14 research outputs found

    Complete Identification of a Dynamic Fractional Order System Under Non-ideal Conditions Using Fractional Differintegral Definitions

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    This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as opposed to the ideal integral order models. A simple and elegant scheme of estimating the parameters for such a fractional order process is proposed. This method employs fractional calculus theory to find equations relating the parameters that are to be estimated, and then estimates the process parameters after solving the simultaneous equations. The data used for the calculations are intentionally corrupted to simulate real-life conditions. Results show that the proposed scheme offers a very high degree of accuracy even for erroneous data.Comment: 16th IEEE International Conference on Advanced Computing and Communication, 200

    A Study of the Grunwald-Letnikov Definition for Minimizing the Effects of Random Noise on Fractional Order Differential Equations

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    Of the many definitions for fractional order differintegral, the Grunwald-Letnikov definition is arguably the most important one. The necessity of this definition for the description and analysis of fractional order systems cannot be overstated. Unfortunately, the Fractional Order Differential Equation (FODE) describing such a systems, in its original form, highly sensitive to the effects of random noise components inevitable in a natural environment. Thus direct application of the definition in a real-life problem can yield erroneous results. In this article, we perform an in-depth mathematical analysis the Grunwald-Letnikov definition in depth and, as far as we know, we are the first to do so. Based on our analysis, we present a transformation scheme which will allow us to accurately analyze generalized fractional order systems in presence of significant quantities of random errors. Finally, by a simple experiment, we demonstrate the high degree of robustness to noise offered by the said transformation and thus validate our scheme.Comment: 4th IEEE International Conference on Information and Automation for Sustainability, 200

    Mathematical Analysis and Applications

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    Investigations involving the theory and applications of mathematical analytic tools and techniques are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. In this Special Issue, we invite and welcome review, expository and original research articles dealing with the recent advances in mathematical analysis and its multidisciplinary applications

    ANALIZA MODELU UŁAMKOWEGO RZĘDU PROCESÓW SZYBKICH REAKTORA JĄDROWEGO

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    The paper presents the results concerning numerical solutions of the fractional point kinetics and heat exchange model for nuclear reactor. The fractional neutron point kinetics model with six groups of delayed neutron precursors was developed and numerical solutions were proposed. Mathematical model has been implemented in the Matlab environment and tested using typical step input change. The analysis of the impact of chosen parameters was conducted.W artykule przedstawiono wyniki badań dotyczące rozwiązań numerycznych punktowego modelu ułamkowego rzędu kinetyki neutronów oraz wymiany ciepła w reaktorze jądrowym. Zbudowano model ułamkowego rzędu z sześcioma grupami neutronów opóźnionych wraz równaniami wymiany ciepła. Model matematyczny został zaimplementowany w środowisku Matlab i zbadany symulacyjnie dla skoków reaktywności. Przeprowadzono analizę wpływu wybranych parametrów modelu na uzyskiwane rozwiązania

    Modelling Human-Driver Behaviour Using a Biofidelic Approach

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    This dissertation is concerned with the subject of modelling human steering control of ground vehicles. Special care has been taken with respect to designing a model that is biofidelic, i.e., a model that operates according to the principles of human control. With this aim, first classical human control theory has been revisited, both from a literature review and an experimental perspective; data have been recorded from test subjects in compensatory and pursuit tracking tasks. The tracking experiments are the first ever to be performed with fractional order plants, which are plants suitable to represent system memory. From the data, an extension of the Crossover model by McRuer’s is designed, to include the control of such category of plants. The proposed model is referred to as the Fractional Crossover Model. This is followed by a study on modelling memory in human-machine systems from a classical control theory viewpoint. These results broaden the existing array of manual control modelling techniques and can be employed in a modular manner, combined with current models. More significantly – and still with respect to the domain of generic human control and human-machine systems – a new approach for modelling the human-operator is proposed. This approach consists in treating the problem from a statistical viewpoint. With this methodology a novel human control model based on multiplicative dynamics is presented. The model, which was inspired on actual results in neuroscience, is validated with the tracking data obtained from test subjects and by comparing it to classical models in the literature. Hence the model is useful to analyse human performance or to reproduce human control in simulation, field tests or in the video game industry. With respect to steering control modelling, which is the main topic of this dissertation, additional experiments with test subjects were conducted in a simple vehicle simulator – with hardware and software specifically developed during this research program to test multiple hypotheses. The data were analysed with the intent of identifying which optical variables drivers employ while controlling a vehicle on public roads; it is seen that the splay angles– which are the projections of the road lines on the retina – are likely candidates for lane keeping at low speeds. This brings on a novel human-centred driver model first proposed here. This model includes multiplicative human control over the splay angles, and far-point error perception for lane keeping at higher speeds. The human-centred model has its domain of applicability in the intelligent transportation industry, in particular for the development of shared control systems and advanced driver-assistance systems for semi-autonomous ground vehicles. Additionally, the model can be employed in field testing of ground vehicles – for example, in vehicle durability tests. Furthermore, the topic of alternative steering devices for driving autonomous and semi-autonomous vehicles is investigated. This leads to another of the contributions in this dissertation. Here it is proposed that for such vehicles, and for the control of systems with a shared control perspective, anisometric steering wheel can be advantageous under certain schemes – tight rein or loose rein modes according to the H-metaphor. This is supported by additional data collected in the driving simulation experiments. Resulting from this, fractional order transfer functions are employed to increment steering stability and control accuracy with the isometric device. This prototypical steering system is applicable for the control of ground vehicles with the so-called by-wire controls, which are already incorporated in some commercially available vehicles

    On the outer synchronization of complex dynamical networks

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    Complex network models have become a major tool in the modeling and analysis of many physical, biological and social phenomena. A complex network exhibits behaviors which emerge as a consequence of interactions between its constituent elements, that is, remarkably, not the same as individual components. One particular topic that has attracted the researchers' attention is the analysis of how synchronization occurs in this class of models, with the expectation of gaining new insights of the interactions taking place in real-world complex systems. Most of the work in the literature so far has been focused on the synchronization of a collection of interconnected nodes (forming one single network), where each node is a dynamical system governed by a set of nonlinear differential equations, possibly displaying chaotic dynamics. In this thesis, we study an extended version of this problem. In particular, we consider a setup consisting of two complex networks which are coupled unidirectionally, in such a way that a set of signals from the master network are injected into the response network, and then investigate how synchronization is attained. Our analysis is fairly general. We impose few conditions on the network structure and do not assume that the nodes in a single network are synchronized. This work can be divided into two main parts; outer synchronization in fractional-order networks, and outer synchronization in ordinary networks. In both cases the system parameters are perturbed by bounded, time varying and unknown perturbations. The synchronizer feedback matrix is possibly perturbed with the same type of perturbations as well. In both cases, of fractional-order and ordinary networks, we build up several theorems that ensure the attainment of synchronization in various scenarios, including, e.g., cases in which the coupling matrix of the networks is non-diffusive (hence we can avoid this assumption, which is almost invariably made in the literature). In all the cases of interest, we show that the scheme for coupling the networks is very simple, as it reduces to the computation of a single gain matrix whose dimension is independent of the number of network nodes. The structure of the designed synchronizer is also very simple, making it convenient for real-world applications. Although all of the proposed schemes are assessed analytically, numerical results (obtained by computer simulations) are also provided to illustrate the proposed methods. ---------------------------------------Las redes complejas se han convertido en una herramienta fundamental en el análisis de muchos sistemas físicos, biológicos y sociales. Una red compleja presenta comportamientos que "emergen" como consecuencia de las interacciones entre sus elementos constituyentes pero que no se observan de forma individual en estos elementos. Un aspecto en concreto que ha atrapado la atención de muchos investigadores es el análisis de cómo se producen fenómenos de sincronización en esta clase de modelos, con la esperanza de alcanzar una mayor comprensión de las interacciones que tienen lugar en sistemas complejos del mundo real. La mayor parte del trabajo publicado hasta ahora ha estado centrado en la sincronización de una colección de nodos interconectados (que forman una única red con entidad propia), donde cada nodo es un sistema dinámico gobernado por un conjunto de ecuaciones diferenciales no lineales, posiblemente caóticas. En esta tesis estudiamos una versión extendida de este problema. En concreto, consideramos un sistema formado por dos redes complejas acopladas unidireccionalmente, de manera que un conjunto de señales de la red principal se inyectan en la red secundaria, e investigamos cómo se alcanza un estado de sincronización. Este fenómeno se conoce como "sincronización externa". Nuestro análisis es muy general. Se imponen pocas condiciones a las estructura de las redes y no es necesario suponer que los nodos de cada red estén sincronizados entre sí previamente. Esta memoria se puede dividir en dos bloques: la sincronización externa de redes descritas por ecuaciones diferenciales de orden fraccionario y la sincronización externa de redes ordinarias (descritas por ecuaciones diferenciales de orden entero). En ambos casos, se admite que los parámetros del sistema puedan estar sujetos a perturbaciones desconocidas, posiblemente variables con el tiempo, pero acotadas. La matriz de realimentación del esquema de sincronización puede sufrir el mismo tipo de perturbación. En ambos casos, con ecuaciones de orden fraccionario o entero, construimos varios teoremas que aseguran que se alcance la sincronización en escenarios diversos, incluyendo, por ejemplo, casos en los que la matriz de acoplamiento de las redes es no difusiva (por lo tanto, podemos evitar esta hipótesis, que es ubicua en la literatura). En todos los casos de interés, mostramos que el esquema necesario para interconectar las redes es muy simple, puesto que se reduce al cálculo de una única matriz de ganancia cuya dimensión es independiente de la dimensión total (número de nodos) de las redes. La estructura del sincronizados es también muy sencilla, lo que la hace potencialmente adecuada para aplicaciones del mundo real. Aunque todos los esquemas que se proponen se analizan de manera rigurosa, también se muestran resultados numéricos (obtenidos mediante simulación) para ilustrar los métodos propuestos.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Ángel María Bravo Santos.- Secretario: David Luengo García.- Vocal: Irene Sendiña Nada

    Engineering Education and Research Using MATLAB

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    MATLAB is a software package used primarily in the field of engineering for signal processing, numerical data analysis, modeling, programming, simulation, and computer graphic visualization. In the last few years, it has become widely accepted as an efficient tool, and, therefore, its use has significantly increased in scientific communities and academic institutions. This book consists of 20 chapters presenting research works using MATLAB tools. Chapters include techniques for programming and developing Graphical User Interfaces (GUIs), dynamic systems, electric machines, signal and image processing, power electronics, mixed signal circuits, genetic programming, digital watermarking, control systems, time-series regression modeling, and artificial neural networks

    Analog Implementation of Fractional-Order Elements and Their Applications

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    With advancements in the theory of fractional calculus and also with widespread engineering application of fractional-order systems, analog implementation of fractional-order integrators and differentiators have received considerable attention. This is due to the fact that this powerful mathematical tool allows us to describe and model a real-world phenomenon more accurately than via classical “integer” methods. Moreover, their additional degree of freedom allows researchers to design accurate and more robust systems that would be impractical or impossible to implement with conventional capacitors. Throughout this thesis, a wide range of problems associated with analog circuit design of fractional-order systems are covered: passive component optimization of resistive-capacitive and resistive-inductive type fractional-order elements, realization of active fractional-order capacitors (FOCs), analog implementation of fractional-order integrators, robust fractional-order proportional-integral control design, investigation of different materials for FOC fabrication having ultra-wide frequency band, low phase error, possible low- and high-frequency realization of fractional-order oscillators in analog domain, mathematical and experimental study of solid-state FOCs in series-, parallel- and interconnected circuit networks. Consequently, the proposed approaches in this thesis are important considerations in beyond the future studies of fractional dynamic systems
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