tester des conditions opérationnelles extrêmes ainsi que différentes configurations des circuits sans interrompre la production. De toute évidence, la qualité des résultats sera aussi bonne que la capacité du modèle à représenter la réalité, ce qui souligne l’importance d’avoir des modèles précis et des procédures de calibrage appropriées, un sujet fréquemment omis dans la littérature. Un autre aspect essentiel qui n’a pas été rapporté est l’intégration efficace de la libération minérale aux systèmes de contrôle et d’optimisation de procédés. Bien qu’il s’agisse d’une information clé directement liée aux performances de l’étape de concentration, la plupart des stratégies se concentrent exclusivement sur la taille de particule du produit. Ceci est compréhensible étant donné qu’il est impossible de mesurer la distribution de libération présentement. Basée sur une librairie de simulation d’usines de traitement des minerais déjà existante, cette recherche aborde lesdits problèmes en (1) développant un modèle de libération minérale visant à coupler les étapes de broyage et de concentration ; (2) programmant et validant par calibrage un modèle phénoménologique de broyeur autogène/semi-autogène (BA/BSA), nécessaire pour compléter la librairie de simulation ; (3) couplant un simulateur de circuit de broyage à un procédé de concentration avec le modèle de libération, et (4) développant un système de contrôle et d’optimisation qui considère explicitement des données de libération minérale pour évaluer les avantages économiques. Les principaux résultats confirment que le modèle de libération est capable de reproduire avec précision des distributions de libération minérale couramment observées dans l’industrie. Cependant, si les données de calibrage correspondent à un point d’opération unique, la validité pourrait être limitée aux régions voisines proches. Le problème de caractériser l’évolution de la libération minérale aux diverses conditions d’opération ainsi qu’aux régimes transitoires reste à être abordé. Le modèle de libération s’est aussi révélé utile pour coupler des circuits de broyage avec des procédés de concentration, en particulier pour une unité de flottation. Quant au modèle de BA/BSA, celui-ci peut capturer le régime statique ainsi que la dynamique d’un broyeur réel et conjointement avec le reste des équipements dans la librairie de simulation, des circuits de broyage industriels. Ceci a été confirmé par le calibrage à partir des données d’opération d’une usine et des tests en laboratoire, tout en suivant une procédure systématique, contribuant aussi au sujet de l’établissement de méthodologies de calibrage standardisées. Pour terminer, les expériences concernant la stratégie de contrôle et d’optimisation basée sur la libération minérale suggèrent que l’utilisation de cette information peut améliorer la performance globale des circuits de broyage-séparation en réagissant aux variations des caractéristiques de libération, qui à leur tour influencent l’efficacité de séparation. L’étude de cas réalisé révèle que cela peut entraîner une augmentation du débit massique et de la teneur du concentré, de la récupération des métaux et des revenus de l’ordre de +0.5%, +1%, +1% et +5%, respectivement, par rapport au cas où ces informations sont omises.As minerals frequently appear in complex associations in nature, mineral liberation is one of the most relevant aspects in ore processing and is achieved through comminution. This operation is one of the most important, but also one of the most expensive ones in industry. The global efficiency of a plant often depends on the performance of the grinding circuit, since there is a compromise to achieve the particle size liberating the targetted minerals in order to obtain high purity concentrates while maintaining low operating costs, which are largely influenced by the energy consumption. In recent years, companies have been facing more demanding performance targets, stronger competition, and more stringent environmental and safety regulations. Additional challenges are inherent to the grinding circuits themselves, e.g. the nonlinear responses, high degree of intercorrelation of the different variables, and material recirculations. The abovementioned issues highlight the relevance of adequate process control and optimisation, and practitioners rely more often on model-based approaches in order to face them systematically. Modeling and simulation are powerful tools with significant advantages such as low costs, required times for conducting experiments are relatively short, and the possibility of testing extreme operational conditions as well as different circuit configurations without disrupting production. Evidently, the quality of the results will only be as good as the model capacity to represent the reality, which emphasises the relevance of having precise models and proper calibration procedures, the latter being a topic frequently omitted in the literature. Another crucial aspect that has not been reported yet is the effective integration of mineral liberation in control and optimisation schemes. Although it is a key piece of information directly related to the performance of the concentration stage, most strategies focus exclusively on the particle size. This is understandable given that it is currently impossible to measure the liberation distribution online. Based on an existing mineral processing plant simulation library, this research addresses these problems by (1) developing a mineral liberation model aiming at linking the grinding and concentration stages; (2) programming a phenomenological autogenous/semiautogenous (AG/SAG) mill model, required to complement the simulation toolbox, and validating it through calibration; (3) coupling a grinding circuit simulator to a concentration process by means of the liberation model, and (4) developing a plantwide control and optimisation scheme considering mineral liberation data explicitly to evaluate the economic benefits. The main results confirm that the liberation model is capable of reproducing accurately mineral distributions observed in industry. If calibration data correspond to a single operating point, its validity may however be limited to the close neighbourhood. Characterising the evolution of mineral liberation in different operating conditions and transient states remains to be addressed. The liberation model proved to be equally useful in coupling grinding circuits with concentration processes, specifically for flotation. As for the AG/SAG mill model, it can capture the steady state and dynamic behaviour of an actual device and, along with the rest of pieces of equipment in the simulation toolbox, of industrial grinding circuits. This was confirmed through calibration from plant data and laboratory testwork following a systematic procedure, contributing to the endeavour of establishing standard calibration methodologies. Lastly, the results of the designed control and optimisation scheme suggest that using liberation data for control and real-time optimisation can improve the overall performance of grinding-separation circuits by reacting to variations in the liberation characteristics, which in turn influence the concentration performance. The case study reveals that doing so can lead to increases in the concentrate mass flow rate and grade, metal recovery, and global profits in the order of +0.5%, +1%, +1%, and +5%, respectively, compared to the case omitting this information

Error Bounds of Gaussian Quadratures for One Class of Bernstein-Szego Weight Functions

We consider the action of the automorphism group I(n) of Zn on the set of k−sets of Zn in the natural way. Although elementary in its nature, it has not been fully analyzed and understood yet. The vast class of enumerative and computational problems problems is related to this action. For example, the number of orbits on the set of k−sets of Zn is one of them that we are interested in. Those enumerative problems are mainly resolved by application of P olya's theory