Search results for: Statistical Quality Control.

Authors: M. Shakir Saat, M. Noh Ahmad, Dr, Amat Amir

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A cart-ball system is a challenging system from the control engineering point of view. This is due to the nonlinearities, multivariable, and non-minimum phase behavior present in this system. This paper is concerned with the problem of modeling and control of such system. The objective of control strategy is to place the cart at a desired position while balancing the ball on the top of the arc-shaped track fixed on the cart. A State-Feedback Controller (SFC) with a pole-placement method will be designed in order to control the system. At first, the mathematical model of a cart-ball system in the state-space form is developed. Then, the linearization of a model will be established in order to design a SFC. The integral control strategy will be performed as to control the cart position of a system. Simulation work is then performed using MATLAB/SIMULINK software in order to study the performance of SFC when applied to the system.

Keywords: Cart-Ball System, Integral Control, Pole-PlacementMethod, State-Feedback Controller.

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Authors: M-M. Mohamed Ahmed, Nacer K. M’Sirdi, Aziz Naamane

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In this paper, a longitudinal and lateral control approach based on a nonlinear observer is proposed for a convoy of autonomous vehicles to follow a desired trajectory. To authors best knowledge, this topic has not yet been sufficiently addressed in the literature for the control of multi vehicles. The modeling of the convoy of the vehicles is revisited using a robotic method for simulation purposes and control design. With these models, a sliding mode observer is proposed to estimate the states of each vehicle in the convoy from the available sensors, then a sliding mode control based on this observer is used to control the longitudinal and lateral movement. The validation and performance evaluation are done using the well-known driving simulator Scanner-Studio. The results are presented for different maneuvers of 5 vehicles.

Keywords: Autonomous vehicles, convoy, nonlinear control, nonlinear observer, sliding mode.

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Authors: Kazuya Sato, Toru Kasahara, Junji Kuroda, Tomoyuki Izu

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In this paper, an autonomous hovering control method of multicopter using only Web camera is proposed. Recently, various control method of an autonomous flight for multicopter are proposed. But, in the previous proposed methods, a motion capture system (i. e., OptiTrack) and laser range finder are often used to measure the position and posture of multicopter. To achieve an autonomous flight control of multicopter with simple equipments, we propose an autonomous flight control method using AR marker and Web camera. AR marker can measure the position of multicopter with Cartesian coordinate in three dimensional, then its position connects with aileron, elevator, and accelerator throttle operation. A simple PID control method is applied to the each operation and adjust the controller gains. Experimental results are given to show the effectiveness of our proposed method. Moreover, another simple operation method for autonomous flight control multicopter is also proposed.

Keywords: Autonomous hovering control, multicopter, Web camera.

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Authors: Aleem Khalid Alvi, M. Yousuf Bin Azhar, Mehmood Usman, Suleman Mumtaz, Sameer Rafiq, RaziUr Rehman, Israr Ahmed

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Sign language recognition has been a topic of research since the first data glove was developed. Many researchers have attempted to recognize sign language through various techniques. However none of them have ventured into the area of Pakistan Sign Language (PSL). The Boltay Haath project aims at recognizing PSL gestures using Statistical Template Matching. The primary input device is the DataGlove5 developed by 5DT. Alternative approaches use camera-based recognition which, being sensitive to environmental changes are not always a good choice.This paper explains the use of Statistical Template Matching for gesture recognition in Boltay Haath. The system recognizes one handed alphabet signs from PSL.

Keywords: Gesture Recognition, Pakistan Sign Language, DataGlove, Human Computer Interaction, Template Matching, BoltayHaath

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Authors: Yohei Saika, Tatsuya Uezu

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We constructed a method of phase unwrapping for a typical wave-front by utilizing the maximizer of the posterior marginal (MPM) estimate corresponding to equilibrium statistical mechanics of the three-state Ising model on a square lattice on the basis of an analogy between statistical mechanics and Bayesian inference. We investigated the static properties of an MPM estimate from a phase diagram using Monte Carlo simulation for a typical wave-front with synthetic aperture radar (SAR) interferometry. The simulations clarified that the surface-consistency conditions were useful for extending the phase where the MPM estimate was successful in phase unwrapping with a high degree of accuracy and that introducing prior information into the MPM estimate also made it possible to extend the phase under the constraint of the surface-consistency conditions with a high degree of accuracy. We also found that the MPM estimate could be used to reconstruct the original wave-fronts more smoothly, if we appropriately tuned hyper-parameters corresponding to temperature to utilize fluctuations around the MAP solution. Also, from the viewpoint of statistical mechanics of the Q-Ising model, we found that the MPM estimate was regarded as a method for searching the ground state by utilizing thermal fluctuations under the constraint of the surface-consistency condition.

Keywords: Bayesian inference, maximizer of the posterior marginal estimate, phase unwrapping, Monte Carlo simulation, statistical mechanics

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Authors: Anton Golubkov, Gleb Ermachkov, Aleksandr Smerdin, Oleg Sidorov, Victor Philippov

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Current collection quality is one of the limiting factors when increasing trains movement speed in the rail sector. With the movement speed growth, the impact forces on the current collector from the rolling stock and the aerodynamic influence increase, which leads to the spread in the contact pressure values, separation of the current collector head from the contact wire, contact arcing and excessive wear of the contact elements. The upcoming trend in resolving this issue is the use of the automatic control systems providing stabilization of the contact pressure value. The present paper considers the features of the contemporary automatic control systems of the current collector’s pressure; their major disadvantages have been stated. A scheme of current collector pressure automatic control has been proposed, distinguished by a proactive influence on undesirable effects. A mathematical model of contact strips wearing has been presented, obtained in accordance with the provisions of the central composition rotatable design program. The analysis of the obtained dependencies has been carried out. The procedures for determining the optimal current collector pressure on the contact wire and the pressure control principle in the pneumatic drive have been described.

Keywords: High-speed running, current collector, contact strip, mathematical model, contact pressure, program control, wear, life cycle.

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Authors: B. Nassar, W. Hussein, M. Mokhtar

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The critical concern of satellite operations is to ensure the health and safety of satellites. The worst case in this perspective is probably the loss of a mission, but the more common interruption of satellite functionality can result in compromised mission objectives. All the data acquiring from the spacecraft are known as Telemetry (TM), which contains the wealth information related to the health of all its subsystems. Each single item of information is contained in a telemetry parameter, which represents a time-variant property (i.e. a status or a measurement) to be checked. As a consequence, there is a continuous improvement of TM monitoring systems to reduce the time required to respond to changes in a satellite's state of health. A fast conception of the current state of the satellite is thus very important to respond to occurring failures. Statistical multivariate latent techniques are one of the vital learning tools that are used to tackle the problem above coherently. Information extraction from such rich data sources using advanced statistical methodologies is a challenging task due to the massive volume of data. To solve this problem, in this paper, we present a proposed unsupervised learning algorithm based on Principle Component Analysis (PCA) technique. The algorithm is particularly applied on an actual remote sensing spacecraft. Data from the Attitude Determination and Control System (ADCS) was acquired under two operation conditions: normal and faulty states. The models were built and tested under these conditions, and the results show that the algorithm could successfully differentiate between these operations conditions. Furthermore, the algorithm provides competent information in prediction as well as adding more insight and physical interpretation to the ADCS operation.

Keywords: Space telemetry monitoring, multivariate analysis, PCA algorithm, space operations.

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Authors: Ljubica Dokić, Ivana Nikolić, Dragana Šoronja–Simović, Biljana Pajin, Nils Juul

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In this work sensory characteristics of cookies with different amount of chestnut flour were determined by sensory and instrumental methods. The wheat flour for cookies was substituted with chestnut flour in three different levels (20, 40 and 60%) and the dough moisture was 22%. The control sample was with 100% of wheat flour. Sensory quality of the cookies was described using quantity descriptive method (QDA) by six trained members of descriptive panel. Instrumental evaluation included texture characterization by texture analyzer, the color measurements (CIE L*a*b* system) and determination by videometer.

The samples with 20% of chestnut flour were with highest ponderated score for overall sensory impression (17.6), which is very close to score for control sample (18). Increase in amount of chestnut flour caused decrease in scores for all sensory properties, thus overall sensory score decreased also. Compared to control sample and with increase in amount of chestnut flour, instrumental determination of the samples confirmed the sensory analysis results. The hardness of the cookies increased, as well as the values of red a^* and yellow (b*) component coordinate, but the values for lightness (L*) decreased. Also the values, evaluated by videometer at defined wavelength, were the highest for control cookies and decreased with increase in amount of chestnut flour.

Keywords: Cookies, chestnut flour, sensory characteristics.

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Authors: Mary L. G. S. Senna, Afonso R. Aquino, Veruska C. Dutra, Carlos H. C. Tolentino

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The quality of life index, despite elucidating many discussions, the conceptual subjectivity of the term does not show precision, and consequently, many researchers seek to develop methods aiming to measure this concept, bringing it to a more concrete approach. In this study, the quality of life index method was used to analyze the population of Mateiros, Tocantins, Brazil for quality of life. After data collection, it was compared the quality of life index between the population and the group of beneficiaries of the Brazilian government assistance program Bolsa Família (Family Allowance). Some of the people interviewed receive financial aid from the federal government program Bolsa Família (22%). Comparisons were made among the final score of the quality of life index of the Mateiros population and the following factors: Gender, age, education, those working or not with tourism and those who receive or do not receive the Bolsa Família. It was observed that only the factor, Bolsa Família (p-score 0.0138), shows an association with quality of life improvement, noticing that those who have financial aid had a higher quality of life improvement than the rest of the population. It was concluded that, government assistance has shown a decisive element on the enhancement of Mateiros population quality of life, indicating that similar actions should be maintained.

Keywords: Quality of life index, government aid to families, sustainable tourism, Bolsa Familia.

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Authors: Sharareh Mirsaeidi Farahani , Gholamreza Chitsaz

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Management Systems are powerful tools for businesses to manage quality , environmental and occupational health and safety requirements . where once these systems were considered as stand alone control mechanisms , industry is now opting to increase the efficiency of these documented systems through a more integrated approach . System integration offers a significant step forward, where there are similarities between system components , reducing duplication and adminstration costs and increasing efficiency . At first , this paper reviews integrated management system structure and its benefits. The second part of this paper focuses on the one example implementation of such a system at Imam Khomeini Hospital and in final part of the paper will be discuss outcomes of that proccess .

Keywords: environmental management , Integratedmanagement systems, occupational healt and safetymanagement , quality management.

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Authors: A. Elakkary, A. Echchatbi, N. Elalami

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In this paper, we are interested in attitude control of a satellite, which using wheels of reaction, by state feedback. First, we develop a method allowing us to put the control and its integral in the state-feedback form. Then, by using the theorem of Gronwall- Bellman, we put the sufficient conditions so that the nonlinear system modeling the satellite is stabilisable and observed by state feedback.

Keywords: Satellite, attitude control, state feedback, attitude stabilization.

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Authors: A. R. Tavakolpour-Saleh, H. Jokar

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Liquid level control of conical tank system is known to be a great challenge in many industries such as food processing, hydrometallurgical industries and wastewater treatment plant due to its highly nonlinear characteristics. In this research, an adaptive fuzzy PID control scheme is applied to the problem of liquid level control in a nonlinear tank process. A conical tank process is first modeled and primarily simulated. A PID controller is then applied to the plant model as a suitable benchmark for comparison and the dynamic responses of the control system to different step inputs were investigated. It is found that the conventional PID controller is not able to fulfill the controller design criteria such as desired time constant due to highly nonlinear characteristics of the plant model. Consequently, a nonlinear control strategy based on gain-scheduling adaptive control incorporating a fuzzy logic observer is proposed to accurately control the nonlinear tank system. The simulation results clearly demonstrated the superiority of the proposed adaptive fuzzy control method over the conventional PID controller.

Keywords: Adaptive control, fuzzy logic, conical tank, PID controller.

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Authors: Jędrzej Minda

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In aviation a very narrow spectrum of control inceptors exists, namely centre-sticks, side-sticks, pedals and yokes. However, new types of aircraft are emerging and with them a need for new inceptors. A manned multicopter created at AGH University of Science and Technology is an aircraft in which the pilot takes a specific orientation in which classical inceptors may be impractical to use. In this paper unique kind of control inceptor is described, which aims to provide a handling quality not unlike standard solutions and provide a firm grip point for the pilot without the risk of involuntary stick movement. Simulations of pilot-inceptor model were performed in order to compare dynamic amplification factors of design described in this paper with classical one. Functional prototype is built on which drone pilots carried out a comfort of use evaluation. This paper provides a general overview of the project, including literature review, reasoning behind components selection and mechanism design finalized by conclusions.

Keywords: Mechanisms, mechatronics, embedded control, serious gaming, rescue missions, rescue robotics.

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Authors: Mostafa A. Shokshok, Omran Ali Abu Krais

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This paper describes the collection and analysis of data obtained from face-to-face interviews conducted in selected Libyan industrial companies. The objectives of the interviews are to enhance understanding, and generate explanations of current issues in culture and quality management systems in Libyan companies. The method used in analyzing the questions, as well as the main finding of each question are explained. The interviews probed areas identify national and organizational culture, quality management systems, current methods, effects, barriers and other factors affecting the success of quality management implementation. Eleven questions are prepared and been discussed with the interviewees.

Keywords: Interviews, quality, culture, Libyan industrial companies.

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Authors: M.Saleem Khan, Khaled Benkrid

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This paper presents a time control liquids mixing system in the tanks as an application of fuzzy time control discrete model. The system is designed for a wide range of industrial applications. The simulation design of control system has three inputs: volume, viscosity, and selection of product, along with the three external control adjustments for the system calibration or to take over the control of the system autonomously in local or distributed environment. There are four controlling elements: rotatory motor, grinding motor, heating and cooling units, and valves selection, each with time frame limit. The system consists of three controlled variables measurement through its sensing mechanism for feed back control. This design also facilitates the liquids mixing system to grind certain materials in tanks and mix with fluids under required temperature controlled environment to achieve certain viscous level. Design of: fuzzifier, inference engine, rule base, deffuzifiers, and discrete event control system, is discussed. Time control fuzzy rules are formulated, applied and tested using MATLAB simulation for the system.

Keywords: Fuzzy time control, industrial application and timecontrol systems, adjustment of Fuzzy system, liquids mixing system, design of fuzzy time control DEV system.

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Authors: Hyeon-Cheol Lee

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The adaptive power control of Code Division Multiple Access (CDMA) communications using Remote Radio Head (RRH) between multiple Unmanned Aerial Vehicles (UAVs) with a link-budget based Signal-to-Interference Ratio (SIR) estimate is applied to four inner loop power control algorithms. It is concluded that Base Station (BS) can calculate not only UAV distance using linearity between speed and Consecutive Transmit-Power-Control Ratio (CTR) of Adaptive Step-size Closed Loop Power Control (ASCLPC), Consecutive TPC Ratio Step-size Closed Loop Power Control (CS-CLPC), Fixed Step-size Power Control (FSPC), but also UAV position with Received Signal Strength Indicator (RSSI) ratio of RRHs.

Keywords: speed estimation, adaptive power control, link-budget, SIR, multi-bit quantizer, RRH

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Authors: Mohammad A. Talaat, Magdi A. Koutb, Hoda S. Sorour

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In this paper we investigated a number of the Internet congestion control algorithms that has been developed in the last few years. It was obviously found that many of these algorithms were designed to deal with the Internet traffic merely as a train of consequent packets. Other few algorithms were specifically tailored to handle the Internet congestion caused by running media traffic that represents audiovisual content. This later set of algorithms is considered to be aware of the nature of this media content. In this context we briefly explained a number of congestion control algorithms and hence categorized them into the two following categories: i) Media congestion control algorithms. ii) Common congestion control algorithms. We hereby recommend the usage of the media congestion control algorithms for the reason of being media content-aware rather than the other common type of algorithms that blindly manipulates such traffic. We showed that the spread of such media content-aware algorithms over Internet will lead to better congestion control status in the coming years. This is due to the observed emergence of the era of digital convergence where the media traffic type will form the majority of the Internet traffic.

Keywords: Congestion Control, Media Traffic.

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Authors: Qamar Saeed, Vali Uddin, Reza Katebi

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In this paper multivariable predictive PID controller has been implemented on a multi-inputs multi-outputs control problem i.e., quadruple tank system, in comparison with a simple multiloop PI controller. One of the salient feature of this system is an adjustable transmission zero which can be adjust to operate in both minimum and non-minimum phase configuration, through the flow distribution to upper and lower tanks in quadruple tank system. Stability and performance analysis has also been carried out for this highly interactive two input two output system, both in minimum and non-minimum phases. Simulations of control system revealed that better performance are obtained in predictive PID design.

Keywords: Proportional-integral-derivative Control, GeneralizedPredictive Control, Predictive PID Control, Multivariable Systems

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Authors: Saif Ul Haq

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The current study intends to examine the safety and quality considerations of clients of housing projects and their impact on the adoption of Quality Function Deployment (QFD) by the construction firm. Mixed method research technique has been used to collect and analyze the data wherein a survey was conducted to collect the data from 220 clients of housing projects in Saudi Arabia. Then, the telephonic and Skype interviews were conducted to collect data of 15 professionals working in the top ten real estate companies of Saudi Arabia. Data were analyzed by using partial least square (PLS) and thematic analysis techniques. Findings reveal that today’s customer prioritizes the safety and quality requirements of their houses and as a result, construction firms adopt QFD to address the needs of customers. The findings are of great importance for the clients of housing projects as well as for the construction firms as they could apply QFD in housing projects to address the safety and quality concerns of their clients.

Keywords: Construction industry, quality considerations, quality function deployment, safety considerations.

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Authors: Hamed Homaei, Iraj Mahdavi, Ali Tajdin

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One of the main concerns of miners is to increase the quality level of their products because the mining metals price depends on their quality level; however, increasing the quality level of these products has different costs at different levels of the supply chain. These costs usually increase after extractor level. This paper studies the coordination issue of a decentralized three-level supply chain with one supplier (extractor), one mineral processor and one manufacturer in which the increasing product quality level cost at the processor level is higher than the supplier and at the level of the manufacturer is more than the processor. We identify the optimal product quality level for each supply chain member by designing a revenue sharing contract. Finally, numerical examples show that the designed contract not only increases the final product quality level but also provides a win-win condition for all supply chain members and increases the whole supply chain profit.

Keywords: Three-stage supply chain, product quality improvement, channel coordination, revenue sharing.

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Authors: Ndidi F. Amulu, Calistus N. Ude, Patrick E. Amulu, Nneka N. Uchegbu

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The effects of temperature and enzyme concentration on the quality of mixed pineapple and pawpaw blended fruits juice were studied. Extracts of the two fruit juices were separately treated at 70  for 15 min each so as to inactivate micro-organisms. They were analyzed and blended in different proportions of 70% pawpaw and 30% pineapple, 60% pawpaw and 40% pineapple, 50% pineapple and 50% pawpaw, 40% pawpaw and 60% pineapple. The characterization of the fresh pawpaw and pineapple juice before blending showed that the juices have good quality. The high water content of the product may have affected the viscosity, vitamin C content and total soluble solid of the blended juice to be low. The effects of the process parameters on the quality showed that better quality of the blended juice can be obtained within the optimum temperature range of (50-70 °C) and enzyme concentration range (0.12-0.18 w/v). The ratio of mix 60% pineapple juice: 40% pawpaw juice has better quality. This showed that pawpaw and pineapple juices can blend effectively to produce a quality juice.

Keywords: Clarification, pawpaw, pineapple, viscosity, vitamin C.

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Authors: T. Benmiloud, A. Omari

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This paper presents a new technique of compensation of the effect of variation parameters in the direct field oriented control of induction motor. The proposed method uses an adaptive tuning of the value of synchronous speed to obtain the robustness for the field oriented control. We show that this adaptive tuning allows having robustness for direct field oriented control to changes in rotor resistance, load torque and rotational speed. The effectiveness of the proposed control scheme is verified by numerical simulations. The numerical validation results of the proposed scheme have presented good performances compared to the usual direct-field oriented control.

Keywords: Induction motor, direct field-oriented control, compensation of variation parameters, fuzzy logic controller.

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Authors: Ramy H. Mohammed

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Understanding the behavior of airflow in a room is essential for building designers to provide the most efficient design of ventilation system, and having acceptable indoor air quality. This trend is the motive to solve the relationship between airflow parameters and thermal comfort. This paper investigates airflow characteristics, indoor air quality (IAQ), and the thermal comfort (TC) in a ventilated room with a displacement ventilation system using three dimensional CFD code [AirPak 2.0.6]. After validation of the code, a numerical study is executed for a typical room with dimensions of 5m by 3m by 3m height according to a variety of supply air velocities, supply air temperature and supply air relative humidity. The finite volume method and the indoor zero equation turbulence models are employed for solving the governing equations numerically. The temperature field and the mean age of air (MAA) in the modeled room for a displacement ventilation system are determined according to a variety of the above parameters. The variable air volume (VAV) systems with different supply air velocity are applicable to control room air temperature for a displacement ventilation system.

Keywords: Displacement ventilation, AirPak, Indoor zero equation, MAA.

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Authors: Toshinori Nawata

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In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) for nonlinear systems with constrained input using weighted gradient optimization automatic choosing functions. Constant term which arises from linearization of a given nonlinear system is treated as a coefficient of a stable zero dynamics. Parameters of the control are suboptimally selected by maximizing the stable region in the sense of Lyapunov with the aid of a genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: Augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: Jasna Dragosavac, Žarko Janda, J.V. Milanović, Dušan Arnautović

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This paper discusses coordinated reactive power - voltage (Q-V) control in a multi machine steam power plant. The drawbacks of manual Q-V control are briefly listed, and the design requirements for coordinated Q-V controller are specified. Theoretical background and mathematical model of the new controller are presented next followed by validation of developed Matlab/Simulink model through comparison with recorded responses in real steam power plant and description of practical realisation of the controller. Finally, the performance of commissioned controller is illustrated on several examples of coordinated Q-V control in real steam power plant and compared with manual control.

Keywords: Coordinated Voltage Control, Power Plant Control, Reactive Power Control, Sensitivity Matrix

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Authors: M. Soyaslan, A. Fenercioglu, C. Kozkurt

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Automated storage and retrieval systems (AS/RS) become frequently used systems in warehouses. There has been a transition from human based forklift applications to fast and safe AS/RS applications in firm-s warehouse systems. In this study, basic components and automation systems of the AS/RS are examined. Proposed system's automation components and their tasks in the system control algorithm were stated. According to this control algorithm the control system structure was obtained.

Keywords: AS/RS, Automatic Storage and Retrieval System, Warehouse Control System

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Authors: Alireza Bolhari, Ali Rezaeean, Jafar Bolhari, Fatemeh Zare

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With the advent of new technologies, factors related to mental health in e-workspaces are taken into consideration more than ever. Studies have revealed that one of the factors affecting the productivity of employees in an organization is occupational stress. Another influential factor is quality of work life which is important in the improvement of work environment conditions and organizational efficiency. In order to uncover the quality of work life level and to investigate the impact of occupational stress on quality of work life among information technology employees in Iran, a cross-sectional study design was applied and data were gathered using a questionnaire validated by a group of experts. The results of the study showed that information technology staffs have average level of both occupational stress and quality of work life. Furthermore, it was found that occupational stress has a negative impact on quality of work life. In addition, the same results were observed for role ambiguity, role conflict, role under-load, work-pace, work repetitiveness and tension toward quality of work life. No significant relation was found between role overload and quality of work life. Finally, directions for future research are proposed and discussed.

Keywords: Information Technology, e-Workspace, Healthcare, IT Staff, Occupational Stress, Quality of Work Life

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Authors: Markus Reichhartinger, Martin Horn

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In this paper, the position control of an electronic throttle actuator is outlined. The dynamic behavior of the actuator is described with the help of an uncertain plant model. This motivates the controller design based on the ideas of higher-order slidingmodes. As a consequence anti-chattering techniques can be omitted. It is shown that the same concept is applicable to estimate unmeasureable signals. The control law and the observer are implemented on an electronic control unit. Results achieved by numerical simulations and real world experiments are presented and discussed.

Keywords: higher order sliding-mode, throttle actuator, electromechanicalsystem, robust and nonlinear control.

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Authors: S. Anbu, N. Jaya

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Nonlinearity is the inherent characteristics of all the industrial processes. The Classical control approach used for a generation often fails to show better results particularly for non-linear systems and in the systems, whose parameters changes over a period of time for a variety of reasons. Alternatively, adaptive control strategies provide very good performance. The Model Reference Adaptive Control based on Lyapunov stability analysis and classical PI control strategies are designed and evaluated for Continuous Stirred Tank Reactor, which shows appreciable dynamic nonlinear characteristics.

Keywords: Adaptive Control, CSTR, Lyapunov stability, MRAS, PID.

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Authors: Omid S. Fard, Akbar H. Borzabadi

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In this paper we apply one of approaches in category of heuristic methods as Genetic Algorithms for obtaining approximate solution of optimal control problems. The firs we convert optimal control problem to a quasi Assignment Problem by defining some usual characters as defined in Genetic algorithm applications. Then we obtain approximate optimal control function as an piecewise constant function. Finally the numerical examples are given.

Keywords: Optimal control, Integer programming, Genetic algorithm, Discrete approximation, Linear programming.

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