Search results for: Preview control

Authors: Chin-Yin Chen, Chi-Cheng Cheng

Abstract:

This paper aims at to develop a robust optimization methodology for the mechatronic modules of machine tools by considering all important characteristics from all structural and control domains in one single process. The relationship between these two domains is strongly coupled. In order to reduce the disturbance caused by parameters in either one, the mechanical and controller design domains need to be integrated. Therefore, the concurrent integrated design method Design For Control (DFC), will be employed in this paper. In this connect, it is not only applied to achieve minimal power consumption but also enhance structural performance and system response at same time. To investigate the method for integrated optimization, a mechatronic feed drive system of the machine tools is used as a design platform. Pro/Engineer and AnSys are first used to build the 3D model to analyze and design structure parameters such as elastic deformation, nature frequency and component size, based on their effects and sensitivities to the structure. In addition, the robust controller,based on Quantitative Feedback Theory (QFT), will be applied to determine proper control parameters for the controller. Therefore, overall physical properties of the machine tool will be obtained in the initial stage. Finally, the technology of design for control will be carried out to modify the structural and control parameters to achieve overall system performance. Hence, the corresponding productivity is expected to be greatly improved.

Keywords: Machine tools, integrated structure and control design, design for control, multilevel decomposition, quantitative feedback theory.

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Authors: B. Baigzadeh, V.Nazarzehi, H.Khaloozadeh

Abstract:

The two cart inverted pendulum system is a good bench mark for testing the performance of system dynamics and control engineering principles. Devasia introduced this system to study the asymptotic tracking problem for nonlinear systems. In this paper the problem of asymptotic tracking of the two-cart with an inverted-pendulum system to a sinusoidal reference inputs via introducing a novel method for solving finite-horizon nonlinear optimal control problems is presented. In this method, an iterative method applied to state dependent Riccati equation (SDRE) to obtain a reliable algorithm. The superiority of this technique has been shown by simulation and comparison with the nonlinear approach.

Keywords: Nonlinear optimal control, State dependent Riccatiequation, Asymptotic tracking, inverted pendulum

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Authors: H. Shayeghi, H.A. Shayanfar, A. Jalili

Abstract:

In the LFC problem, the interconnections among some areas are the input of disturbances, and therefore, it is important to suppress the disturbances by the coordination of governor systems. In contrast, tie-line power flow control by TCPS located between two areas makes it possible to stabilize the system frequency oscillations positively through interconnection, which is also expected to provide a new ancillary service for the further power systems. Thus, a control strategy using controlling the phase angle of TCPS is proposed for provide active control facility of system frequency in this paper. Also, the optimum adjustment of PID controller's parameters in a robust way under bilateral contracted scenario following the large step load demands and disturbances with and without TCPS are investigated by Particle Swarm Optimization (PSO), that has a strong ability to find the most optimistic results. This newly developed control strategy combines the advantage of PSO and TCPS and has simple stricture that is easy to implement and tune. To demonstrate the effectiveness of the proposed control strategy a three-area restructured power system is considered as a test system under different operating conditions and system nonlinearities. Analysis reveals that the TCPS is quite capable of suppressing the frequency and tie-line power oscillations effectively as compared to that obtained without TCPS for a wide range of plant parameter changes, area load demands and disturbances even in the presence of system nonlinearities.

Keywords: LFC, TCPS, Dregulated Power System, PowerSystem Control, PSO.

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Authors: Reza Kazemi , Iman Mousavinejad

Abstract:

Steer-By-Wire ( SBW ) has several advantages of packaging flexibility , advanced vehicle control system ,and superior performance . SBW has no mechanical linkage between the steering gear and the steering column. It is possible to control the steering wheel and the front-wheel steering independently. SBW system is composed of two motors controlled by ECU. One motor in the steering wheel is to improve the driver's steering feel and the other motor in the steering linkage is to improve the vehicle maneuverability and stability. This paper shows a new approach at modeling of SBW system by Bond Graph theory. The mechanical parts , the steering wheel motor and the front wheel motor will be modeled by this theory. The work in the paper will help to guide further researches on control algorithm of the SBW system .

Keywords: Steer-By-Wire ( SBW ), Bond Graph theory, Electronic-Control-Unit ( ECU ) , Modeling

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Authors: Ali Reza Mehrabian, Caro Lucas

Abstract:

In this paper a new control strategy based on Brain Emotional Learning (BEL) model has been introduced. A modified BEL model has been proposed to increase the degree of freedom, controlling capability, reliability and robustness, which can be implemented in real engineering systems. The performance of the proposed BEL controller has been illustrated by applying it on different nonlinear uncertain systems, showing very good adaptability and robustness, while maintaining stability.

Keywords: Learning control systems, emotional decision making, nonlinear systems, adaptive control.

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Authors: Irtaza M. Syed, Kaamran Raahemifar

Abstract:

This paper presents a model predictive control (MPC) of a utility interactive (UI) single phase inverter (SPI) for a photovoltaic (PV) system at residential/distribution level. The proposed model uses single-phase phase locked loop (PLL) to synchronize SPI with the grid and performs MPC control in a dq reference frame. SPI model consists of boost converter (BC), maximum power point tracking (MPPT) control, and a full bridge (FB) voltage source inverter (VSI). No PI regulators to tune and carrier and modulating waves are required to produce switching sequence. Instead, the operational model of VSI is used to synthesize sinusoidal current and track the reference. Model is validated using a three kW PV system at the input of UI-SPI in Matlab/Simulink. Implementation and results demonstrate simplicity and accuracy, as well as reliability of the model.

Keywords: Matlab/Simulink, Model Predictive Control, Phase Locked Loop, Single Phase Inverter, Voltage Source Inverter.

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Authors: Saeed Vaneshani, Hooshang Jazayeri-Rad

Abstract:

Fuzzy logic control (FLC) systems have been tested in many technical and industrial applications as a useful modeling tool that can handle the uncertainties and nonlinearities of modern control systems. The main drawback of the FLC methodologies in the industrial environment is challenging for selecting the number of optimum tuning parameters. In this paper, a method has been proposed for finding the optimum membership functions of a fuzzy system using particle swarm optimization (PSO) algorithm. A synthetic algorithm combined from fuzzy logic control and PSO algorithm is used to design a controller for a continuous stirred tank reactor (CSTR) with the aim of achieving the accurate and acceptable desired results. To exhibit the effectiveness of proposed algorithm, it is used to optimize the Gaussian membership functions of the fuzzy model of a nonlinear CSTR system as a case study. It is clearly proved that the optimized membership functions (MFs) provided better performance than a fuzzy model for the same system, when the MFs were heuristically defined.

Keywords: continuous stirred tank reactor (CSTR), fuzzy logiccontrol (FLC), membership function(MF), particle swarmoptimization (PSO)

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Authors: Shyam S.N. Perera

Abstract:

An optimal control problem for a mathematical model of efficiency of antiviral therapy in hepatitis B virus infections is considered. The aim of the study is to control the new viral production, block the new infection cells and maintain the number of uninfected cells in the given range. The optimal controls represent the efficiency of antiviral therapy in inhibiting viral production and preventing new infections. Defining the cost functional, the optimal control problem is converted into the constrained optimization problem and the first order optimality system is derived. For the numerical simulation, we propose the steepest descent algorithm based on the adjoint variable method. A computer program in MATLAB is developed for the numerical simulations.

Keywords: Virus infection model, Optimal control, Adjoint system, Steepest descent

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Authors: Farzaneh Ahmadzadeh

Abstract:

Quality control charts are very effective in detecting out of control signals but when a control chart signals an out of control condition of the process mean, searching for a special cause in the vicinity of the signal time would not always lead to prompt identification of the source(s) of the out of control condition as the change point in the process parameter(s) is usually different from the signal time. It is very important to manufacturer to determine at what point and which parameters in the past caused the signal. Early warning of process change would expedite the search for the special causes and enhance quality at lower cost. In this paper the quality variables under investigation are assumed to follow a multivariate normal distribution with known means and variance-covariance matrix and the process means after one step change remain at the new level until the special cause is being identified and removed, also it is supposed that only one variable could be changed at the same time. This research applies artificial neural network (ANN) to identify the time the change occurred and the parameter which caused the change or shift. The performance of the approach was assessed through a computer simulation experiment. The results show that neural network performs effectively and equally well for the whole shift magnitude which has been considered.

Keywords: Artificial neural network, change point estimation, monte carlo simulation, multivariate exponentially weighted movingaverage

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Authors: Denisa Ferenčíková, Petr Briš

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Customer audits are generally used to ensure customer that supplier is continuously able to meet his requirements while supplying him required products and services. However, customer audits can be considered as a very useful quality control tool for suppliers as well. In our paper, we analyzed the process of customer audits realized in Czech companies from both perspectives: a supplier´s viewpoint and customer´s viewpoint. At the end, we tried to emphasize some areas that should not be omitted during the audit process.

Keywords: Customer Audit, Quality Control, Quality Management, Product Quality, Service Quality, Process Quality.

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Authors: T. C. Manjunath, B. Bandyopadhyay

Abstract:

This paper deals with the design of a periodic output feedback controller for a flexible beam structure modeled with Timoshenko beam theory, Finite Element Method, State space methods and embedded piezoelectrics concept. The first 3 modes are considered in modeling the beam. The main objective of this work is to control the vibrations of the beam when subjected to an external force. Shear piezoelectric sensors and actuators are embedded into the top and bottom layers of a flexible aluminum beam structure, thus making it intelligent and self-adaptive. The composite beam is divided into 5 finite elements and the control actuator is placed at finite element position 1, whereas the sensor is varied from position 2 to 5, i.e., from the nearby fixed end to the free end. 4 state space SISO models are thus developed. Periodic Output Feedback (POF) Controllers are designed for the 4 SISO models of the same plant to control the flexural vibrations. The effect of placing the sensor at different locations on the beam is observed and the performance of the controller is evaluated for vibration control. Conclusions are finally drawn.

Keywords: Smart structure, Timoshenko beam theory, Periodic output feedback control, Finite Element Method, State space model, SISO, Embedded sensors and actuators, Vibration control.

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Authors: Maziar A. Sharbafi, Caro Lucas, Aida Mohammadinejad, Mostafa Yaghobi

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The Combination of path planning and path following is the main purpose of this paper. This paper describes the developed practical approach to motion control of the MRL small size robots. An intelligent controller is applied to control omni-directional robots motion in simulation and real environment respectively. The Brain Emotional Learning Based Intelligent Controller (BELBIC), based on LQR control is adopted for the omni-directional robots. The contribution of BELBIC in improving the control system performance is shown as application of the emotional learning in a real world problem. Optimizing of the control effort can be achieved in this method too. Next the implicit communication method is used to determine the high level strategies and coordination of the robots. Some simple rules besides using the environment as a memory to improve the coordination between agents make the robots' decision making system. With this simple algorithm our team manifests a desirable cooperation.

Keywords: multi-agent systems (MAS), Emotional learning, MIMO system, BELBIC, LQR, Communication via environment

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Authors: Jai Raj, Jito Vanualailai, Bibhya Sharma, Shonal Singh

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This paper proposes a solution to the motion planning and control problem of car-like mobile robots which is required to move safely to a designated target in a priori known workspace cluttered with swarm of boids exhibiting collective emergent behaviors. A generalized algorithm for target convergence and swarm avoidance is proposed that will work for any number of swarms. The control laws proposed in this paper also ensures practical stability of the system. The effectiveness of the proposed control laws are demonstrated via computer simulations of an emergent behavior.

Keywords: Swarm, practical stability, motion planning, emergent.

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Authors: Igor Astrov, Andrus Pedai

Abstract:

This paper focuses on a critical component of the situational awareness (SA), the neural control of depth flight of an autonomous underwater vehicle (AUV). Constant depth flight is a challenging but important task for AUVs to achieve high level of autonomy under adverse conditions. With the SA strategy, we proposed a multirate neural control of an AUV trajectory for a nontrivial mid-small size AUV “r2D4" stochastic model. This control system has been demonstrated and evaluated by simulation of diving maneuvers using software package Simulink. From the simulation results it can be seen that the chosen AUV model is stable in the presence of noises, and also can be concluded that the proposed research technique will be useful for fast SA of similar AUV systems in real-time search-and-rescue operations.

Keywords: Autonomous underwater vehicles, multirate systems, neurocontrollers, situational awareness.

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Authors: Richard W. Longman

Abstract:

Iterative learning control aims to achieve zero tracking error of a specific command. This is accomplished by iteratively adjusting the command given to a feedback control system, based on the tracking error observed in the previous iteration. One would like the iterations to converge to zero tracking error in spite of any error present in the model used to design the learning law. First, this need for stability robustness is discussed, and then the need for robustness of the property that the transients are well behaved. Methods of producing the needed robustness to parameter variations and to singular perturbations are presented. Then a method involving reverse time runs is given that lets the world behavior produce the ILC gains in such a way as to eliminate the need for a mathematical model. Since the real world is producing the gains, there is no issue of model error. Provided the world behaves linearly, the approach gives an ILC law with both stability robustness and good transient robustness, without the need to generate a model.

Keywords: Iterative learning control, stability robustness, monotonic convergence.

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Authors: Abolhassan Razminia, Mohammad-Ali Sadrnia

Abstract:

One of the most attractive and important field of chaos theory is control of chaos. In this paper, we try to present a simple framework for chaotic motion control using the feedback linearization method. Using this approach, we derive a strategy, which can be easily applied to the other chaotic systems. This task presents two novel results: the desired periodic orbit need not be a solution of the original dynamics and the other is the robustness of response against parameter variations. The illustrated simulations show the ability of these. In addition, by a comparison between a conventional state feedback and our proposed method it is demonstrated that the introduced technique is more efficient.

Keywords: chaos, feedback linearization, robust control, periodic motion.

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Authors: Muhammad M. A. S. Mahmoud

Abstract:

Natural gas sweetening process is a controlled process that must be done at maximum efficiency and with the highest quality. In this work, due to complexity and non-linearity of the process, the H2S gas separation and the intelligent fuzzy controller, which is used to enhance the process, are simulated in MATLAB – Simulink. New design of fuzzy control for Gas Separator is discussed in this paper. The design is based on the utilization of linear state-estimation to generate the internal knowledge-base that stores input-output pairs. The obtained input/output pairs are then used to design a feedback fuzzy controller. The proposed closed-loop fuzzy control system maintains the system asymptotically-stability while it enhances the system time response to achieve better control of the concentration of the output gas from the tower. Simulation studies are carried out to illustrate the Gas Separator system performance.

Keywords: Gas separator, gas sweetening, intelligent controller, fuzzy control.

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Authors: Igor Astrov, Mikhail Pikkov, Rein Paluoja

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

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

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Authors: S. Z. Sayed Hassen

Abstract:

The load frequency control problem of power systems has attracted a lot of attention from engineers and researchers over the years. Increasing and quickly changing load demand, coupled with the inclusion of more generators with high variability (solar and wind power generators) on the network are making power systems more difficult to regulate. Frequency changes are unavoidable but regulatory authorities require that these changes remain within a certain bound. Engineers are required to perform the tricky task of adjusting the control system to maintain the frequency within tolerated bounds. It is well known that to minimize frequency variations, a large proportional feedback gain (speed regulation constant) is desirable. However, this improvement in performance using proportional feedback comes about at the expense of a reduced stability margin and also allows some steady-state error. A conventional PI controller is then included as a secondary control loop to drive the steadystate error to zero. In this paper, we propose a robust controller to replace the conventional PI controller which guarantees performance and stability of the power system over the range of variation of the speed regulation constant. Simulation results are shown to validate the superiority of the proposed approach on a simple single-area power system model.

Keywords: Robust control, power system, integral action, minimax LQG control.

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Authors: Marco Soares dos Santos, Jorge Augusto Ferreira, Camila Nicola Boeri, Fernando Neto da Silva

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The present paper proposes high performance nonlinear force controllers for a servopneumatic real-time fatigue test machine. A CompactRIO® controller was used, being fully programmed using LabVIEW language. Fuzzy logic control algorithms were evaluated to tune the integral and derivative components in the development of hybrid controllers, namely a FLC P and a hybrid FLC PID real-time-based controllers. Their behaviours were described by using state diagrams. The main contribution is to ensure a smooth transition between control states, avoiding discrete transitions in controller outputs. Steady-state errors lower than 1.5 N were reached, without retuning the controllers. Good results were also obtained for sinusoidal tracking tasks from 1/¤Ç to 8/¤Ç Hz.

Keywords: Hybrid Fuzzy Selecting, Control, Range Controllers, Servopneumatic Fatigue System.

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Authors: Vinicius Binotte, Guilherme Baldo, Christiane Goulart, Carlos Valadão, Eliete Caldeira, Teodiano Bastos

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Socially assistive robotic has become increasingly active and it is present in therapies of people affected for several neurobehavioral conditions, such as Autism Spectrum Disorder (ASD). In fact, robots have played a significant role for positive interaction with children with ASD, by stimulating their social and cognitive skills. This work introduces a mobile socially-assistive robot, which was built for interaction with children with ASD, using non-linear control techniques for this interaction.

Keywords: Socially assistive robotics, mobile robot, autonomous control, autism.

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Authors: Wei Lifan, Zhang Huaiyu, Yang Yunbin, Li Jia

Abstract:

Through the analysis of the process digital design based on digital mockup, the fact indicates that a distributed cooperative supporting environment is the foundation conditions to adopt design approach based on DMU. Data access authorization is concerned firstly because the value and sensitivity of the data for the enterprise. The access control for administrators is often rather weak other than business user. So authors established an enhanced system to avoid the administrators accessing the engineering data by potential approach and without authorization. Thus the data security is improved.

Keywords: access control, DMU, PLM, virtual prototype.

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Authors: Nan Ding, Motoki Shino, Nobuyasu Tomokuni, Genki Murata

Abstract:

The wheelchair is the major means of transport for physically disabled people. However, it cannot overcome architectural barriers such as curbs and stairs. In this paper, the authors proposed a method to avoid falling down of a wheeled inverted pendulum type robotic wheelchair for climbing stairs. The problem of this system is that the feedback gain of the wheels cannot be set high due to modeling errors and gear backlash, which results in the movement of wheels. Therefore, the wheels slide down the stairs or collide with the side of the stairs, and finally the wheelchair falls down. To avoid falling down, the authors proposed a slider control strategy based on skyhook model in order to decrease the movement of wheels, and a rotary link control strategy based on the staircase dimensions in order to avoid collision or slide down. The effectiveness of the proposed fall avoidance control strategy was validated by ODE simulations and the prototype wheelchair.

Keywords: EPW, fall avoidance control, skyhook, wheeled inverted pendulum.

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Authors: W. Du, X. Wang, Jun Cao, H. F. Wang

Abstract:

Due to the randomness and uncertainty of wind energy, modern power systems integrating large-scale wind generation will be significantly impacted in terms of system performance and technical challenges. System inertia with high wind penetration is decreasing when conventional thermal generators are gradually replaced by wind turbines, which do not naturally contribute to inertia response. The power imbalance caused by wind power or demand fluctuations leads to the instability of system frequency. Accordingly, the need to attach the supplementary virtual inertia control to wind farms (WFs) strongly arises. When multi-wind farms are connected to the grid simultaneously, the selection of which critical WFs to install the virtual inertia control is greatly important to enhance the stability of system frequency. By building the small signal model of wind power systems considering frequency regulation, the installation locations are identified by the geometric measures of the mode observability of WFs. In addition, this paper takes the impacts of grid topology and selection of feedback control signals into consideration. Finally, simulations are conducted on a multi-wind farms power system and the results demonstrate that the designed virtual inertia control method can effectively assist the frequency regulation.

Keywords: Frequency regulation, virtual inertia control, installation locations, observability, wind farms.

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Authors: Mahdi Zolfaghari, Seyed Hossein Hosseinian, Hossein Askarian Abyaneh, Mehrdad Abedi

Abstract:

This paper presents a virtual active power filter (VAPF) using vehicle to grid (V2G) technology to maintain power quality requirements. The optimal discrete operation of the power converter of electric vehicle (EV) is based on recognizing desired switching states using the model predictive control (MPC) algorithm. A fast dynamic response, lower total harmonic distortion (THD) and good reference tracking performance are realized through the presented control strategy. The simulation results using MATLAB/Simulink validate the effectiveness of the scheme in improving power quality as well as good dynamic response in power transferring capability.

Keywords: Virtual active power filter, V2G technology, model predictive control, electric vehicle, power quality.

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Authors: Kayoko Yamamoto

Abstract:

This study focuses on an evaluation of Hokkaido which is the northernmost and largest prefecture by surface area in Japan and particularly on two points: the rivalry between all kinds of land use such as urban land and agricultural and forestry land in various cities and their surrounding areas and the possibilities for forestry biomass in areas other than those mentioned above and grasps which areas require examination of the nature of land use control and guidance through conducting land use analysis at the district level using GIS (Geographic Information Systems). The results of analysis in this study demonstrated that it is essential to divide the whole of Hokkaido into two areas: those within delineated city planning areas and those outside of delineated city planning areas and to conduct an evaluation of each land use control. In delineated urban areas, particularly urban areas, it is essential to re-examine land use from the point of view of compact cities or smart cities along with conducting an evaluation of land use control that focuses on issues of rivalry between all kinds of land use such as urban land and agricultural and forestry land. In areas outside of delineated urban areas, it is desirable to aim to build a specific community recycling range based on forest biomass utilization by conducting an evaluation of land use control concerning the possibilities for forest biomass focusing particularly on forests within and outside of city planning areas.

Keywords: Land Use Control, Urbanization, Forestry Biomass, Geographic Information Systems (GIS), Hokkaido

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Authors: Radovan Holubek, Matus Vlasek, Peter Kostal

Abstract:

Development of intelligent assembly cell conception includes new solution kind of how to create structures of automated and flexible assembly system. The current trend of the final product quality increasing is affected by time analysis of the entire manufacturing process. The primary requirement of manufacturing is to produce as many products as soon as possible, at the lowest possible cost, but of course with the highest quality. Such requirements may be satisfied only if all the elements entering and affecting the production cycle are in a fully functional condition. These elements consist of sensory equipment and intelligent control elements that are essential for building intelligent manufacturing systems. Intelligent behavior of the system as the control system will repose on monitoring of important parameters of the system in the real time. Intelligent manufacturing system itself should be a system that can flexibly respond to changes in entering and exiting the process in interaction with the surroundings.

Keywords: Control system, intelligent manufacturing / assemble systems, manufacturing, monitoring process.

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Authors: Dong Sang Yoo

Abstract:

We consider nonlinear uncertain systems such that a  priori information of the uncertainties is not available. For such  systems, we assume that the upper bound of the uncertainties is  represented as a Fredholm integral equation of the first kind and we  propose an adaptation law that is capable of estimating the upper  bound and design a continuous robust control which renders nonlinear  uncertain systems ultimately bounded.

 

Keywords: Adaptive Control, Estimation, Fredholm Integral, Uncertain System.

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Authors: Arishai Akraudom

Abstract:

The objective of this research was to study the themes of alcoholic beverage advertisements in Thailand after the enactment of the 2008 Alcoholic Beverage Control Act. Data was collected through textual analysis of 35 television and cinema advertisements for alcoholic beverage products broadcast in Thailand. Nine themes were identified, seven of which were themes that had previously been used before the new law (i.e. power, competition, friendship, Thainess, success, romance and safety) and two of which were new themes (volunteerism and conservation) that were introduced as a form of adaptation and negotiation in response to the new law.

Keywords: Alcoholic Beverage Control Act 2008, Alcohol Advertising, Analysis of Themes, Narrative Structure, Health Communication.

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Authors: Jagdeep Singh, Prem Singh

Abstract:

Milk is considered as an essential and complete food. The present study was conducted at Milk Plant Mohali especially in reference to the procurement section where the cash inflow was maximum, with the objective to achieve higher productivity and reduce wastage of milk. In milk plant it was observed that during the month of Jan-2014 to March-2014 the average procurement of milk was Rs. 4, 19, 361 liter per month and cost of procurement of milk is Rs 35/- per liter. The total cost of procurement thereby equal to Rs. 1crore 46 lakh per month, but there was mismatch in procurementproduction of milk, which leads to an average loss of Rs. 12, 94, 405 per month. To solve the procurement-production problem Quality Control Tools like brainstorming, Flow Chart, Cause effect diagram and Pareto analysis are applied wherever applicable. With the successful implementation of Quality Control tools an average saving of Rs. 4, 59, 445 per month is done.

Keywords: Milk, Procurement-demand, quality control tools.

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