Search results for: gravitational settling

Authors: Banaja Mohanty, Prakash Kumar Hota

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This paper demonstrates dynamic performance evaluation of load frequency control (LFC) with different intelligent techniques. All non-linearities and physical constraints have been considered in simulation studies such as governor dead band (GDB), generation rate constraint (GRC) and boiler dynamics. The conventional integral time absolute error has been considered as objective function. The design problem is formulated as an optimisation problem and particle swarm optimisation (PSO), bacterial foraging optimisation algorithm (BFOA) and differential evolution (DE) are employed to search optimal controller parameters. The superiority of the proposed approach has been shown by comparing the results with published fuzzy logic control (FLC) for the same interconnected power system. The comparison is done using various performance measures like overshoot, undershoot, settling time and standard error criteria of frequency and tie-line power deviation following a step load perturbation (SLP). It is noticed that, the dynamic performance of proposed controller is better than FLC. Further, robustness analysis is carried out by varying the time constants of speed governor, turbine, tie-line power in the range of +40% to -40% to demonstrate the robustness of the proposed DE optimized PID controller.

Keywords: Automatic generation control, governor dead band, generation rate constraint, differential evolution.

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Authors: H. Mansor, S. B. Mohd Noor

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This paper presents a design method of self-tuning Quantitative Feedback Theory (QFT) by using improved deadbeat control algorithm. QFT is a technique to achieve robust control with pre-defined specifications whereas deadbeat is an algorithm that could bring the output to steady state with minimum step size. Nevertheless, usually there are large peaks in the deadbeat response. By integrating QFT specifications into deadbeat algorithm, the large peaks could be tolerated. On the other hand, emerging QFT with adaptive element will produce a robust controller with wider coverage of uncertainty. By combining QFT-based deadbeat algorithm and adaptive element, superior controller that is called selftuning QFT-based deadbeat controller could be achieved. The output response that is fast, robust and adaptive is expected. Using a grain dryer plant model as a pilot case-study, the performance of the proposed method has been evaluated and analyzed. Grain drying process is very complex with highly nonlinear behaviour, long delay, affected by environmental changes and affected by disturbances. Performance comparisons have been performed between the proposed self-tuning QFT-based deadbeat, standard QFT and standard dead-beat controllers. The efficiency of the self-tuning QFTbased dead-beat controller has been proven from the tests results in terms of controller’s parameters are updated online, less percentage of overshoot and settling time especially when there are variations in the plant.

Keywords: Deadbeat control, quantitative feedback theory (QFT), robust control, self-tuning control.

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Authors: Gyu-Jin Shim, Seung-Moon Baek, Choon-Geun Moon, Ho-Saeng Lee, Jung-In Yoon

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The experimental thermal performance of two heat exchangers in closed-wet cooling tower (CWCT) was investigated in this study. The test sections are heat exchangers which have multi path that is used as the entrance of cooling water and are consisting of bare-type copper tubes between 15.88mm and 19.05mm. The process fluids are the cooling water that flows from top part of heat exchanger to bottom side in the inner side of tube, and spray water that flows gravitational direction in the outer side of it. Air contacts its outer side of that as it counterflows. Heat and mass transfer coefficients and cooling capacity were calculated with variations of process fluids, multi path and different diameter tubes to figure out the performance of characteristics of CWCT. The main results were summarized as follows: The results show this experiment is reliable with values of heat and mass transfer coefficients comparing to values of correlations. Heat and mass transfer coefficients and cooling capacity of two paths are higher than these with one path using 15.88 and 19.05mm tubes. Cooling capacity per unit volume with 15.88mm tube using one and two paths are higher than 19.05mm tube due to increase of surface area per unit volume.

Keywords: Closed–Wet Cooling Tower, Cooling Capacity, Heatand Mass Transfer Coefficients.

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Authors: Nuo Duan, Yi Pik Cheng

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This paper presents the data of a series of two-dimensional Discrete Element Method (DEM) simulations of a large-diameter rigid monopile subjected to cyclic loading under a high gravitational force. At present, monopile foundations are widely used to support the tall and heavy wind turbines, which are also subjected to significant from wind and wave actions. A safe design must address issues such as rotations and changes in soil stiffness subject to these loadings conditions. Design guidance on the issue is limited, so are the availability of laboratory and field test data. The interpretation of these results in sand, such as the relation between loading and displacement, relies mainly on empirical correlations to pile properties. Regarding numerical models, most data from Finite Element Method (FEM) can be found. They are not comprehensive, and most of the FEM results are sensitive to input parameters. The micro scale behaviour could change the mechanism of the soil-structure interaction. A DEM model was used in this paper to study the cyclic lateral loads behaviour. A non-dimensional framework is presented and applied to interpret the simulation results. The DEM data compares well with various set of published experimental centrifuge model test data in terms of lateral deflection. The accumulated permanent pile lateral displacements induced by the cyclic lateral loads were found to be dependent on the characteristics of the applied cyclic load, such as the extent of the loading magnitudes and directions.

Keywords: Cyclic loading, DEM, numerical modelling, sands.

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Authors: Ji-il Park, Hyungtae Seo, Jihyuk Park, Kwang jin Choi, Kyung-Soo Kim, Soohyun Kim

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The purpose of the research is to investigate the energetic feature of the backpack load on soldier’s gait with variation of the trunk flexion angle. It is believed that the trunk flexion variation of the loaded gait may cause a significant difference in the energy cost which is often in practice in daily life. To this end, seven healthy Korea military personnel participated in the experiment and are tested under three different walking postures comprised of the small, natural and large trunk flexion. There are around 5 degree differences of waist angle between each trunk flexion. The ground reaction forces were collected from the force plates and motion kinematic data are measured by the motion capture system. Based on these data, the impulses, momentums and mechanical works done on the center of body mass (COM) during the double support phase were computed. The result shows that the push-off and heel strike impulse are not relevant to the trunk flexion change, however the mechanical work by the push-off and heel strike were changed by the trunk flexion variation. It is because the vertical velocity of the COM during the double support phase is increased significantly with an increase in the trunk flexion. Therefore, we can know that the gait efficiency of the loaded gait depends on the trunk flexion angle. Also, even though the gravitational impulse and pre-collision momentum are changed by the trunk flexion variation, the after-collision momentum is almost constant regardless of the trunk flexion variation.

Keywords: Loaded gait, collision, impulse, gravity, heel strike, push-off, gait analysis.

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Authors: M. G. Papoutsidakis, G. Chamilothoris, F. Dailami, N. Larsen, A Pipe

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Due to their high power-to-weight ratio and low cost, pneumatic actuators are attractive for robotics and automation applications; however, achieving fast and accurate control of their position have been known as a complex control problem. A methodology for obtaining high position accuracy with a linear pneumatic actuator is presented. During experimentation with a number of PID classical control approaches over many operations of the pneumatic system, the need for frequent manual re-tuning of the controller could not be eliminated. The reason for this problem is thermal and energy losses inside the cylinder body due to the complex friction forces developed by the piston displacements. Although PD controllers performed very well over short periods, it was necessary in our research project to introduce some form of automatic gain-scheduling to achieve good long-term performance. We chose a fuzzy logic system to do this, which proved to be an easily designed and robust approach. Since the PD approach showed very good behaviour in terms of position accuracy and settling time, it was incorporated into a modified form of the 1st order Tagaki- Sugeno fuzzy method to build an overall controller. This fuzzy gainscheduler uses an input variable which automatically changes the PD gain values of the controller according to the frequency of repeated system operations. Performance of the new controller was significantly improved and the need for manual re-tuning was eliminated without a decrease in performance. The performance of the controller operating with the above method is going to be tested through a high-speed web network (GRID) for research purposes.

Keywords: Fuzzy logic, gain scheduling, leaky integrator, pneumatic actuator.

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Authors: Javier Romera, Alberto Justo, Ignacio Fidalgo, Javier Araluce, Joshué Pérez

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Nowadays, individuals with mobility needs face a significant challenge when docking vehicles. In many cases, after parking, they encounter insufficient space to exit, leading to two undesired outcomes: either avoiding parking in that spot or settling for improperly placed vehicles. To address this issue, this paper presents a parking control system employing gestural teleoperation. The system comprises three main phases: capturing body markers, interpreting gestures, and transmitting orders to the vehicle. The initial phase is centered around the MediaPipe framework, a versatile tool optimized for real-time gesture recognition. MediaPipe excels at detecting and tracing body markers, with a special emphasis on hand gestures. Hands detection is done by generating 21 reference points for each hand. Subsequently, after data capture, the project employs the MultiPerceptron Layer (MPL) for in-depth gesture classification. This tandem of MediaPipe’s extraction prowess and MPL’s analytical capability ensures that human gestures are translated into actionable commands with high precision. Furthermore, the system has been trained and validated within a built-in dataset. To prove the domain adaptation, a framework based on the Robot Operating System 2 (ROS2), as a communication backbone, alongside CARLA Simulator, is used. Following successful simulations, the system is transitioned to a real-world platform, marking a significant milestone in the project. This real-vehicle implementation verifies the practicality and efficiency of the system beyond theoretical constructs.

Keywords: Gesture detection, MediaPipe, MultiLayer Perceptron Layer, Robot Operating System.

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Authors: Shidvash Vakilipour, Scott Ormiston, Masoud Mohammadi, Rouzbeh Riazi, Kimia Amiri, Sahar Barati

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Two-phase and multi-phase flows are common flow types in fluid mechanics engineering. Among the basic and applied problems of these flow types, two-phase parallel flow is the one that two immiscible fluids flow in the vicinity of each other. In this type of flow, fluid properties (e.g. density, viscosity, and temperature) are different at the two sides of the interface of the two fluids. The most challenging part of the numerical simulation of two-phase flow is to determine the location of interface accurately. In the present work, a coupled interface tracking algorithm is developed based on Arbitrary Lagrangian-Eulerian (ALE) approach using a cell-centered, pressure-based, coupled solver. To validate this algorithm, an analytical solution for fully developed two-phase flow in presence of gravity is derived, and then, the results of the numerical simulation of this flow are compared with analytical solution at various flow conditions. The results of the simulations show good accuracy of the algorithm despite using a nearly coarse and uniform grid. Temporal variations of interface profile toward the steady-state solution show that a greater difference between fluids properties (especially dynamic viscosity) will result in larger traveling waves. Gravity effect studies also show that favorable gravity will result in a reduction of heavier fluid thickness and adverse gravity leads to increasing it with respect to the zero gravity condition. However, the magnitude of variation in favorable gravity is much more than adverse gravity.

Keywords: Coupled solver, gravitational force, interface tracking, Reynolds number to Froude number, two-phase flow.

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Authors: V.D. Hatamipour, M.A. Akhavan-Behabadi

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Evaporator is an important and widely used heat exchanger in air conditioning and refrigeration industries. Different methods have been used by investigators to increase the heat transfer rates in evaporators. One of the passive techniques to enhance heat transfer coefficient is the application of microfin tubes. The mechanism of heat transfer augmentation in microfin tubes is dependent on the flow regime of two-phase flow. Therefore many investigations of the flow patterns for in-tube evaporation have been reported in literatures. The gravitational force, surface tension and the vapor-liquid interfacial shear stress are known as three dominant factors controlling the vapor and liquid distribution inside the tube. A review of the existing literature reveals that the previous investigations were concerned with the two-phase flow pattern for flow boiling in horizontal tubes [12], [9]. Therefore, the objective of the present investigation is to obtain information about the two-phase flow patterns for evaporation of R-134a inside horizontal smooth and microfin tubes. Also Investigation of heat transfer during flow boiling of R-134a inside horizontal microfin and smooth tube have been carried out experimentally The heat transfer coefficients for annular flow in the smooth tube is shown to agree well with Gungor and Winterton-s correlation [4]. All the flow patterns occurred in the test can be divided into three dominant regimes, i.e., stratified-wavy flow, wavy-annular flow and annular flow. Experimental data are plotted in two kinds of flow maps, i.e., Weber number for the vapor versus weber number for the liquid flow map and mass flux versus vapor quality flow map. The transition from wavy-annular flow to annular or stratified-wavy flow is identified in the flow maps.

Keywords: Flow boiling, Flow pattern, Heat transfer, Horizontal, Smooth tube, Microfin tube.

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Authors: M.karavanmasjedi, N.Hedayat , A.Rohani, H.Shirin

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Sedimentation process resulting from soil erosion in the water basin especially in arid and semi-arid where poor vegetation cover in the slope of the mountains upstream could contribute to sediment formation. The consequence of sedimentation not only makes considerable change in the morphology of the river and the hydraulic characteristics but would also have a major challenge for the operation and maintenance of the canal network which depend on water flow to meet the stakeholder-s requirements. For this reason mathematical modeling can be used to simulate the effective factors on scouring, sediment transport and their settling along the waterways. This is particularly important behind the reservoirs which enable the operators to estimate the useful life of these hydraulic structures. The aim of this paper is to simulate the sedimentation and erosion in the eastern and western water intake structures of the Dez Diversion weir using GSTARS-3 software. This is done to estimate the sedimentation and investigate the ways in which to optimize the process and minimize the operational problems. Results indicated that the at the furthest point upstream of the diversion weir, the coarser sediment grains tended to settle. The reason for this is the construction of the phantom bridge and the outstanding rocks just upstream of the structure. The construction of these along the river course has reduced the momentum energy require to push the sediment loads and make it possible for them to settle wherever the river regime allows it. Results further indicated a trend for the sediment size in such a way that as the focus of study shifts downstream the size of grains get smaller and vice versa. It was also found that the finding of the GSTARS-3 had a close proximity with the sets of the observed data. This suggests that the software is a powerful analytical tool which can be applied in the river engineering project with a minimum of costs and relatively accurate results.

Keywords: Erosion, sedimentation, Dez Diversion weir, GSTARS-3

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Authors: S. Gokul Prassad, S. Aakash, K. Malar Mohan

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In the process to cope with the challenges faced by the automobile industry in providing ride comfort, the electronics and control systems play a vital role. The control systems in an automobile monitor various parameters, controls the performances of the systems, thereby providing better handling characteristics. The automobile suspension system is one of the main systems that ensure the safety, stability and comfort of the passengers. The system is solely responsible for the isolation of the entire automobile from harmful road vibrations. Thus, integration of the control systems in the automobile suspension system would enhance its performance. The diverse road conditions of India demand the need of an efficient suspension system which can provide optimum ride comfort in all road conditions. For any passenger vehicle, the design of the suspension system plays a very important role in assuring the ride comfort and handling characteristics. In recent years, the air suspension system is preferred over the conventional suspension systems to ensure ride comfort. In this article, the ride comfort of the adaptive suspension system is compared with that of the passive suspension system. The schema is created in MATLAB/Simulink environment. The system is controlled by a proportional integral differential controller. Tuning of the controller was done with the Particle Swarm Optimization (PSO) algorithm, since it suited the problem best. Ziegler-Nichols and Modified Ziegler-Nichols tuning methods were also tried and compared. Both the static responses and dynamic responses of the systems were calculated. Various random road profiles as per ISO 8608 standard are modelled in the MATLAB environment and their responses plotted. Open-loop and closed loop responses of the random roads, various bumps and pot holes are also plotted. The simulation results of the proposed design are compared with the available passive suspension system. The obtained results show that the proposed adaptive suspension system is efficient in controlling the maximum over shoot and the settling time of the system is reduced enormously.

Keywords: Automobile suspension, MATLAB, control system, PID, PSO.

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Authors: F. Boustani

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To make use of the limited amounts of water in arid region, the Iranians developed man-made underground water channels called qanats (kanats) .In fact, qanats may be considered as the first long-distance water transfer system. Qanats are an ancient water transfer system found in arid regions wherein groundwater from mountainous areas, aquifers and sometimes from rivers, was brought to points of re-emergence such as an oasis, through one or more underground tunnels. The tunnels, many of which were kilometers in length, had designed for slopes to provide gravitational flow. The tunnels allowed water to drain out to the surface by gravity to supply water to lower and flatter agricultural land. Qanats have been an ancient, sustainable system facilitating the harvesting of water for centuries in Iran, and more than 35 additional countries of the world such as India, Arabia, Egypt, North Africa, Spain and even to New world. There are about 22000 qanats in Iran with 274000 kilometers of underground conduits all built by manual labor. The amount of water of the usable qanats of Iran produce is altogether 750 to 1000 cubic meter per second. The longest chain of qanat is situated in Gonabad region in Khorasan province. It is 70 kilometers long. Qanats are renewable water supply systems that have sustained agricultural settlement on the Iranian plateau for millennia. The great advantages of Qanats are no evaporation during transit, little seepage , no raising of the water- table and no pollution in the area surrounding the conduits. Qanat systems have a profound influence on the lives of the water users in Iran, and conform to Iran-s climate. Qanat allows those living in a desert environment adjacent to a mountain watershed to create a large oasis in an otherwise stark environment. This paper explains qanats structure designs, their history, objectives causing their creation, construction materials, locations and their importance in different times, as well as their present sustainable role in Iran.

Keywords: Iran, qanat, Sustainable water utilization.

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Authors: N. Elgendy, N. Hussein

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The current Syrian crisis has caused unprecedented practices of global mobility. The process of forced eviction and the resettlement of refugees could be seen through the insights of the “new mobilities paradigm”. The mobility of refugees in terms of meaning and practice is a subject that calls for further studies. There is a need for the development of an approach to human mobility to understand a practice that is turning into a phenomenon in the 21^st century. This paper aims at studying, from a qualitative point of view, the process of movement within the six constituents of mobility defined as the first phase of the journey of a refugee. The second phase would include the process of settling in and re-defining the host country as new “home” to refugees. The change in the refugee state of mind and crossing the physical and mental borders from a “foreigner” to a citizen is encouraged by both the governmental policies and the local communities’ efforts to embrace these newcomers. The paper would focus on these policies of social and economic integration. The concept of integration connotes the idea that refugees would enjoy the opportunities, rights and services available to the citizens of the refugee’s new community. So, this paper examines this concept through showcasing the two hosting countries of Canada and Egypt, as they provide two contrasting situations in terms of cultural, geographical, economic and political backgrounds. The analysis would highlight the specific policies defined towards the refugees including the mass communication, media calls, and access to employment. This research is part of a qualitative research project on the process of Urban Mobility practiced by the Syrian Refugees, drawing on conversational interviews with new-settlers who have moved to the different hosting countries, from their home in Syria. It explores these immigrants’ practical and emotional relationships with the process of movement and settlement. It uses the conversational interviews as a tool to document analysis and draw relationships in an attempt to establish an understanding of the factors that contribute to the new-settlers feeling of home and integration within the new community.

Keywords: Mobility, refugees, home, integration.

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Authors: P. Novosad, L. Osuska, M. Tazky, T. Tazky

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Current trends in the building industry are oriented towards the reduction of maintenance costs and the ecological benefits of buildings or building materials. Surface treatment of building materials with photocatalytic active titanium dioxide added into concrete can offer a good solution in this context. Architectural concrete has one disadvantage – dust and fouling keep settling on its surface, diminishing its aesthetic value and increasing maintenance e costs. Concrete surface – silicate material with open porosity – fulfils the conditions of effective photocatalysis, in particular, the self-cleaning properties of surfaces. This modern material is advantageous in particular for direct finishing and architectural concrete applications. If photoactive titanium dioxide is part of the top layers of road concrete on busy roads and the facades of the buildings surrounding these roads, exhaust fumes can be degraded with the aid of sunshine; hence, environmental load will decrease. It is clear that options for removing pollutants like nitrogen oxides (NOx) must be found. Not only do these gases present a health risk, they also cause the degradation of the surfaces of concrete structures. The photocatalytic properties of titanium dioxide can in the long term contribute to the enhanced appearance of surface layers and eliminate harmful pollutants dispersed in the air, and facilitate the conversion of pollutants into less toxic forms (e.g., NOx to HNO₃). This paper describes verification of the photocatalytic properties of titanium dioxide and presents the results of mechanical and physical tests on samples of architectural lightweight self-compacting concretes (LWSCC). The very essence of the use of LWSCC is their rheological ability to seep into otherwise extremely hard accessible or inaccessible construction areas, or sections thereof where concrete compacting will be a problem, or where vibration is completely excluded. They are also able to create a solid monolithic element with a large variety of shapes; the concrete will at the same meet the requirements of both chemical aggression and the influences of the surrounding environment. Due to their viscosity, LWSCCs are able to imprint the formwork elements into their structure and thus create high quality lightweight architectural concretes.

Keywords: Photocatalytic concretes, titanium dioxide, architectural concretes, LWSCC.

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Authors: Luminiţa Duţică, Gheorghe Duţică

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One of the most powerful language innovation in the twentieth century music was the heterophony–hypostasis of the vertical syntax entered into the sphere of interest of many composers, such as George Enescu, Pierre Boulez, Mauricio Kagel, György Ligeti and others. The heterophonic syntax has a history of its growth, which means a succession of different concepts and writing techniques. The trajectory of settling this phenomenon does not necessarily take into account the chronology: there are highly complex primary stages and advanced stages of returning to the simple forms of writing. In folklore, the plurimelodic simultaneities are free or random and originate from the (unintentional) differences/‘deviations’ from the state of unison, through a variety of ornaments, melismas, imitations, elongations and abbreviations, all in a flexible rhythmic and non-periodic/immeasurable framework, proper to the parlando-rubato rhythmics. Within the general framework of the multivocal organization, the heterophonic syntax in elaborate (academic) version has imposed itself relatively late compared with polyphony and homophony. Of course, the explanation is simple, if we consider the causal relationship between the sound vocabulary elements – in this case, the modalism – and the typologies of vertical organization appropriate for it. Therefore, adding up the ‘classic’ pathway of the writing typologies (monody – polyphony – homophony), heterophony - applied equally to the structures of modal, serial or synthesis vocabulary – reclaims necessarily an own macrotemporal form, in the sense of the analogies enshrined by the evolution of the musical styles and languages: polyphony→fugue, homophony→sonata. Concerned about the prospect of edifying a new musical ontology, the composer Ştefan Niculescu experienced – along with the mathematical organization of heterophony according to his own original methods – the possibility of extrapolation of this phenomenon in macrostructural plan, reaching this way to the unique form of ‘synchrony’. Founded on coincidentia oppositorum principle (involving the ‘one-multiple’ binom), the sound architecture imagined by Ştefan Niculescu consists in one (temporal) model / algorithm of articulation of two sound states: 1. monovocality state (principle of identity) and 2. multivocality state (principle of difference). In this context, the heterophony becomes an (auto)generative mechanism, with macrotemporal amplitude, strategy that will be grown by the composer, practically throughout his creation (see the works: Ison I, Ison II, Unisonos I, Unisonos II, Duplum, Triplum, Psalmus, Héterophonies pour Montreux (Homages to Enescu and Bartók etc.). For the present demonstration, we selected one of the most edifying works of Ştefan Niculescu – Simphony II, Opus dacicum – where the form of (heterophony-)synchrony acquires monumental-symphonic features, representing an emblematic case for the complexity level achieved by this type of vertical syntax in the twentieth century music.

Keywords: Heterophony, modalism, serialism, synchrony, syntax.

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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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