Search results for: blades%20for%20gas%20turbine%20engines

Authors: Tung-Hui Hsu, Wen-Yuh Jywe

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Five-axis computer numerical control (CNC) machine tools (three linear and two rotary axes) are ideally suited to the fabrication of complex work pieces, such as dies, turbo blades, and cams. The locations of the axis average line and centerline of the rotary axes strongly influence the performance of these machines; however, techniques to compensate for eccentric error in the rotary axes remain weak. This paper proposes optical (Non-Bar) techniques capable of calibrating five-axis CNC machine tools and compensating for eccentric error in the rotary axes. This approach employs the measurement path in ISO/CD 10791-6 to determine the eccentric error in two rotary axes, for which compensatory measures can be implemented. Experimental results demonstrate that the proposed techniques can improve the performance of various five-axis CNC machine tools by more than 90%. Finally, a result of the cutting test using a B-type five-axis CNC machine tool confirmed to the usefulness of this proposed compensation technique.

Keywords: Calibration, compensation, rotary axis, five-axis computer numerical control (CNC) machine tools, eccentric error, optical calibration system, ISO/CD 10791-6

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Authors: Thochi Seb Rengma, Mahendra Kumar Gupta, P. M. V. Subbarao

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Hydrokinetic turbines can be used to produce power in inaccessible villages located near rivers. The hydrokinetic turbine uses the kinetic energy of the water and maybe put it directly into the natural flow of water without dams. For off-grid power production, the Savonius-type vertical axis turbine is the easiest to design and manufacture. This proposal uses three-dimensional Computational Fluid Dynamics (CFD) simulations to measure the considerable interaction and complexity of turbine blades. Savonius hydrokinetic turbine (SHKT) performance is affected by a blockage in the river, canals, and waterways. Putting a large object in a water channel causes water obstruction and raises local free stream velocity. The blockage correction factor or velocity increment measures the impact of velocity on the performance. SHKT performance is evaluated by comparing power coefficient (Cp) with tip-speed ratio (TSR) at various blockage ratios. The maximum Cp was obtained at a TSR of 1.1 with a blockage ratio of 45%, whereas TSR of 0.8 yielded the highest Cp without blockage. The greatest Cp of 0.29 was obtained with a 45% blockage ratio compared to a Cp max of 0.18 without a blockage.

Keywords: Savonius hydrokinetic turbine, blockage ratio, vertical axis turbine, power coefficient.

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Authors: K. Arunachalam, P. Mannar Jawahar

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This paper deals with design of walking beam pendel axle suspension system. This axles and suspension systems are mainly required for transportation of heavy duty and Over Dimension Consignment (ODC) cargo, which is exceeding legal limit in terms of length, width and height. Presently, in Indian transportation industry, ODC movement growth rate has increased in transportation of bridge sections (pre-cast beams), transformers, heavy machineries, boilers, gas turbines, windmill blades etc. However, current Indian standard road transport vehicles are facing lot of service and maintenance issues due to non availability of suitable axle and suspension to carry the ODC cargoes. This in turn will lead to increased number of road accidents, bridge collapse and delayed deliveries, which finally result in higher operating cost. Understanding these requirements, this work was carried out. These axles and suspensions are designed for optimum self – weight with maximum payload carrying capacity with better road stability.

Keywords: Heavy duty trailer, Off–highway trucks, Over dimension cargo, Walking beam pendel axle suspension.

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Authors: Senda Trabelsi, Sébastien Poncet, Michel Poirier

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Ice slurries are considered as a promising phase-changing secondary fluids for air-conditioning, packaging or cooling industrial processes. An experimental study has been here carried out to measure the rheological characteristics of ice slurries. Ice slurries consist in a solid phase (flake ice crystals) and a liquid phase. The later is composed of a mixture of liquid water and an additive being here either (1) Propylene-Glycol (PG) or (2) Ethylene-Glycol (EG) used to lower the freezing point of water. Concentrations of 5%, 14% and 24% of both additives are investigated with ice mass fractions ranging from 5% to 85%. The rheological measurements are carried out using a Discovery HR-2 vane-concentric cylinder with four full-length blades. The experimental results show that the behavior of ice slurries is generally non-Newtonian with shear-thinning or shear-thickening behaviors depending on the experimental conditions. In order to determine the consistency and the flow index, the Herschel-Bulkley model is used to describe the behavior of ice slurries. The present results are finally validated against an experimental database found in the literature and the predictions of an Artificial Neural Network model.

Keywords: Ice slurry, propylene-glycol, ethylene-glycol, rheology, artificial neural network.

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Authors: Minho Bang, Seok Min Choi, Jun Su Park, Hokyu Moon, Hyung Hee Cho

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Present study investigates the effect of unsteady wakes on heat transfer in blade tip. Heat/mass transfer was measured in blade tip region depending on a variety of strouhal number by naphthalene sublimation technique. Naphthalene sublimation technique measures heat transfer using a heat/mass transfer analogy. Experiments are performed in linear cascade which is composed of five turbine blades and rotating rods. Strouhal number of inlet flow are changed ranging from 0 to 0.22. Reynolds number is 100,000 based on 11.4 m/s of outlet flow and axial chord length. Three different squealer tip geometries such as base squealer tip, vertical rib squealer tip, and camber line squealer tip are used to study how unsteady wakes affect heat transfer on a blade tip. Depending on squealer tip geometry, different flow patterns occur on a blade tip. Also, unsteady wakes cause reduced tip leakage flow and turbulent flow. As a result, as strouhal number increases, heat/mass transfer coefficients decrease due to the reduced leakage flow. As strouhal number increases, heat/ mass transfer coefficients on a blade tip increase in vertical rib squealer tip.

Keywords: Gas turbine, blade tip, heat transfer, unsteady wakes.

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Authors: John S. Anagnostopoulos, Dimitrios E. Papantonis

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The incorporation of computational fluid dynamics in the design of modern hydraulic turbines appears to be necessary in order to improve their efficiency and cost-effectiveness beyond the traditional design practices. A numerical optimization methodology is developed and applied in the present work to a Turgo water turbine. The fluid is simulated by a Lagrangian mesh-free approach that can provide detailed information on the energy transfer and enhance the understanding of the complex, unsteady flow field, at very small computing cost. The runner blades are initially shaped according to hydrodynamics theory, and parameterized using Bezier polynomials and interpolation techniques. The use of a limited number of free design variables allows for various modifications of the standard blade shape, while stochastic optimization using evolutionary algorithms is implemented to find the best blade that maximizes the attainable hydraulic efficiency of the runner. The obtained optimal runner design achieves considerably higher efficiency than the standard one, and its numerically predicted performance is comparable to a real Turgo turbine, verifying the reliability and the prospects of the new methodology.

Keywords: Turgo turbine, Lagrangian flow modeling, Surface parameterization, Design optimization, Evolutionary algorithms.

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Authors: Kewei Xu, Jens Friedrich, Kevin Dwinger, Wei Fan, Xijin Zhang

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Parallel Compressor Model (PCM) is a simplified approach to predict compressor performance with inlet distortions. In PCM calculation, it is assumed that the sub-compressors’ outlet static pressure is uniform and therefore simplifies PCM calculation procedure. However, if the compressor’s outlet duct is not long and straight, such assumption frequently induces error ranging from 10% to 15%. This paper provides a revised calculation method of PCM that can correct the error. The revised method employs energy equation, momentum equation and continuity equation to acquire needed parameters and replace the equal static pressure assumption. Based on the revised method, PCM is applied on two compression system with different blades types. The predictions of their performance in non-uniform inlet conditions are yielded through the revised calculation method and are employed to evaluate the method’s efficiency. Validating the results by experimental data, it is found that although little deviation occurs, calculated result agrees well with experiment data whose error ranges from 0.1% to 3%. Therefore, this proves the revised calculation method of PCM possesses great advantages in predicting the performance of the distorted compressor with limited exhaust duct.

Keywords: Parallel Compressor Model (PCM), Revised Calculation Method, Inlet Distortion, Outlet Unequal Pressure Distribution.

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Authors: Raza Abdulla Saeed

Abstract:

In this study, the three-dimensional cavitating turbulent flow in a complete Francis turbine is simulated using mixture model for cavity/liquid two-phase flows. Numerical analysis is carried out using ANSYS CFX software release 12, and standard k-ε turbulence model is adopted for this analysis. The computational fluid domain consist of spiral casing, stay vanes, guide vanes, runner and draft tube. The computational domain is discretized with a threedimensional mesh system of unstructured tetrahedron mesh. The finite volume method (FVM) is used to solve the governing equations of the mixture model. Results of cavitation on the runner’s blades under three different boundary conditions are presented and discussed. From the numerical results it has been found that the numerical method was successfully applied to simulate the cavitating two-phase turbulent flow through a Francis turbine, and also cavitation is clearly predicted in the form of water vapor formation inside the turbine. By comparison the numerical prediction results with a real runner; it’s shown that the region of higher volume fraction obtained by simulation is consistent with the region of runner cavitation damage.

Keywords: Computational Fluid Dynamics, Hydraulic Francis Turbine, Numerical Simulation, Two-Phase Mixture Cavitation Model.

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Authors: Eisa Noveiri, Adel Taheri Nia

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The Non-Rotating Adjustable Stabilizer / Directional Solution (NAS/DS) is the imitation of a mechanical process or an object by a directional drilling operation that causes a respond mathematically and graphically to data and decision to choose the best conditions compared to the previous mode. The NAS/DS Auto Guide rotary steerable tool is undergoing final field trials. The point-the-bit tool can use any bit, work at any rotating speed, work with any MWD/LWD system, and there is no pressure drop through the tool. It is a fully closed-loop system that automatically maintains a specified curvature rate. The Non–Rotating Adjustable stabilizer (NAS) can be controls curvature rate by exactly positioning and run with the optimum bit, use the most effective weight (WOB) and rotary speed (RPM) and apply all of the available hydraulic energy to the bit. The directional simulator allowed to specify the size of the curvature rate performance errors of the NAS tool and the magnitude of the random errors in the survey measurements called the Directional Solution (DS). The combination of these technologies (NAS/DS) will provide smoother bore holes, reduced drilling time, reduced drilling cost and incredible targeting precision. This simulator controls curvature rate by precisely adjusting the radial extension of stabilizer blades on a near bit Non-Rotating Stabilizer and control process corrects for the secondary effects caused by formation characteristics, bit and tool wear, and manufacturing tolerances.

Keywords: non-rotating, Adjustable stabilizer, simulator, Directional Drilling, optimization, Oil Well Drilling

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Authors: Mohammad T. Shervani-Tabar, Navid Shervani-Tabar

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Tip vortex cavitation is one of well known patterns of cavitation phenomenon which occurs in axial pumps. This pattern of cavitation occurs due to pressure difference between the pressure and suction sides of blades of an axial pump. Since the pressure in the pressure side of the blade is higher than the pressure in its suction side, thus a very small portion of liquid flow flows back from pressure side to the suction side. This fact is cause of tip vortex cavitation and gap cavitation that may occur in axial pumps. In this paper the results of our experimental investigation about movement of tip vortex cavitation along blade edge due to reduction of pump flow rate in an axial pump is reported. Results show that reduction of pump flow rate in conjunction with increasing of outlet pressure causes movement of tip vortex cavitation along blade edge towards the blade tip. Results also show that by approaching tip vortex cavitation to the blade tip, vortex tip pattern of cavitation replaces with a cavitation phenomenon on the blade tip. Furthermore by further reduction of pump flow rate and increasing of outlet pressure, an unstable cavitation phenomenon occurs between each blade leading edge and the next blade trailing edge.

Keywords: Axial Flow Pump, Cavitation, Gap Cavitation, Tip Vortex Cavitation.

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Authors: J. Chatthong, W. Boonchouytan, R. Burapa

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The purpose of study was to design and construction the semi-automatic sliced ginger machine for reduce production times in sheet and slice ginger procedure furthermore, reduced amount of labor of slides and cutting method. Take consider into clean and safety of workers and consumers. The principle of machines, used 1 horsepower motor, rotation speed of sliced blade 967 rpm, the diameter of sliced dish 310 mm, consists of 2 blades for sheet cutting ginger and the power from motor which transfer to rotate the sliced blade roller, rotation speed 440 rpm. The slice cutter roller was sliced ginger from sheet ginger to line ginger. The conveyer could adjustment level of motors, used to the beginning area that sheet ginger was transference to the roller for sheet and sliced cutting in next process. The cover of sliced cutting had channel for 1 tuber of ginger. The semi-automatic sliced ginger machine could produced sheet ginger 81.8 kg/h (6.2 times of labor) and line ginger 17.9 kg/h (2.5 times of labor) compare with, labor work could produced sheet ginger 13.2 kg/h and line ginger 7.1 kg/h, and when timekeeper, the total times of semi auto machine 30.86 kg/h and labor 4.6 kg/h, there for the semi auto machine was 6.7 times of labor. The semiautomatic sliced ginger machine convenient, easy for use and maintain, in addition to reduce fatigue of body and seriousness from works; must be used high skill, and protection accident in slicing procedure. Beside, machine could used with other vegetables for example potato, carrot .etc

Keywords: Sliced Machine, Sliced Ginger, Line Ginger

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Authors: Evgeniia V. Mekhonoshina, Vladimir Ya. Modorskii, Vasilii Yu. Petrov

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At present, vibrations of rotors of gas transmittal unit evade sustainable forecasting. This paper describes elastic oscillation modes in resilient supports and rotor impellers modeled during computational experiments with regard to interference in the system of gas-dynamic flow and compressor rotor. Verification of aeroelastic approach was done on model problem of interaction between supersonic jet in shock tube with deformed plate. ANSYS 15.0 engineering analysis system was used as a modeling tool of numerical simulation in this paper. Finite volume method for gas dynamics and finite elements method for assessment of the strain stress state (SSS) components were used as research methods. Rotation speed and material’s elasticity modulus varied during calculations, and SSS components and gas-dynamic parameters in the dynamic system of gas-dynamic flow and compressor rotor were evaluated. The analysis of time dependence demonstrated that gas-dynamic parameters near the rotor blades oscillate at 200 Hz, and SSS parameters at the upper blade edge oscillate four times higher, i.e. with blade frequency. It has been detected that vibration amplitudes correction in the test points at magnetic bearings by aeroelasticity may correspond up to 50%, and about -π/4 for phases.

Keywords: Centrifugal compressor, aeroelasticity, interdisciplinary calculation, oscillation phase displacement, vibration, nonstationarity.

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Authors: Pankaj Chandna, Dinesh Kumar

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The present work analyses different parameters of end milling to minimize the surface roughness for AISI D2 steel. D2 Steel is generally used for stamping or forming dies, punches, forming rolls, knives, slitters, shear blades, tools, scrap choppers, tyre shredders etc. Surface roughness is one of the main indices that determines the quality of machined products and is influenced by various cutting parameters. In machining operations, achieving desired surface quality by optimization of machining parameters, is a challenging job. In case of mating components the surface roughness become more essential and is influenced by the cutting parameters, because, these quality structures are highly correlated and are expected to be influenced directly or indirectly by the direct effect of process parameters or their interactive effects (i.e. on process environment). In this work, the effects of selected process parameters on surface roughness and subsequent setting of parameters with the levels have been accomplished by Taguchi’s parameter design approach. The experiments have been performed as per the combination of levels of different process parameters suggested by L9 orthogonal array. Experimental investigation of the end milling of AISI D2 steel with carbide tool by varying feed, speed and depth of cut and the surface roughness has been measured using surface roughness tester. Analyses of variance have been performed for mean and signal-to-noise ratio to estimate the contribution of the different process parameters on the process.

Keywords: D2 Steel, Orthogonal Array, Optimization, Surface Roughness, Taguchi Methodology.

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Authors: Rabeb Triki, Hassene Djemel, Mounir Baccar

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Surface scraping is a passive heat transfer enhancement technique that is directly used in scraped surface heat exchanger (SSHE). The scraping action prevents the accumulation of the product on the inner wall, which intensifies the heat transfer and avoids the formation of dead zones. SSHEs are widely used in industry for several applications such as crystallization, sterilization, freezing, gelatinization, and many other continuous processes. They are designed to deal with products that are viscous, sticky or that contain particulate matter. This research work presents a three-dimensional numerical simulation of the coupled thermal and hydrodynamic behavior within a SSHE which includes Archimedes’ screw instead of scraper blades. The finite volume Fluent 15.0 was used to solve continuity, momentum and energy equations using multiple reference frame formulation. The process fluid investigated under this study is the pure glycerin. Different geometrical parameters were studied in the case of steady, non-isothermal, laminar flow. In particular, attention is focused on the effect of the conicity of the rotor and the pitch of Archimedes’ screw on temperature and velocity distribution and heat transfer rate. Numerical investigations show that the increase of the number of turns in the screw from five to seven turns leads to amelioration of heat transfer coefficient, and the increase of the conicity of the rotor from 0.1 to 0.15 leads to an increase in the rate of heat transfer. Further studies should investigate the effect of different operating parameters (axial and rotational Reynolds number) on the hydrodynamic and thermal behavior of the SSHE.

Keywords: ANSYS-Fluent, hydrodynamic behavior, SSHE, thermal behavior.

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Authors: Young-Tae Lee, Hee-Chang Lim

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This paper presents the performance characteristics of Darrieus-type vertical axis wind turbine (VAWT) with NACA airfoil blades. The performance of Darrieus-type VAWT can be characterized by torque and power. There are various parameters affecting the performance such as chord length, helical angle, pitch angle and rotor diameter. To estimate the optimum shape of Darrieustype wind turbine in accordance with various design parameters, we examined aerodynamic characteristics and separated flow occurring in the vicinity of blade, interaction between flow and blade, and torque and power characteristics derived from it. For flow analysis, flow variations were investigated based on the unsteady RANS (Reynolds-averaged Navier-Stokes) equation. Sliding mesh algorithm was employed in order to consider rotational effect of blade. To obtain more realistic results we conducted experiment and numerical analysis at the same time for three-dimensional shape. In addition, several parameters (chord length, rotor diameter, pitch angle, and helical angle) were considered to find out optimum shape design and characteristics of interaction with ambient flow. Since the NACA airfoil used in this study showed significant changes in magnitude of lift and drag depending on an angle of attack, the rotor with low drag, long cord length and short diameter shows high power coefficient in low tip speed ratio (TSR) range. On the contrary, in high TSR range, drag becomes high. Hence, the short-chord and long-diameter rotor produces high power coefficient. When a pitch angle at which airfoil directs toward inside equals to -2° and helical angle equals to 0°, Darrieus-type VAWT generates maximum power.

Keywords: Darrieus wind turbine, VAWT, NACA airfoil, performance.

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Authors: Najmeh Bolbolamiri, Maryam Setayesh Sanai, Ahmad Mirabadi

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This paper deals with condition monitoring of electric switch machine for railway points. Point machine, as a complex electro-mechanical device, switch the track between two alternative routes. There has been an increasing interest in railway safety and the optimal management of railway equipments maintenance, e.g. point machine, in order to enhance railway service quality and reduce system failure. This paper explores the development of Kolmogorov- Smirnov (K-S) test to detect some point failures (external to the machine, slide chairs, fixing, stretchers, etc), while the point machine (inside the machine) is in its proper condition. Time-domain stator Current signatures of normal (healthy) and faulty points are taken by 3 Hall Effect sensors and are analyzed by K-S test. The test is simulated by creating three types of such failures, namely putting a hard stone and a soft stone between stock rail and switch blades as obstacles and also slide chairs- friction. The test has been applied for those three faults which the results show that K-S test can effectively be developed for the aim of other point failures detection, which their current signatures deviate parametrically from the healthy current signature. K-S test as an analysis technique, assuming that any defect has a specific probability distribution. Empirical cumulative distribution functions (ECDF) are used to differentiate these probability distributions. This test works based on the null hypothesis that ECDF of target distribution is statistically similar to ECDF of reference distribution. Therefore by comparing a given current signature (as target signal) from unknown switch state to a number of template signatures (as reference signal) from known switch states, it is possible to identify which is the most likely state of the point machine under analysis.

Keywords: stator currents monitoring, railway points, point failures, fault detection and diagnosis, Kolmogorov-Smirnov test, time-domain analysis.

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Authors: S. Apprich, F. Wulle, A. Lechler, A. Pott, A. Verl

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Large-scale machine tools for the manufacturing of large work pieces, e.g. blades, casings or gears for wind turbines, feature pose-dependent dynamic behavior. Small structural damping coefficients lead to long decay times for structural vibrations that have negative impacts on the production process. Typically, these vibrations are handled by increasing the stiffness of the structure by adding mass. This is counterproductive to the needs of sustainable manufacturing as it leads to higher resource consumption both in material and in energy. Recent research activities have led to higher resource efficiency by radical mass reduction that is based on controlintegrated active vibration avoidance and damping methods. These control methods depend on information describing the dynamic behavior of the controlled machine tools in order to tune the avoidance or reduction method parameters according to the current state of the machine. This paper presents the appearance, consequences and challenges of the pose-dependent dynamic behavior of lightweight large-scale machine tool structures in production. It starts with the theoretical introduction of the challenges of lightweight machine tool structures resulting from reduced stiffness. The statement of the pose-dependent dynamic behavior is corroborated by the results of the experimental modal analysis of a lightweight test structure. Afterwards, the consequences of the pose-dependent dynamic behavior of lightweight machine tool structures for the use of active control and vibration reduction methods are explained. Based on the state of the art of pose-dependent dynamic machine tool models and the modal investigation of an FE-model of the lightweight test structure, the criteria for a pose-dependent model for use in vibration reduction are derived. The description of the approach for a general posedependent model of the dynamic behavior of large lightweight machine tools that provides the necessary input to the aforementioned vibration avoidance and reduction methods to properly tackle machine vibrations is the outlook of the paper.

Keywords: Dynamic behavior, lightweight, machine tool, pose-dependency.

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

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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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