A survey of recent advances in fractional order control for time delay systems

Several papers reviewing fractional order calculus in control applications have been published recently. These papers focus on general tuning procedures, especially for the fractional order proportional integral derivative controller. However, not all these tuning procedures are applicable to all kinds of processes, such as the delicate time delay systems. This motivates the need for synthesizing fractional order control applications, problems, and advances completely dedicated to time delay processes. The purpose of this paper is to provide a state of the art that can be easily used as a basis to familiarize oneself with fractional order tuning strategies targeted for time delayed processes. Solely, the most recent advances, dating from the last decade, are included in this review

Computation of the optimal H∞ controller for a fractional order system

Ankara : The Department of Electrical and Electronics Engineering and The Graduate School of Engineering and Science of Bilkent University, 2014.Thesis (Master's) -- Bilkent University, 2014.Includes bibliographical references leaves 49-54.This work investigates the H∞ optimal controller design for a fractional order system with time delay. For illustrative purposes, a magnetic suspension system model, derived by Knospe and Zhu is considered. The transfer function is infinite dimensional including e −hs and a rational function of √ s, where h > 0 represents the delay. Recently in a paper by Ozbay, a formulation is given to design the ¨ H∞ optimal controller for the mixed sensitivity minimization problem for unstable infinite dimensional plants with low order weights. This formulation is used to design the H∞ optimal controller for the fractional order system considered, and it is compared to alternative computation methods for H∞ control of infinite dimensional systems. To implement the controller, approximation methods are also investigated. Furthermore, finite dimensional rational approximation techniques of the fractional order integrator are evaluated for simulation purposes.Karagül, Abidin ErdemM.S

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

Applications of Mathematical Models in Engineering

The most influential research topic in the twenty-first century seems to be mathematics, as it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. Therefore, the intention of this Special Issue is to deal with mathematical works related to engineering and multidisciplinary problems. Modern developments in theoretical and applied science have widely depended our knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges in the theory and applications of fractional calculus in engineering sciences. The special issue included some original research articles that address significant issues and contribute towards the development of new concepts, methodologies, applications, trends and knowledge in mathematics. Potential topics include, but are not limited to, the following: Fractional mathematical models; Computational methods for the fractional PDEs in engineering; New mathematical approaches, innovations and challenges in biotechnologies and biomedicine; Applied mathematics; Engineering research based on advanced mathematical tools

Dynamic state estimation for mobile robots

The scientific goal of this thesis is to tackle different approaches for effective state estimation and modelling of relevant problems in the context of mobile robots. The starting point of this dissertation is the concept of probabilistic robotics, an emerging paradigm that combines state-of-the-art methods with the classic probabilistic theory, developing stochastic frameworks for understanding the uncertain nature of the interaction between a robot and its environment. This allows introducing relevant concepts which are the foundation of the localisation system implemented on the main experimental platform used on this dissertation. An accurate estimation of the position of a robot with respect to a fixed frame is fundamental for building navigation systems that can work in dynamic unstructured environments. This development also allows introducing additional contributions related with global localisation, dynamic obstacle avoidance, path planning and position tracking problems. Kinematics on generalised manipulators are characterised for dealing with complex nonlinear systems. Nonlinear formulations are needed to properly model these systems, which are not always suitable for real-time realisation, lacking analytic formulations in most cases. In this context, this thesis tackles the serial-parallel dual kinematic problem with a novel approach, demonstrating state-of-the-art accuracy and real-time performance. With a spatial decomposition method, the forward kinematics problem on parallel robots and the inverse kinematics problem on serial manipulators is solved modelling the nonlinear behaviour of the pose space using Support Vector Machines. The results are validated on different topologies with the analytic solution for such manipulators, which demonstrates the applicability of the proposed method. Modelling and control of complex dynamical systems is another relevant field with applications on mobile robots. Nonlinear techniques are usually applied to tackle problems like feature or object tracking. However, some nonlinear integer techniques applied for tasks like position tracking in mobile robots with complex dynamics have limited success when modelling such systems. Fractional calculus has demonstrated to be suitable to model complex processes like viscoelasticity or super diffusion. These tools, that take advantage of the generalization of the derivative and integral operators to a fractional order, have been applied to model and control different topics related with robotics in recent years with remarkable success. With the proposal of a fractional-order PI controller, a suitable controller design method is presented to solve the position tracking problem. This is applied to control the distance of a self-driving car with respect to an objective, which can also be applied to other tracking applications like following a navigation path. Furthermore, this thesis introduces a novel fractional-order hyperchaotic system, stabilised with a full-pseudo-state-feedback controller and a located feedback method. This theoretical contribution of a chaotic system is introduced hoping to be useful in this context. Chaos theory has recently started to be applied to study manipulators, biped robots and autonomous navigation, achieving new and promising results, highlighting the uncertain and chaotic nature which also has been found on robots. All together, this thesis is devoted to different problems related with dynamic state estimation for mobile robots, proposing specific contributions related with modelling and control of complex nonlinear systems. These findings are presented in the context of a self-driving electric car, Verdino, jointly developed in collaboration with the Robotics Group of Universidad de La Laguna (GRULL)

Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Stabilizing Parameterization for Uncertain Delay Systems

Ph.DDOCTOR OF PHILOSOPH

Hybrid and Thin Power Electronics for Electrical Power Networks

A new hybrid diverter design for an On-Load Tap Changer (OLTC) is presented and experimentally validated. The design differs from existing semiconductor-assisted OLTC systems in that the part of the system containing semiconductor devices is connected in a purely shunt con guration to the main current path, resulting in a system that is electrically robust and very low loss. The new design provides zero-current, zero-voltage operation of both diverter switches at all times, eff ectively eliminating arc-induced contact wear. Contact lifetime of over twenty-five million operations is demonstrated. Contact wear rates under the new design are compared experimentally with those under alternative contact protection schemes and are shown to be dramatically reduced. A fast electromechanical switch intended for use under the new hybrid diverter is presented. The low-wear conditions created by the new diverter allows a dramatic reduction in the switch moving mass when compared to that of the standard OLTC, allowing sub-half-cycle actuation times to be achieved. A study of switch topology is made in order to guide the design process. An analysis of a magnetic actuator providing both high actuation and static contact forces is also presented. In a second strand of this thesis, a general method of formulating optimal modulation problems for thin power electronic systems incorporating a buck converter is presented. The method is employs a frequency domain representation of the buck converter where the describing equations are formed into a square matrix relating a set of input harmonics to sets of output harmonics. This allows the interaction between the buck converter and a set of linear filters to be modelled in a systematic way. Two example circuits, the Inverter-Less Active Filter and the Controllable Network Transformer, are used as example problems. The use of general-purpose optimisation software for finding optimal modulation waveforms for these circuits is demonstrated