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

https://biblio.ugent.be/publication/8562472/file/8562482.pdf

Multivariable Fractional Order PI Autotuning Method for Heterogeneous Dynamic Systems

The main goal of the research is to design a low-cost, performing quadrotor unmaned aerial vehicle (UAV) system. Because of low cost limits, the performance must be ensured by other ways. The present proposal is a quaternion-based estimator used in the control loop. In order to make the proposed solution easy to be reproduced by the reader, step-by-step instructions are given, including component choices, design, and implementation. Throughout the article, detailed description of the system model is given. The efficacy of the suggested quaternion-based predictive control is evaluated by extended experimental results.

https://www.mdpi.com/2227-7390/8/10/1829/pdf

An Efficient Design and Implementation of a Quadrotor Unmanned Aerial Vehicle Using Quaternion-Based Estimator

Fractional order controllers have been used intensively over the last decades in controlling different types of processes. The main methods for tuning such controllers are based on a frequency domain approach followed by optimization routine, generally in the form of the Matlab fminsearch, but also evolving to more complex routines, such as the genetic algorithms. An alternative to these time consuming optimization routines, a simple graphical method has been proposed. However, these graphical methods are not suitable for all combinations of the imposed performance specifications. To preserve their simplicity, but also to make these graphical methods generally applicable, a modified graphical method using a very straightforward and simple optimization routine is proposed within the paper. Two case studies are presented, for tuning fractional order PI and PD controllers.

/pdf/simplified-optimization-routine-for-tuning-robust-fractional-2xrnqcmwzh.pdf

Simplified Optimization Routine for Tuning Robust Fractional Order Controllers

https://biblio.ugent.be/publication/8726085/file/8726086.pdf

An alternative design approach for Fractional Order Internal Model Controllers for time delay systems.

Fractional calculus has been opening new doors in terms of better modeling and control of several phenomena and processes. Biomedical engineering has seen a lot of combined attention from clinicians, control engineers and researchers in their attempt to offer individualized treatment. A large number of medical procedures require anesthesia, which in turn requires a closely monitored and controlled level of hypnosis, analgesia and neuromuscular blockade, as well maintenance of hemodynamic variables in a safe range. Computer-controlled anesthesia has been given a tremendous amount of attention lately. Hemodynamic stabilization via computer-based control is also a hot topic. However, very few studies on automatic control of combined anesthesia–hemodynamic systems exist despite the fact that hemodynamics is strongly influenced by hypnotic drugs, while the depth of hypnosis is affected by drugs used in hemodynamic control. The very first multivariable fractional-order controller is developed in this paper for the combined anesthesia–hemodynamic system. Simulation studies on 24 patients show the effectiveness of the proposed approach.

/pdf/fractional-order-control-strategy-for-anesthesia-hemodynamic-1zba3y86.pdf

Cristina I. Muresan

Papers

Multivariable Fractional Order PI Autotuning Method for Heterogeneous Dynamic Systems

An Efficient Design and Implementation of a Quadrotor Unmanned Aerial Vehicle Using Quaternion-Based Estimator

Simplified Optimization Routine for Tuning Robust Fractional Order Controllers

An alternative design approach for Fractional Order Internal Model Controllers for time delay systems.

Fractional-Order Control Strategy for Anesthesia–Hemodynamic Stabilization in Patients Undergoing Surgical Procedures