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

Several important domains, such as the aerospace industry, are confronted with problems related to vibration. The solutions for reducing these vibrations are numerous, but are limited to a large number of passive methods, while the active solutions involve classical and intelligent control techniques. The present paper proposes a fractional order PD controller, for which the control parameters are computed in order to directly limit the vibrations at the resonance frequencies. The case study consists in a beam containing smart sensors and actuators using piezoelectric materials. The simulation results, considering both free and forced vibrations responses of the smart beam, show that the proposed method is simple and leads to an improvement of the closed loop behavior.

Vibration suppression in smart structures using fractional order PD controllers

Fractional order controllers are receiving an ever-increasing interest from the research community due to their advantages. However, most of the tuning procedures for fractional order controllers assume a fully known mathematical model of the process. In this paper, an autotuning method for the design of a fractional order PD controller is presented and applied to the vibration suppression in airplane wings. To validate the designed controller, an experimental unit consisting of a smart beam that simulates the behaviour of an airplane wing is used. The experimental results demonstrate the efficiency of the designed controller in suppressing unwanted vibrations.

https://biblio.ugent.be/publication/8726094/file/8726095.pdf

An Autotuning Method for a Fractional Order PD Controller for Vibration Suppression

In this paper, a systematic tuning procedure for a fractional order PD controller for seismic mitigation is proposed. The tuning is based upon reducing the magnitude of the compensated system at the resonance frequency as compared to the magnitude of the uncompensated structure. For simplicity, a laboratory scale 1DOF (one degree of freedom) steel structure is used as the case study, The simulation results considering the El Centro earthquake accelerograms show that the designed control strategy is highly suitable for solving seismic mitigation of steel structures and ensures improved response in comparison with steel structures equipped with passive protection. 

Seismic Mitigation in Civil Structures Using a Fractional Order PD Controller

The present paper presentes the tuning of a Fractional Order Proportional Integral (FOPI) controller for second-order-plus-time-delay (SOPDT) plants. The tuning procedure is based on imposing frequency domain constraints for the open loop system with the FOPI controller and the SOPDT plant. The gain crossover frequency, phase margin and the iso-damping property that guarantees a certain degree of robustness to gain variations are imposed in order to obtain the parameters of the fractional order controller. The proposed method is validated by real life implementation on a process whose dynamics are approximated to a SOPDT model. The settling time, steady state error, robustness and disturbance rejection capabilities are analyzed using experimental test cases.

Experimental results of fractional order PI controller designed for second order plus dead time (SOPDT) processes

Fractional calculus is currently gaining more and more popularity in the control engineering world. Several tuning algorithms for fractional order controllers have been proposed so far. This chapter describes a simple tuning rule for fractional order PI controllers for single-input–single-output processes and an extension of this method to the multivariable case. The implementation of a fractional order PI on an FPGA target for controlling the DC motor speed, as well as the implementation of a multivariable fractional order PI controller for a time delay system is presented. Experimental results are given to show the efficiency and robustness of the tuning algorithm.

Cristina I. Muresan

Papers

Vibration suppression in smart structures using fractional order PD controllers

An Autotuning Method for a Fractional Order PD Controller for Vibration Suppression

Seismic Mitigation in Civil Structures Using a Fractional Order PD Controller

Experimental results of fractional order PI controller designed for second order plus dead time (SOPDT) processes

Fractional Calculus: From Simple Control Solutions to Complex Implementation Issues