Fractional Processes And Fractional Order Signal Processing Techniques And Applications Signals And Communication Technology
Fractional Processes And Fractional Order Signal Processing Techniques And Applications Signals And Communication Technology
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2021
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本书报道了一项致力于使用分数阶微积分对动态系统进行建模和控制的杰出研究。它描述了用于分数动态模型描述的系统的基于模型的控制设计方法的开发。自从牛顿和莱布尼茨开发出一套我们现在称为微积分的数学工具以来，已经过去了 300 多年。从那时起，非整数导数和积分（通常称为分数阶微积分）的概念一直引起许多研究人员的兴趣。然而，由于各种问题，分数阶模型在实际应用中的使用受到限制。现代计算机科学的进步使得将有效的数值方法应用于分数阶导数和积分的计算成为可能。本书介绍了作者为分数建模和控制开发的新颖方法，以及它们在实际过程控制场景中的成功应用。本书详细研究了分数阶、设定点、加权 PID 控制策略以及基于曲线拟合的分数阶参数近似技术的开发。此外，在所有情况下，它都包含基于 Scilab 的命令和函数，以便于实现和更好地理解，并吸引使用该软件的广大读者。所提出的基于 Scilab 的工具箱是第一个用于用开源软件开发的分数阶系统的工具箱。该工具箱允许对分数阶系统和控制器进行时域和频域以及稳定性分析。本书还提供了使用开发的基于分数阶的 PID 控制策略和近似技术来控制过程工厂的实时示例。工业界和学术界的分数阶控制器、近似技术、过程建模、控制和优化领域的读者都对本书感兴趣。在工业中，这本书在研发 (R&D) 领域以及 PID 控制器足以满足需求的领域特别有价值 - 应该指出的是，工业中大约 80% 的低级控制器都是基于 PID 的。在传统 PID 受到限制的情况下（例如存在长期延迟和非线性的行业），本书也很有用。
This book reports on an outstanding research devoted to modeling and control of dynamic systems using fractional-order calculus. It describes the development of model-based control design methods for systems described by fractional dynamic models. More than 300 years had passed since Newton and Leibniz developed a set of mathematical tools we now know as calculus. Ever since then the idea of non-integer derivatives and integrals, universally referred to as fractional calculus, has been of interest to many researchers. However, due to various issues, the usage of fractional-order models in real-life applications was limited. Advances in modern computer science made it possible to apply efficient numerical methods to the computation of fractional derivatives and integrals. This book describes novel methods developed by the author for fractional modeling and control, together with their successful application in real-world process control scenarios. This book presents a detailed study on fractional-order, set-point, weighted PID control strategies and the development of curve-fitting-based approximation techniques for fractional-order parameters. Furthermore, in all the cases, it includes the Scilab-based commands and functions for easy implementation and better understanding, and to appeal to a wide range of readers working with the software. The presented Scilab-based toolbox is the first toolbox for fractional-order systems developed in open-source software. The toolboxes allow time and frequency domains as well as stability analysis of the fractional-order systems and controllers. The book also provides real-time examples of the control of process plants using the developed fractional-order based PID control strategies and the approximation techniques. The book is of interest to readers in the areas of fractional-order controllers, approximation techniques, process modeling, control, and optimization, both in industry and academia. In industry, the book is particularly valuable in the areas of research and development (R&D) as well as areas where PID controllers suffice – and it should be noted that around 80% of low-level controllers in industry are PID based. The book is also useful where conventional PIDs are constrained, such as in industries where long-term delay and non-linearity are present.