There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Fractional Differential Equations

Review of fractional PID controller

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Formulas For Natural Frequency And Mode Shape

Introduction of vehicle-to-grid technology offer electric vehicles (EVs) to participate in different ancillary services under competitive electric market. EVs provide an opportunity to grow new products and services for grid management. Particularly, EVs, which is a new form of distributed energy storage, can be used to compensate the uncontracted power in the local area if the contracts between the market players are violated. This paper presents the participation of EVs for load frequency control (LFC) under deregulated environment along with other conventional sources such as hydro, thermal, and gas turbine units. An aggregate model of EV fleets and improved version of fractional order (FO) controller is provided in all the areas for robust LFC considering bilateral transactions. Flower pollination algorithm, which is one of the new proven nature inspired algorithm employed to choose the optimal parameters of the FO controllers under several scenarios. Numerous simulations are conducted to validate the superiority of the proposed control strategy.

Utilizing Electric Vehicles for LFC in Restructured Power Systems Using Fractional Order Controller

Cantilever beams have an important role in day to day life in bridges, towers, buildings and aircraft wings, making active vibration suppression a highly researched field. The purpose of this paper is to detail the design of fractional order PID controllers for smart beams. A novel tuning procedure is proposed based on solving a set of nonlinear complex equations that directly aim at reducing the resonant peak. The control parameters are computed through optimization techniques, making sure that the best ones are chosen. The practical stand was realized using magnet-coil approach and not piezoelectric actuators. The experimentally obtained vibration results prove that fractional order PID controllers can be used in practice to significantly reduce the amplitude and settling time of the vibrating system.

/pdf/vibration-suppression-with-fractional-order-pildm-controller-51ziogzqs9.pdf

Vibration suppression with fractional-order PIλDμ controller

Biochemical processes present complex mechanisms and can be described by various computational models. Complex systems present a variety of problems, especially the loss of intuitive understanding. The present work uses fractional-order calculus to obtain mathematical models for erythritol and mannitol synthesis. The obtained models are useful for both prediction and process optimization. The models present the complex behavior of the process due to the fractional order, without losing the physical meaning of gain and time constants. To validate each obtained model, the simulation results were compared with experimental data. In order to highlight the advantages of fractional-order models, comparisons with the corresponding integer-order models are presented.

https://www.mdpi.com/2504-3110/4/2/12/pdf

Fractional-Order Models for Biochemical Processes

Targeted drug delivery is a focus point in recent advances in the nanomedical field due to its many advantages such as decreased side effects, faster action and better drug absorption with less substance used. The paper presents an experimental platform that simulates the circulatory system: the passing of blood from arteries to smaller blood vessels, while also capturing the non-Newtonian characteristic of the blood. The targeted drug delivery is ensured by a scalable submersible equipped with various sensors and actuators such that the real-time position of the submersible can be determined and controlled in the circulatory system. The purpose of the presented work is to provide a solid foundation for experimental modeling of the interaction between the submersible and non-Newtonian fluids and for validating different control strategies suitable for velocity control. The experimental setup takes into account the real life difficulties of targeted drug delivery.

An experimental nanomedical platform for controller validation on targeted drug delivery

This paper presents an approach for developing an extended prediction self-adaptive controller employing graphical programming of industrial standard devices for controlling fast processes. For comparison purposes, the algorithm has been implemented on three different field-programmable gate arrays (FPGAs) chips. This paper presents research aspects regarding graphical-programming controller design, showing that a single advanced control application can run on different targets without requiring significant program modifications. Based on the time needed for processing the control signal and on the application, one can efficiently and easily select the most appropriate device. To exemplify the procedure, a conclusive case study is presented.

/pdf/a-portable-implementation-on-industrial-devices-of-a-zwtw4fjlb7.pdf

A Portable Implementation on Industrial Devices of a Predictive Controller Using Graphical Programming

In this paper, a sliding mode control strategy is discussed for a class of nonlinear mechanical sub-systems with varying trajectory dynamics. The proposed class of sub-systems are represented in this simulation example by a two link robot actuator/manipulator. The fractional order is introduced in the setpoint definition as to represent changes in the desired trajectory of this sub-system. Furthermore, the same order is used to adapt the control law to the new dynamics. Uncertainties are introduced in the model used for the control law, hence robustness is intrinsic.

/pdf/sliding-mode-control-for-a-class-of-sub-systems-with-4v11lzznoy.pdf

Cristina I. Muresan

Papers

Vibration suppression with fractional-order PIλDμ controller

Fractional-Order Models for Biochemical Processes

An experimental nanomedical platform for controller validation on targeted drug delivery

A Portable Implementation on Industrial Devices of a Predictive Controller Using Graphical Programming

Sliding mode control for a class of sub-systems with fractional order varying trajectory dynamics