Search results for: Fixed Assets

Authors: Sagir M. Yusuf, Chris Baber

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In this paper, we describe how to achieve knowledge understanding and prediction (Situation Awareness (SA)) for multiple-agents conducting searching activity using Bayesian inferential reasoning and learning. Bayesian Belief Network was used to monitor agents' knowledge about their environment, and cases are recorded for the network training using expectation-maximisation or gradient descent algorithm. The well trained network will be used for decision making and environmental situation prediction. Forest fire searching by multiple UAVs was the use case. UAVs are tasked to explore a forest and find a fire for urgent actions by the fire wardens. The paper focused on two problems: (i) effective agents’ path planning strategy and (ii) knowledge understanding and prediction (SA). The path planning problem by inspiring animal mode of foraging using Lévy distribution augmented with Bayesian reasoning was fully described in this paper. Results proof that the Lévy flight strategy performs better than the previous fixed-pattern (e.g., parallel sweeps) approaches in terms of energy and time utilisation. We also introduced a waypoint assessment strategy called k-previous waypoints assessment. It improves the performance of the ordinary levy flight by saving agent’s resources and mission time through redundant search avoidance. The agents (UAVs) are to report their mission knowledge at the central server for interpretation and prediction purposes. Bayesian reasoning and learning were used for the SA and results proof effectiveness in different environments scenario in terms of prediction and effective knowledge representation. The prediction accuracy was measured using learning error rate, logarithm loss, and Brier score and the result proves that little agents mission that can be used for prediction within the same or different environment. Finally, we described a situation-based knowledge visualization and prediction technique for heterogeneous multi-UAV mission. While this paper proves linkage of Bayesian reasoning and learning with SA and effective searching strategy, future works is focusing on simplifying the architecture.

Keywords: Lèvy flight, situation awareness, multi-agent system, multi-robot coordination, autonomous system, swarm intelligence.

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Authors: Birgül Şakar

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This study1 holds for the formation of international financial crisis and political factors for economic crisis in Turkey, are evaluated in chronological order. The international arena and relevant studies conducted in Turkey work in the literature are assessed. The main purpose of the study is to hold the linkage between the crises and political stability in Turkey in details, and to examine the position of Turkey in this regard. The introduction part follows the literature survey on the models explaining causes and results of the crises, the second part of the study. In the third part, the formations of the world financial crises are studied. The fourth part, financial crisis in Turkey in 1994, 2000, 2001 and 2008 are reviewed and their political reasons are analyzed. In the last part of the study the results and recommendations are held. Political administrations have laid the grounds for an economic crisis in Turkey. In this study, the emergence of an economic crisis in Turkey and the developments after the crisis are chronologically examined and an explanation is offered as to the cause and effect relationship between the political administration and economic equilibrium in the country. Economic crises can be characterized as follows: high prices of consumables, high interest rates, current account deficits, budget deficits, structural defects in government finance, rising inflation and fixed currency applications, rising government debt, declining savings rates and increased dependency on foreign capital stock. Entering into the conditions of crisis during a time when the exchange value of the country-s national currency was rising, speculative finance movements and shrinking of foreign currency reserves happened due to expectations for devaluation and because of foreign investors- resistance to financing national debt, and a financial risk occurs. During the February 2001 crisis and immediately following, devaluation and reduction of value occurred in Turkey-s stock market. While changing over to the system of floating exchange rates in the midst of this crisis, the effects of the crisis on the real economy are discussed in this study. Administered politics include financial reforms, such as the rearrangement of banking systems. These reforms followed with the provision of foreign financial support. There have been winners and losers in the imbalance of income distribution, which has recently become more evident in Turkey-s fragile economy.

Keywords: Economics, marketing crisis, financial reforms, political economy

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Authors: Irene Perez-Alfaro, Nieves Murillo, Carlos Bernal, Daniel Gil-Hernandez

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Nowadays, the increasing applicability of internet of things (IoT) systems has changed the way that the world around is perceived. The massive interconnection of systems by means of sensing, processing and communication, allows multitude of data to be at our fingertips. In this way, countless advances have been made in different fields such as personal care, predictive maintenance in industry, quality control in production processes, security, and in everything imaginable. However, all these electronic systems have in common the need to be electrically powered. In this context, batteries and wires are the most commonly used solutions, but they are not a definitive solution in some applications, because of the attainability, the serviceability, or the performance requirements. Therefore, the need arises to look for other types of solutions based on energy harvesting and long-life electronics. Energy Harvesting can be defined as the action of capturing energy from the environment and store it for an instantaneous use or later use. Among the materials capable of harvesting energy from the environment, such as thermoelectrics, electromagnetics, photovoltaics or triboelectrics, the most suitable is the piezoelectric material. The phenomenon of piezoelectricity is one of the most powerful sources for energy harvesting, ranging from a few micro wats to hundreds of wats, depending on certain factors such as material type, geometry, excitation frequency, mechanical and electrical configurations, among others. In this research work, an exhaustive study is carried out on how different types of piezoelectric materials and electrical configurations influence the maximum power that a bimorph harvester is able to extract from mechanical vibrations. A series of experiments has been carried out in which the manufactured bimorph specimens are excited under fixed inertial vibrational conditions. In addition, in order to evaluate the dependence of the maximum transferred power, different load resistors are tested. In this way, the pure active power that achieves the maximum power transfer can be approximated. In this paper, we present the design of low-cost energy harvesting solutions based on piezoelectric smart materials with tunable frequency. The results obtained show the differences in energy extraction between the PZT materials studied and their electrical configurations. The aim of this work is to gain a better understanding of the behavior of piezoelectric materials, and the design process of bimorph PZT harvesters to optimize environmental energy extraction.

Keywords: Bimorph harvesters, electrical impedance, energy harvesting, piezoelectric, smart material.

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Authors: Jožef Ritonja, Bojan Grčar, Boštjan Polajžer

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In recent years, electricity trade between neighboring countries has become increasingly intense. Increasing power transmission over long distances has resulted in an increase in the oscillations of the transmitted power. The damping of the oscillations can be carried out with the reconfiguration of the network or the replacement of generators, but such solution is not economically reasonable. The only cost-effective solution to improve the damping of power oscillations is to use power system stabilizers. Power system stabilizer represents a part of synchronous generator control system. It utilizes semiconductor’s excitation system connected to the rotor field excitation winding to increase the damping of the power system. The majority of the synchronous generators are equipped with the conventional power system stabilizers with fixed parameters. The control structure of the conventional power system stabilizers and the tuning procedure are based on the linear control theory. Conventional power system stabilizers are simple to realize, but they show non-sufficient damping improvement in the entire operating conditions. This is the reason that advanced control theories are used for development of better power system stabilizers. In this paper, the adaptive control theory for power system stabilizers design and synthesis is studied. The presented work is focused on the use of model reference adaptive control approach. Control signal, which assures that the controlled plant output will follow the reference model output, is generated by the adaptive algorithm. Adaptive gains are obtained as a combination of the "proportional" term and with the σ-term extended "integral" term. The σ-term is introduced to avoid divergence of the integral gains. The necessary condition for asymptotic tracking is derived by means of hyperstability theory. The benefits of the proposed model reference adaptive power system stabilizer were evaluated as objectively as possible by means of a theoretical analysis, numerical simulations and laboratory realizations. Damping of the synchronous generator oscillations in the entire operating range was investigated. Obtained results show the improved damping in the entire operating area and the increase of the power system stability. The results of the presented work will help by the development of the model reference power system stabilizer which should be able to replace the conventional stabilizers in power systems.

Keywords: Power system, stability, oscillations, power system stabilizer, model reference adaptive control.

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Authors: Abubakar Dikko

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The research investigates the causes of unemployment in Namibia, Nigeria and South Africa and the role of Capital Accumulation in reducing the unemployment profile of these economies as proposed by the post-Keynesian economics. This is conducted through extensive review of literature on the NAIRU models and focused on the post-Keynesian view of unemployment within the NAIRU framework. The NAIRU (non-accelerating inflation rate of unemployment) model has become a dominant framework used in macroeconomic analysis of unemployment. The study views the post-Keynesian economics arguments that capital accumulation is a major determinant of unemployment. Unemployment remains the fundamental socio-economic challenge facing African economies. It has been a burden to citizens of those economies. Namibia, Nigeria, and South Africa are great African nations battling with high unemployment rates. The high unemployment rate in the country led the citizens to chase away foreigners in the country claiming that they have taken away their jobs. The study proposes there is a strong relationship between capital accumulation and unemployment in Namibia, Nigeria, and South Africa, and capital accumulation is responsible for high unemployment rates in these countries. For the economies to achieve steady state level of employment and satisfactory level of economic growth and development, there is need for capital accumulation to take place. The countries in the study have been selected after a critical research and investigations. They are selected based on the following criteria; African economies with high unemployment rates above 15% and have about 40% of their workforce unemployed. This level of unemployment is the critical level of unemployment in Africa as expressed by International Labour Organization (ILO). And finally, the African countries experience a slow growth in their Gross fixed capital formation. Adequate statistical measures have been employed using a time-series analysis in the study and the results revealed that capital accumulation is the main driver of unemployment performance in the chosen African countries. An increase in the accumulation of capital causes unemployment to reduce significantly. The results of the research work will be useful and relevant to federal governments and ministries, departments and agencies (MDAs) of Namibia, Nigeria and South Africa to resolve the issue of high and persistent unemployment rates in their economies which are great burden that slows growth and development of developing economies. Also, the result can be useful to World Bank, African Development Bank and International Labour Organization (ILO) in their further research and studies on how to tackle unemployment in developing and emerging economies.

Keywords: Capital accumulation, NAIRU, post-Keynesian economics, unemployment.

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Authors: Gela Gelashvili, David Gelenidze, Sulkhan Nanobashvili, Irakli Nanobashvili, George Tavkhelidze, Tsiuri Sitchinava

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Development of new highly efficient plasma arc combustion system of pulverized coal is presented. As it is well-known, coal is one of the main energy carriers by means of which electric and heat energy is produced in thermal power stations. The quality of the extracted coal decreases very rapidly. Therefore, the difficulties associated with its firing and complete combustion arise and thermo-chemical preparation of pulverized coal becomes necessary. Usually, other organic fuels (mazut-fuel oil or natural gas) are added to low-quality coal for this purpose. The fraction of additional organic fuels varies within 35-40% range. This decreases dramatically the economic efficiency of such systems. At the same time, emission of noxious substances in the environment increases. Because of all these, intense development of plasma combustion systems of pulverized coal takes place in whole world. These systems are equipped with Non-Transferred Plasma Arc Torches. They allow practically complete combustion of pulverized coal (without organic additives) in boilers, increase of energetic and financial efficiency. At the same time, emission of noxious substances in the environment decreases dramatically. But, the non-transferred plasma torches have numerous drawbacks, e.g. complicated construction, low service life (especially in the case of high power), instability of plasma arc and most important – up to 30% of energy loss due to anode cooling. Due to these reasons, intense development of new plasma technologies that are free from these shortcomings takes place. In our proposed system, pulverized coal-air mixture passes through plasma arc area that burns between to carbon electrodes directly in pulverized coal muffler burner. Consumption of the carbon electrodes is low and does not need a cooling system, but the main advantage of this method is that radiation of plasma arc directly impacts on coal-air mixture that accelerates the process of thermo-chemical preparation of coal to burn. To ensure the stability of the plasma arc in such difficult conditions, we have developed a power source that provides fixed current during fluctuations in the arc resistance automatically compensated by the voltage change as well as regulation of plasma arc length over a wide range. Our combustion system where plasma arc acts directly on pulverized coal-air mixture is simple. This should allow a significant improvement of pulverized coal combustion (especially low-quality coal) and its economic efficiency. Preliminary experiments demonstrated the successful functioning of the system.

Keywords: Coal combustion, plasma arc, plasma torches, pulverized coal.

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Authors: M. Amanipour, J. Towfighi, E. Ganji Babakhani, M. Heidari

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Cylindrical alumina microfiltration membrane (GMITM Corporation, inside diameter=9 mm, outside diameter=13 mm, length= 50 mm) with an average pore size of 0.5 micrometer and porosity of about 0.35 was used as the support for membrane reactor. This support was soaked in boehmite sols, and the mean particle size was adjusted in the range of 50 to 500 nm by carefully controlling hydrolysis time, and calcined at 650 °C for two hours. This process was repeated with different boehmite solutions in order to achieve an intermediate layer with an average pore size of about 50 nm. The resulting substrate was then coated with a thin and dense layer of silica by counter current chemical vapour deposition (CVD) method. A boehmite sol with 10 wt.% of nickel which was prepared by a standard procedure was used to make the catalytic layer. BET, SEM, and XRD analysis were used to characterize this layer. The catalytic membrane reactor was placed in an experimental setup to evaluate the permeation and hydrogen separation performance for a steam reforming reaction. The setup consisted of a tubular module in which the membrane was fixed, and the reforming reaction occurred at the inner side of the membrane. Methane stream, diluted with nitrogen, and deionized water with a steam to carbon (S/C) ratio of 3.0 entered the reactor after the reactor was heated up to 500 °C with a specified rate of 2 °C/ min and the catalytic layer was reduced at presence of hydrogen for 2.5 hours. Nitrogen flow was used as sweep gas through the outer side of the reactor. Any liquid produced was trapped and separated at reactor exit by a cold trap, and the produced gases were analyzed by an on-line gas chromatograph (Agilent 7890A) to measure total CH₄ conversion and H₂ permeation. BET analysis indicated uniform size distribution for catalyst with average pore size of 280 nm and average surface area of 275 m².g^-1. Single-component permeation tests were carried out for hydrogen, methane, and carbon dioxide at temperature range of 500-800 °C, and the results showed almost the same permeance and hydrogen selectivity values for hydrogen as the composite membrane without catalytic layer. Performance of the catalytic membrane was evaluated by applying membranes as a membrane reactor for methane steam reforming reaction at gas hourly space velocity (GHSV) of 10,000 h⁻¹ and 2 bar. CH₄ conversion increased from 50% to 85% with increasing reaction temperature from 600 °C to 750 °C, which is sufficiently above equilibrium curve at reaction conditions, but slightly lower than membrane reactor with packed nickel catalytic bed because of its higher surface area compared to the catalytic layer.

Keywords: Catalytic membrane, hydrogen, methane steam reforming, permeance.

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Authors: Suraiya Jabin, Kamal K. Bharadwaj

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In the recent past Learning Classifier Systems have been successfully used for data mining. Learning Classifier System (LCS) is basically a machine learning technique which combines evolutionary computing, reinforcement learning, supervised or unsupervised learning and heuristics to produce adaptive systems. A LCS learns by interacting with an environment from which it receives feedback in the form of numerical reward. Learning is achieved by trying to maximize the amount of reward received. All LCSs models more or less, comprise four main components; a finite population of condition–action rules, called classifiers; the performance component, which governs the interaction with the environment; the credit assignment component, which distributes the reward received from the environment to the classifiers accountable for the rewards obtained; the discovery component, which is responsible for discovering better rules and improving existing ones through a genetic algorithm. The concatenate of the production rules in the LCS form the genotype, and therefore the GA should operate on a population of classifier systems. This approach is known as the 'Pittsburgh' Classifier Systems. Other LCS that perform their GA at the rule level within a population are known as 'Mitchigan' Classifier Systems. The most predominant representation of the discovered knowledge is the standard production rules (PRs) in the form of IF P THEN D. The PRs, however, are unable to handle exceptions and do not exhibit variable precision. The Censored Production Rules (CPRs), an extension of PRs, were proposed by Michalski and Winston that exhibit variable precision and supports an efficient mechanism for handling exceptions. A CPR is an augmented production rule of the form: IF P THEN D UNLESS C, where Censor C is an exception to the rule. Such rules are employed in situations, in which conditional statement IF P THEN D holds frequently and the assertion C holds rarely. By using a rule of this type we are free to ignore the exception conditions, when the resources needed to establish its presence are tight or there is simply no information available as to whether it holds or not. Thus, the IF P THEN D part of CPR expresses important information, while the UNLESS C part acts only as a switch and changes the polarity of D to ~D. In this paper Pittsburgh style LCSs approach is used for automated discovery of CPRs. An appropriate encoding scheme is suggested to represent a chromosome consisting of fixed size set of CPRs. Suitable genetic operators are designed for the set of CPRs and individual CPRs and also appropriate fitness function is proposed that incorporates basic constraints on CPR. Experimental results are presented to demonstrate the performance of the proposed learning classifier system.

Keywords: Censored Production Rule, Data Mining, GeneticAlgorithm, Learning Classifier System, Machine Learning, PittsburgApproach, , Reinforcement learning.

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Authors: Ali Zaker, Zhi Chen

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Due to the concerns about the depletion of fossil fuel sources and the deteriorating environment, the attempt to investigate the production of renewable energy will play a crucial role as a potential to alleviate the dependency on mineral fuels. One particular area of interest is generation of bio-oil through sewage sludge (SS) pyrolysis. SS can be a potential candidate in contrast to other types of biomasses due to its availability and low cost. However, the presence of high molecular weight hydrocarbons and oxygenated compounds in the SS bio-oil hinders some of its fuel applications. In this context, catalytic pyrolysis is another attainable route to upgrade bio-oil quality. Among different catalysts (i.e., zeolites) studied for SS pyrolysis, activated chars (AC) are eco-friendly alternatives. The beneficial features of AC derived from SS comprise the comparatively large surface area, porosity, enriched surface functional groups and presence of a high amount of metal species that can improve the catalytic activity. Hence, a sludge-based AC catalyst was fabricated in a single-step pyrolysis reaction with NaOH as the activation agent and was compared with HZSM5 zeolite in this study. The thermal decomposition and kinetics were invested via thermogravimetric analysis (TGA) for guidance and control of pyrolysis and catalytic pyrolysis and the design of the pyrolysis setup. The results indicated that the pyrolysis and catalytic pyrolysis contain four obvious stages and the main decomposition reaction occurred in the range of 200-600 °C. Coats-Redfern method was applied in the 2nd and 3rd devolatilization stages to estimate the reaction order and activation energy (E) from the mass loss data. The average activation energy (Em) values for the reaction orders n = 1, 2 and 3 were in the range of 6.67-20.37 kJ/mol for SS; 1.51-6.87 kJ/mol for HZSM5; and 2.29-9.17 kJ/mol for AC, respectively. According to the results, AC and HZSM5 both were able to improve the reaction rate of SS pyrolysis by abridging the Em value. Moreover, to generate and examine the effect of the catalysts on the quality of bio-oil, a fixed-bed pyrolysis system was designed and implemented. The composition analysis of the produced bio-oil was carried out via gas chromatography/mass spectrometry (GC/MS). The selected SS to catalyst ratios were 1:1, 2:1 and 4:1. The optimum ratio in terms of cracking the long-chain hydrocarbons and removing oxygen-containing compounds was 1:1 for both catalysts. The upgraded bio-oils with HZSM5 and AC were in the total range of C4-C17 with around 72% in the range of C4-C9. The bio-oil from pyrolysis of SS contained 49.27% oxygenated compounds while the presence of HZSM5 and AC dropped to 7.3% and 13.02%, respectively. Meanwhile, generation of value-added chemicals such as light aromatic compounds were significantly improved in the catalytic process. Furthermore, the fabricated AC catalyst was characterized by BET, SEM-EDX, FT-IR and TGA techniques. Overall, this research demonstrated that AC is an efficient catalyst in the pyrolysis of SS and can be used as a cost-competitive catalyst in contrast to HZSM5.

Keywords: Activated char, bio-oil, catalytic pyrolysis, HZSM5, sewage sludge.

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Authors: Liliia N. Butymova, Vladimir Ya Modorskii

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To ensure the gas transmittal GCU's efficient operation, leakages through the labyrinth packings (LP) should be minimized. Leakages can be minimized by decreasing the LP gap, which in turn depends on thermal processes and possible rotor vibrations and is designed to ensure absence of mechanical contact. Vibration mitigation allows to minimize the LP gap. It is advantageous to research influence of processes in the dynamic gas-structure system on LP vibrations. This paper considers influence of rotor vibrations on LP gas dynamics and influence of the latter on the rotor structure within the FSI unidirectional dynamical coupled problem. Dependences of nonstationary parameters of gas-dynamic process in LP on rotor vibrations under various gas speeds and pressures, shaft rotation speeds and vibration amplitudes, and working medium features were studied. The programmed multi-processor ANSYS CFX was chosen as a numerical computation tool. The problem was solved using PNRPU high-capacity computer complex. Deformed shaft vibrations are replaced with an unyielding profile that moves in the fixed annulus "up-and-down" according to set harmonic rule. This solves a nonstationary gas-dynamic problem and determines time dependence of total gas-dynamic force value influencing the shaft. Pressure increase from 0.1 to 10 MPa causes growth of gas-dynamic force oscillation amplitude and frequency. The phase shift angle between gas-dynamic force oscillations and those of shaft displacement decreases from 3π/4 to π/2. Damping constant has maximum value under 1 MPa pressure in the gap. Increase of shaft oscillation frequency from 50 to 150 Hz under P=10 MPa causes growth of gas-dynamic force oscillation amplitude. Damping constant has maximum value at 50 Hz equaling 1.012. Increase of shaft vibration amplitude from 20 to 80 µm under P=10 MPa causes the rise of gas-dynamic force amplitude up to 20 times. Damping constant increases from 0.092 to 0.251. Calculations for various working substances (methane, perfect gas, air at 25 ˚С) prove the minimum gas-dynamic force persistent oscillating amplitude under P=0.1 MPa being observed in methane, and maximum in the air. Frequency remains almost unchanged and the phase shift in the air changes from 3π/4 to π/2. Calculations for various working substances (methane, perfect gas, air at 25 ˚С) prove the maximum gas-dynamic force oscillating amplitude under P=10 MPa being observed in methane, and minimum in the air. Air demonstrates surging. Increase of leakage speed from 0 to 20 m/s through LP under P=0.1 MPa causes the gas-dynamic force oscillating amplitude to decrease by 3 orders and oscillation frequency and the phase shift to increase 2 times and stabilize. Increase of leakage speed from 0 to 20 m/s in LP under P=1 MPa causes gas-dynamic force oscillating amplitude to decrease by almost 4 orders. The phase shift angle increases from π/72 to π/2. Oscillations become persistent. Flow rate proved to influence greatly on pressure oscillations amplitude and a phase shift angle. Work medium influence depends on operation conditions. At pressure growth, vibrations are mostly affected in methane (of working substances list considered), and at pressure decrease, in the air at 25 ˚С.

Keywords: Aeroelasticity, labyrinth packings, oscillation phase shift, vibration.

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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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