Search results for: Integral variable structure controller (IVSC)

Authors: Samira Laidaoui, Mohammed Djermane, Nazihe Terfaya

Abstract:

The fluid-structure coupling is a natural phenomenon which reflects the effects of two continuums: fluid and structure of different types in the reciprocal action on each other, involving knowledge of elasticity and fluid mechanics. The solution for such problems is based on the relations of continuum mechanics and is mostly solved with numerical methods. It is a computational challenge to solve such problems because of the complex geometries, intricate physics of fluids, and complicated fluid-structure interactions. The way in which the interaction between fluid and solid is described gives the largest opportunity for reducing the computational effort. In this paper, a problem of fluid structure interaction is investigated with two-way coupling method. The formulation Arbitrary Lagrangian-Eulerian (ALE) was used, by considering a dynamic grid, where the solid is described by a Lagrangian formulation and the fluid by a Eulerian formulation. The simulation was made on the ANSYS software.

Keywords: ALE, coupling, FEM, fluid-structure interaction, one-way method, two-way method.

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Authors: B. Ghosh, H. Sahoo, K. K. Mondal

Abstract:

Propagation of arbitrary amplitude nonlinear Alfven waves has been investigated in low but finite β electron-positron-ion plasma including full ion dynamics. Using Sagdeev pseudopotential method an energy integral equation has been derived. The Sagdeev potential has been calculated for different plasma parameters and it has been shown that inclusion of ion parallel motion along the magnetic field changes the nature of slow shear Alfven wave solitons from dip type to hump type. The effects of positron concentration, plasma-β and obliqueness of the wave propagation on the solitary wave structure have also been examined.

Keywords: Alfven waves, Sagdeev potential, Solitary waves.

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Authors: Vahid Rostami, Omid sojodishijani , Saeed Ebrahimijam, Ali MohsenizanjaniNejad

Abstract:

This paper is described one of the intelligent control method in Autonomous systems, which is called fuzzy control to correct the three wheel omnidirectional robot movement while it make mistake to catch the target. Fuzzy logic is especially advantageous for problems that can not be easily represented by mathematical modeling because data is either unavailable, incomplete or the process is too complex. Such systems can be easily up grated by adding new rules to improve performance or add new features. In many cases , fuzzy control can be used to improve existing traditional controller systems by adding an extra layer of intelligence to the current control method. The fuzzy controller designed here is more accurate and flexible than the traditional controllers. The project is done at MRL middle size soccer robot team.

Keywords: Robocup , omnidirectional , fuzzy control, soccer robot , intelligent control.

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Authors: R. K. Singh, P. K. Jain

Abstract:

In the present paper, disc loaded interaction structure for potential application in wideband Gyro-TWT amplifier has been analyzed, taking all the space and modal harmonics into consideration, for the eigenwave solutions. The analysis has been restricted to azimuthally symmetric TE0,n mode. Dispersion characteristics have been plotted by varying the structure parameters and have been validated against HFSS simulation results. The variation of eigenvalue with respect to different structure parameters has also been presented. It has been observed that disc periodicity plays very important role for wideband operation of disc-loaded Gyro-TWT.

Keywords: Broadbanding, Disc-loaded interaction structure, Eigenvalue, Gyro-TWT, HFSS.

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Authors: Mircea Ivanescu, Nirvana Popescu, Decebal Popescu, Dorin Popescu

Abstract:

This paper addresses the control problem of a class of hyper-redundant arms. In order to avoid discrepancy between the mathematical model and the actual dynamics, the dynamic model with uncertain parameters of this class of manipulators is inferred. A procedure to design a feedback controller which stabilizes the uncertain system has been proposed. A PD boundary control algorithm is used in order to control the desired position of the manipulator. This controller is easy to implement from the point of view of measuring techniques and actuation. Numerical simulations verify the effectiveness of the presented methods. In order to verify the suitability of the control algorithm, a platform with a 3D flexible manipulator has been employed for testing. Experimental tests on this platform illustrate the applications of the techniques developed in the paper.

Keywords: Distributed model, flexible manipulator, observer, robot control.

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Authors: S. Massoum, A. Bentaallah, A. Massoum, F. Benaimeche, P. Wira, A. Meroufel

Abstract:

This paper presents a speed fuzzy sliding mode controller for a vector controlled induction machine (IM) fed by a voltage source inverter (PWM). The sliding mode based fuzzy control method is developed to achieve fast response, a best disturbance rejection and to maintain a good decoupling. The problem with sliding mode control is that there is high frequency switching around the sliding mode surface. The FSMC is the combination of the robustness of Sliding Mode Control (SMC) and the smoothness of Fuzzy Logic (FL). To reduce the torque fluctuations (chattering), the sign function used in the conventional SMC is substituted with a fuzzy logic algorithm. The proposed algorithm was simulated by Matlab/Simulink software and simulation results show that the performance of the control scheme is robust and the chattering problem is solved.

Keywords: IM, FOC, FLC, SMC, and FSMC.

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Authors: S.F. Faisal, A.H.M.A. Rahim, J.M. Bakhashwain

Abstract:

Design of a fixed parameter robust STATCOM controller for a multi-machine power system through an H-? based loop-shaping procedure is presented. The trial and error part of the graphical loop-shaping procedure has been eliminated by embedding a particle swarm optimization (PSO) technique in the design loop. Robust controllers were designed considering the detailed dynamics of the multi-machine system and results were compared with reduced order models. The robust strategy employing loop-shaping and PSO algorithms was observed to provide very good damping profile for a wide range of operation and for various disturbance conditions. 

Keywords: STATCOM, Robust control, Power system damping, Particle Swarm Optimization, Loop-shaping.

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Authors: Djilani Kobibi Youcef Islam, Hadjeri Samir, Djehaf Mohamed Abdeldjalil

Abstract:

The Flexible AC Transmission System (FACTS) technology is a new advanced solution that increases the reliability and provides more flexibility, controllability, and stability of a power system. The Unified Power Flow Controller (UPFC), as the most versatile FACTS device for regulating power flow, is able to control respectively transmission line real power, reactive power, and node voltage. The main purpose of this paper is to analyze the effect of the UPFC on the load flow, the power losses, and the voltage stability using NEPLAN software modules, Newton-Raphson load flow is used for the power flow analysis and the modal analysis is used for the study of the voltage stability. The simulation was carried out on the IEEE 14-bus test system.

Keywords: FACTS, load flow, modal analysis, UPFC, voltage stability.

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Authors: Sidshchadhaa Aumted, Shuhei Shiina, Hiroshi Takami

Abstract:

In this paper, we propose an advanced ILQ control for the buck-converter via two-degrees of freedom servo-system. Our presented strategy is based on Inverse Linear Quadratic (ILQ) servo-system controller without solving Riccati-s equation directly. The optimal controller of the current and voltage control system is designed. The stability and robust control are analyzed. A conscious and persistent effort has been made to improve ILQ control via two-degrees of freedom guarantees the optimal gains on the basis of polynomial pole assignment, which our results of the proposed strategy shows that the advanced ILQ control can be controlled independently the step response and the disturbance response by appending a feed-forward compensator.

Keywords: Optimal voltage control, inverse LQ design method, second order polynomial, two-degrees of freedom.

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Authors: Omar GACI, Stefan BALEV, Antoine DUTOT

Abstract:

In this paper we introduce the notion of protein interaction network. This is a graph whose vertices are the protein-s amino acids and whose edges are the interactions between them. Using a graph theory approach, we observe that according to their structural roles, the nodes interact differently. By leading a community structure detection, we confirm this specific behavior and describe thecommunities composition to finally propose a new approach to fold a protein interaction network.

Keywords: interaction network, protein structure, community structure detection.

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Authors: Mahmoud Miri, Soleiman Maramaee

Abstract:

Because of architectural condition and structure application, sometimes mass source and stiffness source are not coincidence, and the structure is irregular. The structure is also might be asymmetric as an asymmetric bracing in plan which leads to unbalance distribution of stiffness or because of unbalance distribution of the mass. Both condition lead to eccentricity and torsion in the structure. The deficiency of ordinary code to evaluate the performance of steel structures against earthquake has been caused designing based on performance level or capacity spectrum be used. By using the mentioned methods it is possible to design a structure that its behavior against different earthquakes be predictive. In this article 5- story buildings with different percentage of asymmetric which is because of stiffness changes have been designed. The static and dynamic nonlinear analysis under three acceleration recording has been done. Finally performance level of the structure has been evaluated.

Keywords: Seismic analysis, torsion, asymmetric, irregular building, stiffness source.

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Authors: Aurobi Das, V. Balakrishnan

Abstract:

This paper focuses on the integration of hybrid renewable energy resources available in remote isolated islands of Sundarban-24 Parganas-South of Eastern part of India to National Grid of conventional power supply to give a Smart-Grid scenario. Before grid-integration, feasibility of optimization of hybrid renewable energy system is monitored through an Intelligent Controller proposed to be installed at Moushuni Island of Sundarban. The objective is to ensure the reliability and efficiency of the system to optimize the utilization of the hybrid renewable energy sources and also a proposition of how theses isolated Hybrid Renewable Energy Systems at remote islands can be grid-connected is analyzed towards vision of green smart-grid.

Keywords: Intelligent controller, hybrid renewable, solar photo voltaic, smart-grid.

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Authors: I. Falconett, K. Nagasaka

Abstract:

This study investigates the performance of radial basis function networks (RBFN) in forecasting the monthly CO2 emissions of an electric power utility. We also propose a method for input variable selection. This method is based on identifying the general relationships between groups of input candidates and the output. The effect that each input has on the forecasting error is examined by removing all inputs except the variable to be investigated from its group, calculating the networks parameter and performing the forecast. Finally, the new forecasting error is compared with the reference model. Eight input variables were identified as the most relevant, which is significantly less than our reference model with 30 input variables. The simulation results demonstrate that the model with the 8 inputs selected using the method introduced in this study performs as accurate as the reference model, while also being the most parsimonious.

Keywords: Correlation analysis, CO2 emissions forecasting, electric power utility, radial basis function networks.

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Authors: Ahmed Sh. Khusheef, Ganesh Kothapalli, Majid Tolouei-Rad

Abstract:

Utilization of various sensors has made it possible to extend capabilities of industrial robots. Among these are vision sensors that are used for providing visual information to assist robot controllers. This paper presents a method of integrating a vision system and a simulation program with an industrial robot. The vision system is employed to detect a target object and compute its location in the robot environment. Then, the target object-s information is sent to the robot controller via parallel communication port. The robot controller uses the extracted object information and the simulation program to control the robot arm for approaching, grasping and relocating the object. This paper presents technical details of system components and describes the methodology used for this integration. It also provides a case study to prove the validity of the methodology developed.

Keywords: industrial robot, integration, simulation, vision system

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Authors: Parchami A., Fatahian Dehkordi RF.

Abstract:

The present investigation aimed to study the histomorphometric characterizations of the thyroid gland of the duck. Five adult male and five adult female ducks were used in the experiment. Results showed that the overall histological structure of the thyroid gland of the duck were similar to those of the other vertebrae. The gland consisted of roughly spherical randomly distributed micro and macrofollicles with very little interstitial tissue between them. Each follicle is lined by a single layer of epithelial cells enclosing a cavity, the follicular cavity, which is filled with colloid. Ultrastructural findings showed that the apical surface of the follicular cells bears a variable number of short, irregularly distributed microvilli which are apparently more numerous on the columnar cells than on the lower, relatively inactive cells. Mitochondria and rough endoplasmic reticulum occupy the subnuclear region of the follicular cell, whereas the Golgi complex, free ribosomes and colloid droplets were found in the apical cytoplasm. At light or electron microscopic levels, there was no sex difference in histomorphometric characteristics of the thyroid glands.ls.

Keywords: Duck, Thyroid gland, Light microscopy, Electron microscopy

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Authors: Barenten Suciu, Yoshiki Tsuji

Abstract:

In this paper, a theoretical investigation on the dynamic characteristics of one degree of freedom vibration system equipped with inerter of variable inertance, is presented. Differential equation of movement was solved under proper initial conditions in the case of free undamped/damped vibration, considered in the absence/presence of the inerter in the mechanical system. Influence of inertance on the amplitude of vibration, phase angle, natural frequency, damping ratio, and logarithmic decrement was clarified. It was mainly found that the inerter decreases the natural frequency of the undamped system and also of the damped system if the damping ratio is below 0.707. On the other hand, the inerter increases the natural frequency of the damped system if the damping ratio exceeds 0.707. Results obtained in this work are useful for the adequate design of inerters.

Keywords: One degree of freedom vibration system, inerter, parallel connection, variable inertance, frequency control, damping.

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Authors: Jung–Min Yang

Abstract:

Solvability of the model matching problem for input/output switched asynchronous sequential machines is discussed in this paper. The control objective is to determine the existence condition and design algorithm for a corrective controller that can match the stable-state behavior of the closed-loop system to that of a reference model. Switching operations and correction procedures are incorporated using output feedback so that the controlled switched machine can show the desired input/output behavior. A matrix expression is presented to address reachability of switched asynchronous sequential machines with output equivalence with respect to a model. The presented reachability condition for the controller design is validated in a simple example.

Keywords: Asynchronous sequential machines, corrective control, model matching, input/output control.

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Authors: Igor Astrov, Mikhail Pikkov, Rein Paluoja

Abstract:

This paper focuses on a critical component of the situational awareness (SA), the control of autonomous vertical flight for vectored thrust aerial vehicle (VTAV). With the SA strategy, we proposed a flight control procedure to address the dynamics variation and performance requirement difference of flight trajectory for an unmanned helicopter model with vectored thrust configuration. This control strategy for chosen model of VTAV has been verified by simulation of take-off and forward maneuvers using software package Simulink and demonstrated good performance for fast stabilization of motors, consequently, fast SA with economy in energy can be asserted during search-and-rescue operations.

Keywords: Neural network predictive controller, situational awareness, vectored thrust aerial vehicle.

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Authors: Mahmoud Miri, Soliman Maramaee

Abstract:

Because of architectural condition and structure application, sometimes mass source and stiffness source are not coincidence, and the structure is irregular. The structure is also might be asymmetric as an asymmetric bracing in plan which leads to unbalance distribution of stiffness or because of unbalance distribution of the mass. Both condition lead to eccentricity and torsion in the structure. The deficiency of ordinary code to evaluate the performance of steel structures against earthquake has been caused designing based on performance level or capacity spectrum be used. By using the mentioned methods it is possible to design a structure that its behavior against different earthquakes be predictive. In this article 5- story buildings with different percentage of asymmetric which is because of stiffness changes and kind of bracing (x and chevron bracing) have been designed. The static and dynamic nonlinear analysis under three acceleration recording has been done. Finally performance level of the structure has been evaluated.

Keywords: Asymmetric, irregular, seismic analysis, torsion.

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Authors: Hanny H. Tumbelaka, Masafumi Miyatake

Abstract:

This paper proposes a three-phase four-wire currentcontrolled Voltage Source Inverter (CC-VSI) for both power quality improvement and PV energy extraction. For power quality improvement, the CC-VSI works as a grid current-controlling shunt active power filter to compensate for harmonic and reactive power of loads. Then, the PV array is coupled to the DC bus of the CC-VSI and supplies active power to the grid. The MPPT controller employs the particle swarm optimization technique. The output of the MPPT controller is a DC voltage that determines the DC-bus voltage according to PV maximum power. The PSO method is simple and effective especially for a partially shaded PV array. From computer simulation results, it proves that grid currents are sinusoidal and inphase with grid voltages, while the PV maximum active power is delivered to loads.

Keywords: Active Power Filter, MPPT, PV Energy Conversion.

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Authors: Husam El-Asfour, Fateh Adhnouss, Kenneth McIsaac, AbdulMutalib Wahaishi, Raafat Aburukba, Idris El-Feghia

Abstract:

Although intelligence is commonly referred to as the observable behavior in various fields and domains, it must also be shown how it develops by exhibiting multiple forms and without observing the inherent behavior. There have been several official and informal definitions of intelligence in various areas; however, no scientific agreement on a definition has been agreed upon. There must be a single definition, structure, and precise modeling for articulating how intelligence is perceived by people and machines in order to comprehend intelligence. Another key challenge is defining the different environment types based on the integral elements (agents) and their possible interactions. On the basis of conceptualization, this paper proposes a formal model for defining and developing intelligence. Forms of intelligence are derived from an ontological view, and thus intelligence is defined, described, and modeled based on the various types of environments.

Keywords: Intelligence, forms, transformation, conceptualization, ontological view.

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Authors: Osama Elsarrar, Marjorie Darrah, Richard Devin

Abstract:

This paper discusses the idea of capturing an expert’s knowledge in the form of human understandable rules and then inserting these rules into a dynamic cell structure (DCS) neural network. The DCS is a form of self-organizing map that can be used for many purposes, including classification and prediction. This particular neural network is considered to be a topology preserving network that starts with no pre-structure, but assumes a structure once trained. The DCS has been used in mission and safety-critical applications, including adaptive flight control and health-monitoring in aerial vehicles. The approach is to insert expert knowledge into the DCS before training. Rules are translated into a pre-structure and then training data are presented. This idea has been demonstrated using the well-known Iris data set and it has been shown that inserting the pre-structure results in better accuracy with the same training.

Keywords: Neural network, rule extraction, rule insertion, self-organizing map.

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Authors: M. Reza Bagerzadeh Karimi, M. Mahdi Bagerzadeh Karimi

Abstract:

In the present paper, active control system is used in different heights of the building and the most effective part was studied where the active control system is applied. The mathematical model of the building is established in MATLAB and in order to active control the system FLC method was used. Three different locations of the building are chosen to apply active control system, namely at the lowest story, the middle height of the building, and at the highest point of the building with TMD system. The equation of motion was written for high rise building and it was solved by statespace method. Also passive control was used with Tuned Mass Damper (TMD) at the top floor of the building to show the robustness of FLC method when compared with passive control system.

Keywords: Fuzzy Logic Controller (FLC), Tuned Mass Damper(TMD), Active control, passive control

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Authors: F.Saadi, A.Aboudi Asl

Abstract:

In this paper, the dynamic analysis of fuel storage tanks has been studied and some equations are presented for the created fluid waves due to storage tank motions. Also, the equations for finite elements of fluid and structure interactions, and boundary conditions dominant on structure and fluid, were researched. In this paper, a numerical simulation is performed for the dynamic analysis of a storage tank contained a fluid. This simulation has carried out by ANSYS software, using FSI solver (Fluid and Structure Interaction solver), and by considering the simulated fluid dynamic motions due to earthquake loading, based on velocities and movements of structure and fluid according to all boundary conditions dominant on structure and fluid.

Keywords: fluid and structure interactions, finite elementmethod, ANSYS – FSI

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Authors: Khaled A. Madi

Abstract:

Induction motors are being used in greater numbers throughout a wide variety of industrial and commercial applications because it provides many benefits and reliable device to convert the electrical energy into mechanical motion. In some application it-s desired to control the speed of the induction motor. Because of the physics of the induction motor the preferred method of controlling its speed is to vary the frequency of the AC voltage driving the motor. In recent years, with the microcontroller incorporated into an appliance it becomes possible to use it to generate the variable frequency AC voltage to control the speed of the induction motor. This study investigates the microcontroller based variable frequency power inverter. the microcontroller is provide the variable frequency pulse width modulation (PWM) signal that control the applied voltage on the gate drive, which is provides the required PWM frequency with less harmonics at the output of the power inverter. The fully controlled bridge voltage source inverter has been implemented with semiconductors power devices isolated gate bipolar transistor (IGBT), and the PWM technique has been employed in this inverter to supply the motor with AC voltage. The proposed drive system for three & single phase power inverter is simulated using Matlab/Simulink. The Matlab Simulation Results for the proposed system were achieved with different SPWM. From the result a stable variable frequency inverter over wide range has been obtained and a good agreement has been found between the simulation and hardware of a microcontroller based single phase inverter.

Keywords: Power, inverter, PWM, microcontroller.

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Authors: M. Nassereddine, J. Rizk, G. Nasserddine

Abstract:

Performing High Voltage (HV) tasks with a multi craft work force create a special set of safety circumstances. This paper aims to present vital information relating to when it is acceptable to use a single or a two-layer soil structure. Also it discusses the implication of the high voltage infrastructure on the earth grid and the safety of this implication under a single or a two-layer soil structure. A multiple case study is investigated to show the importance of using the right soil resistivity structure during the earthing system design.

Keywords: Earth Grid, EPR, High Voltage, Soil Resistivity Structure, Step Voltage, Touch Voltage.

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Authors: F. Khaber, K. Zehar, A. Hamzaoui

Abstract:

In this paper, we introduce a robust state feedback controller design using Linear Matrix Inequalities (LMIs) and guaranteed cost approach for Takagi-Sugeno fuzzy systems. The purpose on this work is to establish a systematic method to design controllers for a class of uncertain linear and non linear systems. Our approach utilizes a certain type of fuzzy systems that are based on Takagi-Sugeno (T-S) fuzzy models to approximate nonlinear systems. We use a robust control methodology to design controllers. This method not only guarantees stability, but also minimizes an upper bound on a linear quadratic performance measure. A simulation example is presented to show the effectiveness of this method.

Keywords: Takagi-Sugeno fuzzy model, state feedback, linear matrix inequalities, robust stability.

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Authors: Hamed Alipour-Banaei, Farhad Mehdizadeh

Abstract:

We report the design and characterization of ultra high quality factor filter based on one-dimensional photonic-crystal Thue- Morse sequence structure. The behavior of aperiodic array of photonic crystal structure is numerically investigated and we show that by changing the angle of incident wave, desired wavelengths could be tuned and a tunable filter is realized. Also it is shown that high quality factor filter be achieved in the telecommunication window around 1550 nm, with a device based on Thue-Morse structure. Simulation results show that the proposed structure has a quality factor more than 100000 and it is suitable for DWDM communication applications.

Keywords: Thue-Morse, filter, quality factor.

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Authors: H.S. Kim

Abstract:

In this study, control performance of a smart base isolation system consisting of a friction pendulum system (FPS) and a magnetorheological (MR) damper has been investigated. A fuzzy logic controller (FLC) is used to modulate the MR damper so as to minimize structural acceleration while maintaining acceptable base displacement levels. To this end, a multi-objective optimization scheme is used to optimize parameters of membership functions and find appropriate fuzzy rules. To demonstrate effectiveness of the proposed multi-objective genetic algorithm for FLC, a numerical study of a smart base isolation system is conducted using several historical earthquakes. It is shown that the proposed method can find optimal fuzzy rules and that the optimized FLC outperforms not only a passive control strategy but also a human-designed FLC and a conventional semi-active control algorithm.

Keywords: Fuzzy logic controller, genetic algorithm, MR damper, smart base isolation system

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Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

Abstract:

This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: Wind turbines, aeroelasticity, repetitive control, periodic systems.

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