Search results for: fractional–order proportional integral (FOPI) controller

Authors: Kamel Al-Khaled

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Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some fields such as cell biology, chemistry, physics, and finance, makes it necessary to apply the results reported here to some numerical examples.

Keywords: fractional partial differential equations, reaction-diffusion equations, adomian decomposition, biological species

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Authors: Ayad Al-Mahturi, Herman Wahid

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This paper presents an optimal state feedback controller based on Linear Quadratic Regulator (LQR) for a two-rotor aero-dynamical system (TRAS). TRAS is a highly nonlinear multi-input multi-output (MIMO) system with two degrees of freedom and cross coupling. There are two parameters that define the behavior of LQR controller: state weighting matrix and control weighting matrix. The two parameters influence the performance of LQR. Particle Swarm Optimization (PSO) is proposed to optimally tune weighting matrices of LQR. The major concern of using LQR controller is to stabilize the TRAS by making the beam move quickly and accurately for tracking a trajectory or to reach a desired altitude. The simulation results were carried out in MATLAB/Simulink. The system is decoupled into two single-input single-output (SISO) systems. Comparing the performance of the optimized proportional, integral and derivative (PID) controller provided by INTECO, results depict that LQR controller gives a better performance in terms of both transient and steady state responses when PSO is performed.

Keywords: LQR controller, optimal control, particle swarm optimization (PSO), two rotor aero-dynamical system (TRAS)

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Authors: Musaab Mohammed Ahmed Ali, Vladimir Vodichev

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work deals with an universal control technique or single controller for linear and nonlinear stabilization and tracing control systems. These systems may be structured as SISO and MIMO. Parameters of controlled plants can vary over a wide range. Introduced a novel control systems design method, construction of stable platform orbits using derivative balance, solved transfer function stability preservation problem of linear system under partial substitution of a rational function. Universal controller is proposed as a polar system with the multiple orbits to simplify design procedure, where each orbit represent single order of controller transfer function. Designed controller consist of proportional, integral, derivative terms and multiple feedback and feedforward loops. The controller parameters synthesis method is presented. In generally, controller parameters depend on new polynomial equation where all parameters have a relationship with each other and have fixed values without requirements of retuning. The simulation results show that the proposed universal controller can stabilize infinity number of linear and nonlinear plants and shaping desired previously ordered performance. It has been proven that sensor errors and poor performance will be completely compensated and cannot affect system performance. Disturbances and noises effect on the controller loop will be fully rejected. Technical and economic effect of using proposed controller has been investigated and compared to adaptive, predictive, and robust controllers. The economic analysis shows the advantage of single controller with fixed parameters to drive infinity numbers of plants compared to above mentioned control techniques.

Keywords: derivative balance, fixed parameters, stable platform, universal control

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Authors: Hakiki Kheira, Belhamiti Omar

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In this paper, we propose a new compartmental fractional order model for the simulation of epidemic obesity dynamics. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. We also present some fractional differential illustrative examples to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense.

Keywords: Caputo derivative, epidemiology, Legendre wavelet method, obesity

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Authors: Bandreddy Anand Babu, Mandadi Srinivasa Rao, Chintala Pradeep Reddy

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The main theme of this paper is to design fuzzy logic Proportional Integral Derivative controller for controlling of Pulse Width Modulator (PWM) based DCDC buck converter in continuous conduction mode of operation and comparing the results of FPID and ANFIS. Simulation is done to fuzzy the given input variables and membership functions of input values, creating the interference rules linking the input and output variables and after then defuzzfies the output variables. Fuzzy logic is simple for nonlinear models like buck converter. Fuzzy logic based PID controller technique is to control, nonlinear plants like buck converters in switching variables of power electronics. The characteristics of FPID are in terms of rise time, settling time, rise time, steady state errors for different inputs and load disturbances.

Keywords: fuzzy logic, PID controller, DC-DC buck converter, pulse width modulation

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Authors: Jorge Gonzalez-Camus

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In this work is proved the existence of at least one minimal and maximal mild solutions to the Cauchy problem, for fractional evolution equation of neutral type, involving a general kernel. An operator A generating a resolvent family and integral resolvent family on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Kuratowski measure of noncompactness and fixed point theorems, specifically Darbo-type, and an iterative method of lower and upper solutions, based in an order in X induced by a normal cone P. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the theory of resolvent families, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, the existence of minimal and maximal mild solutions was proved through in an iterative method of lower and upper solutions, using the Azcoli-Arzela Theorem, and the Gronwall’s inequality. Finally, we recovered the case derivate in Caputo sense.

Keywords: fractional evolution equations, Volterra integral equations, minimal and maximal mild solutions, neutral type equations, non-local in time equations

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Authors: Kazim G. Atman, Hüseyin Sirin

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In theoretical physics, nonlocal phenomena has always been subject of debate. However, in the conventional mathematical approach where the developments of the physical systems are investigated by using the standard mathematical tools, nonlocal effects are not taken into account. In order to investigate the nonlocality in quantum mechanics and fractal property of space, fractional derivative operators are employed in this study. In this manner, fractional creation and annihilation operators are introduced and Einstein coefficients are taken into account as an application of concomitant formalism in quantum field theory. Therefore, each energy mode of photons are considered as fractional quantized harmonic oscillator hereby Einstein coefficients are obtained. Nevertheless, wave function and energy eigenvalues of fractional quantum mechanical harmonic oscillator are obtained via the fractional derivative order α which is a measure of the influence of nonlocal effects. In the case α = 1, where space becomes homogeneous and continuous, standard physical conclusions are recovered.

Keywords: Einstein’s Coefficients, Fractional Calculus, Fractional Quantum Mechanics, Nonlocal Theories

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Authors: Muhammad Danish Khan, Imran Naeem, Mudassar Imran

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In this article, we study time-space Fractional Advection-Dispersion (FADE) equation and time-space Fractional Whitham-Broer-Kaup (FWBK) equation that have a significant role in hydrology. We introduce suitable transformations to convert fractional order derivatives to integer order derivatives and as a result these equations transform into Partial Differential Equations (PDEs). Then the Lie symmetries and corresponding optimal systems of the resulting PDEs are derived. The symmetry reductions and exact independent solutions based on optimal system are investigated which constitute the exact solutions of original fractional differential equations.

Keywords: modified Riemann-Liouville fractional derivative, lie-symmetries, optimal system, invariant solutions

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

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Authors: A. Benbouali, H. Saidi, A. Derrouazin, T. Bessaad

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Aerial robotics is a very exciting research field dealing with a variety of subjects, including the attitude control. This paper deals with the control of a four rotor vertical take-off and landing (VTOL) Unmanned Aerial Vehicle. The paper presents a mathematical model based on the approach of Lagrange for the flight control of an autonomous quad-rotor. It also describes the controller architecture which is based on PID regulators. The control method has been simulated in closed loop in different situations. All the calculation stages and the simulation results have been detailed.

Keywords: quad-rotor, lagrange approach, proportional integral derivate (PID) controller, Matlab/Simulink

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Authors: Santosh Kumar Suman, Vinod Kumar Giri

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The goal of this paper is to outline a speed controller of a DC motor by choice of a PID parameters utilizing genetic algorithms (GAs), the DC motor is extensively utilized as a part of numerous applications such as steel plants, electric trains, cranes and a great deal more. DC motor could be represented by a nonlinear model when nonlinearities such as attractive dissemination are considered. To provide effective control, nonlinearities and uncertainties in the model must be taken into account in the control design. The DC motor is considered as third order system. Objective of this paper three type of tuning techniques for PID parameter. In this paper, an independently energized DC motor utilizing MATLAB displaying, has been outlined whose velocity might be examined utilizing the Proportional, Integral, Derivative (KP, KI , KD) addition of the PID controller. Since, established controllers PID are neglecting to control the drive when weight parameters be likewise changed. The principle point of this paper is to dissect the execution of optimization techniques viz. The Genetic Algorithm (GA) for improve PID controllers parameters for velocity control of DC motor and list their points of interest over the traditional tuning strategies. The outcomes got from GA calculations were contrasted and that got from traditional technique. It was found that the optimization techniques beat customary tuning practices of ordinary PID controllers.

Keywords: DC motor, PID controller, optimization techniques, genetic algorithm (GA), objective function, IAE

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Authors: Arnaud Nougues

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This paper describes a two-stage methodology derived from internal model control (IMC) for tuning a proportional-integral-derivative (PID) controller for levels or other integrating processes in an industrial environment. Focus is the ease of use and implementation speed which are critical for an industrial application. Tuning can be done with minimum effort and without the need for time-consuming open-loop step tests on the plant. The first stage of the method applies to levels only: the vessel residence time is calculated from equipment dimensions and used to derive a set of preliminary proportional-integral (PI) settings with IMC. The second stage, re-tuning in closed-loop, applies to levels as well as other integrating processes: a tuning correction mechanism has been developed based on a series of closed-loop simulations with model errors. The tuning correction is done from a simple closed-loop step test and the application of a generic correlation between observed overshoot and integral time correction. A spin-off of the method is that an estimate of the vessel residence time (levels) or open-loop process gain (other integrating process) is obtained from the closed-loop data.

Keywords: closed-loop model identification, IMC-PID tuning method, integrating process control, on-line PID tuning adaptation

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Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

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In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control

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Authors: Abderraouf Gaaloul, Faouzi Msahli

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The use of standard sliding mode controller, usually, leads to the appearing of an undesirable chattering phenomenon affecting the control signal. Such problem can be overcome using a higher-order sliding mode controller (HOSMC) which preserves the main properties of the standard sliding mode and deliberately increases the control smoothness. In this paper, we propose a new HOSMC for a class of uncertain multi-input multi-output nonlinear systems. Based on high gain and integral sliding mode paradigms, the established control scheme removes theoretically the chattering phenomenon and provides the stability of the control system. Numerical simulations are developed to show the effectiveness of the proposed controller when applied to solve a control problem of two water levels into a quadruple-tank process.

Keywords: nonlinear systems, sliding mode control, high gain, higher order

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Authors: Jianwei Ma, Diriba Gemechu

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In seismic data processing, attenuation of random noise is the basic step to improve quality of data for further application of seismic data in exploration and development in different gas and oil industries. The signal-to-noise ratio of the data also highly determines quality of seismic data. This factor affects the reliability as well as the accuracy of seismic signal during interpretation for different purposes in different companies. To use seismic data for further application and interpretation, we need to improve the signal-to-noise ration while attenuating random noise effectively. To improve the signal-to-noise ration and attenuating seismic random noise by preserving important features and information about seismic signals, we introduce the concept of anisotropic total fractional order denoising algorithm. The anisotropic total fractional order variation model defined in fractional order bounded variation is proposed as a regularization in seismic denoising. The split Bregman algorithm is employed to solve the minimization problem of the anisotropic total fractional order variation model and the corresponding denoising algorithm for the proposed method is derived. We test the effectiveness of theproposed method for synthetic and real seismic data sets and the denoised result is compared with F-X deconvolution and non-local means denoising algorithm.

Keywords: anisotropic total fractional order variation, fractional order bounded variation, seismic random noise attenuation, split Bregman algorithm

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Authors: H. M. Côrtes, J. I. Da Silva Filho, M. F. Blos, B. S. Zanon

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In a modern society the factor corresponding to the increase in the level of quality in industrial production demand new techniques of control and machinery automation. In this context, this work presents the implementation of a Paraconsistent-Fuzzy Digital PID controller. The controller is based on the treatment of inconsistencies both in the Paraconsistent Logic and in the Fuzzy Logic. Paraconsistent analysis is performed on the signals applied to the system inputs using concepts from the Paraconsistent Annotated Logic with annotation of two values (PAL2v). The signals resulting from the paraconsistent analysis are two values defined as Dc - Degree of Certainty and Dct - Degree of Contradiction, which receive a treatment according to the Fuzzy Logic theory, and the resulting output of the logic actions is a single value called the crisp value, which is used to control dynamic system. Through an example, it was demonstrated the application of the proposed model. Initially, the Paraconsistent-Fuzzy Digital PID controller was built and tested in an isolated MATLAB environment and then compared to the equivalent Digital PID function of this software for standard step excitation. After this step, a level control plant was modeled to execute the controller function on a physical model, making the tests closer to the actual. For this, the control parameters (proportional, integral and derivative) were determined for the configuration of the conventional Digital PID controller and of the Paraconsistent-Fuzzy Digital PID, and the control meshes in MATLAB were assembled with the respective transfer function of the plant. Finally, the results of the comparison of the level control process between the Paraconsistent-Fuzzy Digital PID controller and the conventional Digital PID controller were presented.

Keywords: fuzzy logic, paraconsistent annotated logic, level control, digital PID

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Authors: Javier Fernandez, Mayte Medina, Rafael Fernandez de Canete, Nuria Alcain, Juan Carlos Ramos-Diaz

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At present, the experimentation of anesthetic drugs on patients requires a regulation protocol, and the response of each patient to several doses of entry drug must be well known. Therefore, the development of pharmacological dose control systems is a promising field of research in anesthesiology. In this paper, it has been developed a non-linear compartmental the pharmacokinetic-pharmacodynamical model which describes the anesthesia depth effect in a sufficiently reliable way over a set of patients with the depth effect quantified by the Bi-Spectral Index. Afterwards, an Artificial Neural Network (ANN) predictive controller has been designed based on the depth of anesthesia model so as to keep the patient in the optimum condition while he undergoes surgical treatment. For the purpose of quantifying the efficiency of the neural predictive controller, a classical proportional-integral-derivative controller has also been developed to compare both strategies. Results show the superior performance of predictive neural controller during BiSpectral Index reference tracking.

Keywords: anesthesia, bi-spectral index, neural network control, pharmacokinetic-pharmacodynamical model

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Authors: Do Chi Thanh, Dang Ngoc Huy

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Nowadays, there are more and more variable speed drive systems in small-scale and large-scale applications such as the electric vehicle industry, household appliances, medical equipment, and other industrial fields led to the development of BLDC (Brushless DC) motors. BLDC drive has many advantages, such as higher efficiency, better speed torque characteristics, high power density, and low maintenance cost compared to other conventional motors. Most BLDC motors use a proportional-integral (PI) controller and a pulse width modulation (PWM) scheme for speed control. This article describes the simulation model of BLDC motor drive control with the help of MATLAB - SIMULINK simulation software. The built simulation model includes a BLDC motor dynamic block, Hall sensor signal generation block, inverter converter block, and PI controller.

Keywords: brushless DC motor, BLDC, six-step inverter, PI speed

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Authors: Ali Oveysi Sarabi

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In this paper, controller design for the attitude and altitude dynamics of an outdoor quadrotor, which is constructed with low cost actuators and drivers, is aimed. Before designing the controller, the quadrotor is modeled mathematically in Matlab-Simulink environment. To control attitude dynamics, linear quadratic regulator (LQR) based controllers are designed, simulated and applied to the system. Two different proportional-integral-derivative action (PID) controllers are designed to control yaw and altitude dynamics. During the implementation of the designed controllers, different test setups are used. Designed controllers are implemented and tuned on the real system using xPC Target. Tests show that these basic control structures are successful to control the attitude and altitude dynamics.

Keywords: helicopter balance, flight dynamics, autonomous landing, control robotics

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Authors: Oluwaseun Simon Adekanle, M'hammed Guisser, Elhassane Abdelmounim, Mohamed Aboulfatah

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In this paper, modeling and control of a grid connected 660KW Doubly-Fed Induction Generator wind turbine is presented. Stator flux orientation is used to realize active-reactive power decoupling to enable independent control of active and reactive power. The recursive Integral Backstepping technique is used to control generator speed to its optimum value and to obtain unity power factor. The controller is combined with High Gain Observer to estimate the mechanical torque of the machine. The most important advantage of this combination of High Gain Observer and the Integral Backstepping controller is the annulation of static error that may occur due to incertitude between the actual value of a parameter and its estimated value by the controller. Simulation results under Matlab/Simulink show the robustness of this control technique in presence of parameter variation.

Keywords: doubly-fed induction generator, field orientation control, high gain observer, integral backstepping control

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Authors: Om Prakash Bharti, Aanchal Verma, R. K. Saket

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The Doubly-Fed Induction Generator (DFIG) is suggested for Wind Energy Conversion System (WECS) to extract wind power. DFIG is preferably employed due to its robustness towards variable wind and rotor speed. DFIG has the adaptable property because the system parameters are smoothly dealt with, including real power, reactive power, DC-link voltage, and the transient and dynamic responses, which are needed to analyze constantly. The analysis becomes more prominent during any unusual condition in the electrical power system. Hence, the study and improvement in the system parameters and transient response performance of DFIG are required to be accomplished using some controlling techniques. For fulfilling the task, the present work implements and compares the optimization methods for the design of the DFIG controller for WECS. The bio-inspired optimization techniques are applied to get the optimal controller design parameters for DFIG-based WECS. The optimized DFIG controllers are then used to retrieve the transient response performance of the six-order DFIG model with a step input. The results using MATLAB/Simulink show the betterment of the Firefly algorithm (FFA) over other control techniques when compared with the other controller design methods.

Keywords: doubly-fed induction generator, wind turbine, wind energy conversion system, induction generator, transfer function, proportional, integral, derivatives

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Authors: Ramzi B. Albadarneh

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In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given.

Keywords: conformable fractional derivative, finite difference formula, fractional derivative, finite difference formula

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Authors: Neelam Singha

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The present work intends to analyze the system dynamics of Hashimoto’s thyroiditis with the assistance of fractional calculus. Hashimoto’s thyroiditis or chronic lymphocytic thyroiditis is an autoimmune disorder in which the immune system attacks the thyroid gland, which gradually results in interrupting the normal thyroid operation. Consequently, the feedback control of the system gets disrupted due to thyroid follicle cell lysis. And, the patient perceives life-threatening clinical conditions like goiter, hyperactivity, euthyroidism, hyperthyroidism, etc. In this work, we aim to obtain the approximate solution to the posed fractional-order problem describing Hashimoto’s thyroiditis. We employ the Adomian decomposition method to solve the system of fractional-order differential equations, and the solutions obtained shall be useful to provide information about the effect of medical care. The numerical technique is executed in an organized manner to furnish the associated details of the progression of the disease and to visualize it graphically with suitable plots.

Keywords: adomian decomposition method, fractional derivatives, Hashimoto's thyroiditis, mathematical modeling

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Authors: Seyed Jamal Haddadi, M. Reza Mehranpour, Roya Sadat Mortazavi, Zahra Sadat Mortazavi

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Principal aim of this research is trajectory tracking, attitude and position control scheme in real flight mode by an Octorotor helicopter. For more stability, in this Unmanned Aerial Vehicle (UAV), number of motors is increased to eight motors which end of each arm installed two coaxial counter rotating motors. Dynamic model of this Octorotor includes of motion equation for translation and rotation. Utilized controller is proportional-integral-derivative (PID) control loop. The proposed controller is designed such that to be able to attenuate an effect of external wind disturbance and guarantee stability in this condition. The trajectory is determined by a Global Positioning System (GPS). Also an ARM CortexM4 is used as microprocessor. Electronic board of this UAV designed as able to records all of the sensors data, similar to an aircraft black box in external memory. Finally after auto landing of Octorotor, flight data is shown in MATLAB software and Experimental results of the proposed controller show the effectiveness of our approach on the Autonomous Quadrotor in real conditions.

Keywords: octorotor, design, PID controller, autonomous, trajectory tracking

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Authors: Marulasiddappa H. B., Pushparajesh Viswanathan

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Day by day, the uses of internal combustion engines (ICE) are deteriorating because of pollution and less fuel availability. In the present scenario, the electric vehicle (EV) plays a major role in the place of an ICE vehicle. The performance of EVs can be improved by the proper selection of electric motors. Initially, EV preferred induction motors for traction purposes, but due to complexity in controlling induction motor, permanent magnet synchronous motor (PMSM) is replacing induction motor in EV due to its advantages. Direct torque control (DTC) is one of the known techniques for PMSM drive in EV to control the torque and speed. However, the presence of torque ripple is the main drawback of this technique. Many control strategies are followed to reduce the torque ripples in PMSM. In this paper, the adaptive neuro-fuzzy inference system (ANFIS) controller technique is proposed to reduce torque ripples and settling time. Here the performance parameters like torque, speed and settling time are compared between conventional proportional-integral (PI) controller with ANFIS controller.

Keywords: direct torque control, electric vehicle, torque ripple, PMSM

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Authors: Rajesh Kondareddy, Prakash Kumar Nayak, Maunash Das, Vrinatri Velentina Boro

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Today, there is a huge global concern for sustainable development which would include minimizing the consumption of non-renewable energies without affecting the basic global economy. Solar drying is one of the important processes used for extending the shelf life of agricultural products. The performance of a low cost automated solar dryer fitted with cascade control scheme and modified PI controller for drying chilli was investigated. The dryer was composed of designed solar collector (air heater) fitted with cylindrical pipes to improve the air velocity and a solar drying chamber containing rack of two cheese cloth (net) trays both being integrated together. The air allowed in through air inlet is heated up in the solar collector and channelled through the drying chamber where it is utilized in drying (removing the moisture content from the food substance or agricultural produce loaded). Here, to maintain the temperature in the heating chambers and to improve performance, a modified PI (Proportional–Integral) controller was used due its simplicity and robustness. Drying time for drying chilli from the initial moisture content of 88.5% (wb) to 7.3% (wb) was estimated to be 14 hours in solar dryer whereas 32 h was observed in the open sun drying.

Keywords: cascade control, chilli, PI controller, solar dryer

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Authors: Swati Tyagi, Syed Abbas

Abstract:

Fractional-order Hopfield neural networks are generally used to model the information processing among the interacting neurons. To show the constancy of the processed information, it is required to analyze the stability of these systems. In this work, we perform Mittag-Leffler stability for the corresponding Caputo fractional-order bidirectional associative memory (BAM) neural networks with various time-delays. We derive sufficient conditions to ensure the existence and uniqueness of the equilibrium point by using the theory of topological degree theory. By applying the fractional Lyapunov method and Mittag-Leffler functions, we derive sufficient conditions for the global Mittag-Leffler stability, which further imply the global asymptotic stability of the network equilibrium. Finally, we present two suitable examples to show the effectiveness of the obtained results.

Keywords: bidirectional associative memory neural network, existence and uniqueness, fractional-order, Lyapunov function, Mittag-Leffler stability

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Authors: N. Chayaopas, W. Assawinchaichote

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In order to maximize energy capturing from wind energy, controlling the doubly fed induction generator to have optimal power from the wind, generator speed and output electrical power control in wind energy system have a great importance due to the nonlinear behavior of wind velocities. In this paper purposes the design of a control scheme is developed for power control of wind energy system via H∞ fuzzy integral controller. Firstly, the nonlinear system is represented in term of a TS fuzzy control design via linear matrix inequality approach to find the optimal controller to have an H∞ performance are derived. The proposed control method extract the maximum energy from the wind and overcome the nonlinearity and disturbances problems of wind energy system which give good tracking performance and high efficiency power output of the DFIG.

Keywords: doubly fed induction generator, H-infinity fuzzy integral control, linear matrix inequality, wind energy system

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Authors: Jorge Olivares, Fernando Maass, Pablo Martin

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Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function.

Keywords: Caputo, modified Bessel functions, hypergeometric, linear fractional differential equations, transform Laplace

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Authors: Yildiray Keskin, Omer Acan, Murat Akkus

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In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.

Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial

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