Fractional Differential Equations

Preface. Hydrogenation Catalysts. Reactors and Reaction Conditions. Hydrogenation of Alkenes. Hydrogenation of Alkynes. Hydrogenation of Aldehydes and Ketones. Preparation of Amines by Reductive Alkylation. Hydrogenation of Nitriles. Hydrogenation of Imines, Oximes, and Related Compounds. Hydrogenation of Nitro, Nitroso, and Related Compounds. Hydrogenation of Carboxylic Acids, Esters, and Related Compounds. Hydrogenation of Aromatic Compounds. Hydrogenation of Heterocyclic Aromatic Compounds. Hydrogenolysis. General Bibliography. Author Index. Subject Index.

Handbook of heterogeneous catalytic hydrogenation for organic synthesis

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

Design of a fractional order PID controller for hydraulic turbine regulating system using chaotic non-dominated sorting genetic algorithm II

The applicability of fractional order (FO) automatic generation control (AGC) for power system frequency oscillation damping is investigated in this paper, employing distributed energy generation. The hybrid power system employs various autonomous generation systems like wind turbine, solar photovoltaic, diesel engine, fuel-cell, and aqua electrolyzer, along with other energy storage devices like the battery and flywheel. The controller is placed in a remote location while receiving and sending signals over an unreliable communication network with stochastic delay. The controller parameters are tuned using robust optimization techniques employing different variants of particle swarm optimization and are compared with the corresponding optimal solutions. An archival-based strategy is used for reducing the number of function evaluations for the robust optimization methods. The solutions obtained through the robust optimization are able to handle higher variation in the controller gains and orders without significant decrease in the system performance. This is desirable from the FO controller implementation point of view, as the design is able to accommodate variations in the system parameter, which may result due to the approximation of FO operators using different realization methods and order of accuracy. Also a comparison is made between the FO and the integer order controllers to highlight the merits and demerits of each scheme.

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Fractional Order AGC for Distributed Energy Resources Using Robust Optimization

Development and implementation of an FPGA based fractional order controller for a DC motor

In this paper a fractional order (FO) controller is proposed for solving the vibration suppression problem in civil structures. A laboratory scaled steel structure, with one floor, modeled as a single degree-of-freedom system is used as a case study. Two passive control solutions are proposed: a tuned mass damper (TMD) and a viscoelastic damper (VED), the latter being modeled using fractional derivatives. The simulation results show that the VED is able to further reduce the vibrations induced as forced oscillations or due to seismic excitation inputs, as compared to the passive TMD. The FO controller is then tuned using a new approach based on imposing a magnitude condition for the closed-loop system at the structural resonance frequency. The resulting FO active control strategy, together with the VED, ensures an increased seismic mitigation. Structural modeling errors are also considered, with the proposed active FO control strategy behaving robustly in terms of vibration suppression. The novelty of the...

A fractional order controller for seismic mitigation of structures equipped with viscoelastic mass dampers

Although a considerable amount of research has been carried out in the field of fractional-order controllers, a simplified tuning routine has yet to be established. Most of the tuning techniques for fractional-order controllers deal with complex computations and optimization routines. This paper proposes a simple yet efficient methodology based on a vector representation of the fractional-order controllers. This simplifies considerably the computations and derivation of the fractional-order controller parameters. The tuning procedure is exemplified first for a fractional-order PI controller designed for a simple first-order process, as well as for a fractional-order PD controller for a servoing system. In this case, the experimental results are also included, showing that this novel tuning approach is a viable replacement for the more complex tuning procedures currently employed in the design of different fractional-order controllers.

Vector-based tuning and experimental validation of fractional-order PI/PD controllers

Fractional order calculus has been used to generalize various types of controllers, including internal model controllers (IMC). The focus of this manuscript is towards fractional order IMCs for first order plus dead-time (FOPDT) processes, including delay and lag dominant ones. The design is novel at it is based on a new approximation approach, the non-rational transfer function method. This allows for a more accurate approximation of the process dead-time and ensures an improved closed loop response. The main problem with fractional order controllers is concerned with their implementation as higher order transfer functions. In cases where central processing unit CPU, bandwidth allocation, and energy usage are limited, resources need to be efficiently managed. This can be achieved using an event-based implementation. The novelty of this paper resides in such an event-based algorithm for fractional order IMC (FO-IMC) controllers. Numerical results are provided for lag and delay dominant FOPDT processes. For comparison purposes, an integer order PI controller, tuned according to the same performance specifications as the FO-IMC, is also implemented as an event-based control strategy. The numerical results show that the proposed event-based implementation for the FO-IMC controller is suitable and provides for a smaller computational effort, thus being more suitable in various industrial applications.

https://www.mdpi.com/2227-7390/8/8/1378/pdf

Eva H. Dulf

Papers

Development and implementation of an FPGA based fractional order controller for a DC motor

A fractional order controller for seismic mitigation of structures equipped with viscoelastic mass dampers

Vector-based tuning and experimental validation of fractional-order PI/PD controllers

Event-Based Implementation of Fractional Order IMC Controllers for Simple FOPDT Processes

Comparative Analysis of Different Control Strategies for a Train of Cryogenic 13C Separation Columns