43 research outputs found
Design Templates for Some Fractional Order Control Systems
Time domain characteristics of first and second order systems are well known. But the same simplicity and explicitness do not exist for low order fractional order systems (FOSs). Considering the step response, the templates are developed for designing the behavior of simple FOSs with a 2-term denominator polynomial (one is unity and the other involves fractional power). Although the explicit relations between design parameters and the performance parameters such as time constant, rise time, overshoot, settling time for fractional order control systems (FOCSs) do not exist and can't be obtainable as in the ordinary integer order control systems, the obtained templates in this paper can be used for designing low order FOCSs. Hence, the drawback of non-existence of similar explicit formulas for FOCSs is eliminated by using these templates
Digital Filters
The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature
Analog Implementation of Fractional-Order Elements and Their Applications
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
Engineering Education and Research Using MATLAB
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
Applications of MATLAB in Science and Engineering
The book consists of 24 chapters illustrating a wide range of areas where MATLAB tools are applied. These areas include mathematics, physics, chemistry and chemical engineering, mechanical engineering, biological (molecular biology) and medical sciences, communication and control systems, digital signal, image and video processing, system modeling and simulation. Many interesting problems have been included throughout the book, and its contents will be beneficial for students and professionals in wide areas of interest
Dynamical Systems in Spiking Neuromorphic Hardware
Dynamical systems are universal computers. They can perceive stimuli, remember, learn from feedback, plan sequences of actions, and coordinate complex behavioural responses. The Neural Engineering Framework (NEF) provides a general recipe to formulate models of such systems as coupled sets of nonlinear differential equations and compile them onto recurrently connected spiking neural networks – akin to a programming language for spiking models of computation. The Nengo software ecosystem supports the NEF and compiles such models onto neuromorphic hardware. In this thesis, we analyze the theory driving the success of the NEF, and expose several core principles underpinning its correctness, scalability, completeness, robustness, and extensibility. We also derive novel theoretical extensions to the framework that enable it to far more effectively leverage a wide variety of dynamics in digital hardware, and to exploit the device-level physics in analog hardware. At the same time, we propose a novel set of spiking algorithms that recruit an optimal nonlinear encoding of time, which we call the Delay Network (DN). Backpropagation across stacked layers of DNs dramatically outperforms stacked Long Short-Term Memory (LSTM) networks—a state-of-the-art deep recurrent architecture—in accuracy and training time, on a continuous-time memory task, and a chaotic time-series prediction benchmark. The basic component of this network is shown to function on state-of-the-art spiking neuromorphic hardware including Braindrop and Loihi. This implementation approaches the energy-efficiency of the human brain in the former case, and the precision of conventional computation in the latter case
Dynamical Systems
Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...
Fractional Calculus and the Future of Science
Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding
Spectroscopic characterization of ion motion for an optical clock based on Coulomb crystals
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