Search results for: Automatic generation control

Authors: Fangfang Meng, Shuang Cong

Abstract:

In the closed quantum system, if the control system is strongly regular and all other eigenstates are directly coupled to the target state, the control system can be asymptotically stabilized at the target eigenstate by the Lyapunov control based on the state error. However, if the control system is not strongly regular or as long as there is one eigenstate not directly coupled to the target state, the situations will become complicated. In this paper, we propose an implicit Lyapunov control method based on the state error to solve the convergence problems for these two degenerate cases. And at the same time, we expand the target state from the eigenstate to the arbitrary pure state. Especially, the proposed method is also applicable in the control system with multi-control Hamiltonians. On this basis, the convergence of the control systems is analyzed using the LaSalle invariance principle. Furthermore, the relation between the implicit Lyapunov functions of the state distance and the state error is investigated. Finally, numerical simulations are carried out to verify the effectiveness of the proposed implicit Lyapunov control method. The comparisons of the control effect using the implicit Lyapunov control method based on the state distance with that of the state error are given.

Keywords: Implicit Lyapunov control, state error, degenerate cases, convergence.

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Authors: Shiuh-Jer Huang, Su-Shean Chen, Sheam-Chyun Lin

Abstract:

Two-wheel inverted pendulum robot (TWIPR) is designed with two-hub DC motors for human riding and motion control evaluation. In order to measure the tilt angle and angular velocity of the inverted pendulum robot, accelerometer and gyroscope sensors are chosen. The mobile robot’s moving position and velocity were estimated based on DC motor built in hall sensors. The control kernel of this electric mobile robot is designed with embedded Arduino Nano microprocessor. A handle bar was designed to work as steering mechanism. The intelligent model-free fuzzy sliding mode control (FSMC) was employed as the main control algorithm for this mobile robot motion monitoring with different control purpose adjustment. The intelligent controllers were designed for balance control, and moving speed control purposes of this robot under different operation conditions and the control performance were evaluated based on experimental results.

Keywords: Balance control, speed control, intelligent controller and two wheel inverted pendulum.

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Authors: Oluseyi O. Ajayi, Ohiose D. Ohijeagbon, Mercy Ogbonnaya, Ameh Attabo

Abstract:

The study assessed the potential and economic viability of stand-alone wind systems for embedded generation, taking into account its benefits to small off-grid rural communities at 40 meteorological sites in Nigeria. A specific electric load profile was developed to accommodate communities consisting of 200 homes, a school and a community health centre. This load profile was incorporated within the distributed generation analysis producing energy in the MW range, while optimally meeting daily load demand for the rural communities. Twenty-four years (1987 to 2010) of wind speed data at a height of 10m utilized for the study were sourced from the Nigeria Meteorological Department, Oshodi. The HOMER® software optimizing tool was engaged for the feasibility study and design. Each site was suited to 3MW wind turbines in sets of five, thus 15MW was designed for each site. This design configuration was adopted in order to easily compare the distributed generation system amongst the sites to determine their relative economic viability in terms of life cycle cost, as well as levelised cost of producing energy. A net present value was estimated in terms of life cycle cost for 25 of the 40 meteorological sites. On the other hand, the remaining sites yielded a net present cost; meaning the installations at these locations were not economically viable when utilizing the present tariff regime for embedded generation in Nigeria.

Keywords: Wind speed, wind power, distributed generation, cost per kilowatt-hour, clean energy, Nigeria.

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Authors: Bo Yang, Christopher Monterola

Abstract:

Urban intersection control without the use of the traffic light has the potential to vastly improve the efficiency of the urban traffic flow. For most proposals in the literature, such lightless intersection control depends on the mass market commercialization of highly intelligent autonomous vehicles (AV), which limits the prospects of near future implementation. We present an efficient lightless intersection traffic control scheme that only requires Level 1 AV as defined by NHTSA. The technological barriers of such lightless intersection control are thus very low. Our algorithm can also accommodate a mixture of AVs and conventional vehicles. We also carry out large scale numerical analysis to illustrate the feasibility, safety and robustness, comfort level, and control efficiency of our intersection control scheme.

Keywords: Intersection control, autonomous vehicles, traffic modelling, intelligent transport system.

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Authors: Ion Miciu

Abstract:

The system is made with main distributed components: First Level: Industrial Computers placed in Control Room (monitors thermal and electrical processes based on the data provided by the second level); Second Level: PLCs which collects data from process and transmits information on the first level; also takes commands from this level which are further, passed to execution elements from third level; Third Level: field elements consisting in 3 categories: data collecting elements; data transfer elements from the third level to the second; execution elements which take commands from the second level PLCs and executes them after which transmits the confirmation of execution to them. The purpose of the automatic functioning is the optimization of the co-generative electrical energy commissioning in the national energy system and the commissioning of thermal energy to the consumers. The integrated system treats the functioning of all the equipments and devices as a whole: Gas Turbine Units (GTU); MT 20kV Medium Voltage Station (MVS); 0,4 kV Low Voltage Station (LVS); Main Hot Water Boilers (MHW); Auxiliary Hot Water Boilers (AHW); Gas Compressor Unit (GCU); Thermal Agent Circulation Pumping Unit (TPU); Water Treating Station (WTS).

Keywords: Automation System, Cogenerative Power Plant, Control, Monitoring, Real Time

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Authors: M. Almeshal, M. O. Tokhi, K. M. Goher

Abstract:

A novel design of two-wheeled robotic vehicle with moving payload is presented in this paper. A mathematical model describing the vehicle dynamics is derived and simulated in Matlab Simulink environment. Two control strategies were developed to stabilise the vehicle in the upright position. A robust Proportional- Integral-Derivative (PID) control strategy has been implemented and initially tested to measure the system performance, while the second control strategy is to use a hybrid fuzzy logic controller (FLC). The results are given on a comparative basis for the system performance in terms of disturbance rejection, control algorithms robustness as well as the control effort in terms of input torque.

Keywords: double inverted pendulum, modelling, robust control, simulation,

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Authors: N. Sozbir, M. Bulut, M.F.Oktem, A.Kahriman, A. Chaix

Abstract:

TUSAT is a prospective Turkish Communication Satellite designed for providing mainly data communication and broadcasting services through Ku-Band and C-Band channels. Thermal control is a vital issue in satellite design process. Therefore, all satellite subsystems and equipments should be maintained in the desired temperature range from launch to end of maneuvering life. The main function of the thermal control is to keep the equipments and the satellite structures in a given temperature range for various phases and operating modes of spacecraft during its lifetime. This paper describes the thermal control design which uses passive and active thermal control concepts. The active thermal control is based on heaters regulated by software via thermistors. Alternatively passive thermal control composes of heat pipes, multilayer insulation (MLI) blankets, radiators, paints and surface finishes maintaining temperature level of the overall carrier components within an acceptable value. Thermal control design is supported by thermal analysis using thermal mathematical models (TMM).

Keywords: Spacecraft thermal control, design of thermal control.

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Authors: A-Q. Nguyen. A. Amrhar, J. Zambrano, G. Brown, O.A. Yeste-Ojeda, R. Jr. Landry

Abstract:

Since the presence of Next Generation Air Transportation System (NextGen), Automatic Dependent Surveillance-Broadcast (ADS-B) has raised specific concerns related to the privacy and security, due to its vulnerable, low-level of security and limited payload. In this paper, the authors introduce and analyze the combination of Pulse Amplitude Modulation (PAM) and Phase Shift Keying (PSK) Modulation in conventional ADS-B, forming Secure ADS-B (SADS-B) avionics. In order to demonstrate the potential of this combination, Hardware-in-the-loop (HIL) simulation was used. The tests' results show that, on the one hand, SADS-B can offer five times the payload as its predecessor. This additional payload of SADS-B can be used in various applications, therefore enhancing the ability and efficiency of the current ADS-B. On the other hand, by using the extra phase modulated bits as a digital signature to authenticate ADS-B messages, SADS-B can increase the security of ADS-B, thus ensure a more secure aviation as well. More importantly, SADS-B is compatible with the current ADS-B In and Out. Hence, no significant modifications will be needed to implement this idea. As a result, SADS-B can be considered the most promising approach to enhance the capability and security of ADS-B.

Keywords: ADS-B authentication, ADS-B security, NextGen ADS-B, PSK signature, secure ADS-B.

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Authors: M. Z Md Zain, M. O. Tokhi, M. S. Alam

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This paper describes a practical approach to design and develop a hybrid learning with acceleration feedback control (HLC) scheme for input tracking and end-point vibration suppression of flexible manipulator systems. Initially, a collocated proportionalderivative (PD) control scheme using hub-angle and hub-velocity feedback is developed for control of rigid-body motion of the system. This is then extended to incorporate a further hybrid control scheme of the collocated PD control and iterative learning control with acceleration feedback using genetic algorithms (GAs) to optimize the learning parameters. Experimental results of the response of the manipulator with the control schemes are presented in the time and frequency domains. The performance of the HLC is assessed in terms of input tracking, level of vibration reduction at resonance modes and robustness with various payloads.

Keywords: Flexible manipulator, iterative learning control, vibration suppression.

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Authors: A. A. Jafari, A. M. Khoshnood, J. Roshanian

Abstract:

Attitude control of aerospace system with liquid containers may face to a problem associate with fuel sloshing. The sloshing phenomena can degrade the stability of control system and in the worst case, interaction between the attitude control system and fuel vibration leading to resonance. In this paper, a full process of nonlinear dynamic modeling of an aerospace launch vehicle with fuel sloshing is given. Then, a new control system based on model reference adaptive filter is proposed and its algorithm is extracted. This controller implemented on the main attitude control system. Finally, numerical simulation of nonlinear model and control system is carried out to examine the performance of the new controller. Results of simulations show that the inconvenient effects of the fuel sloshing by augmenting this control system are reduced and attitude control system performs, satisfactorily.

Keywords: nonlinear dynamic modeling, fuel sloshing, vibration control, model reference, adaptive filter

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Authors: M. Ovinis, D. Kerr, K. Bouazza-Marouf, M. Vloeberghs

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In this paper, algorithms for the automatic localisation of two anatomical soft tissue landmarks of the head the medial canthus (inner corner of the eye) and the tragus (a small, pointed, cartilaginous flap of the ear), in CT images are describet. These landmarks are to be used as a basis for an automated image-to-patient registration system we are developing. The landmarks are localised on a surface model extracted from CT images, based on surface curvature and a rule based system that incorporates prior knowledge of the landmark characteristics. The approach was tested on a dataset of near isotropic CT images of 95 patients. The position of the automatically localised landmarks was compared to the position of the manually localised landmarks. The average difference was 1.5 mm and 0.8 mm for the medial canthus and tragus, with a maximum difference of 4.5 mm and 2.6 mm respectively.The medial canthus and tragus can be automatically localised in CT images, with performance comparable to manual localisation

Keywords: Anatomical soft tissue landmarks, automatic localisation, Computed Tomography (CT)

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Authors: V. Gomathi, Dr. K. Ramar, A. Santhiyaku Jeevakumar

Abstract:

Facial expression analysis plays a significant role for human computer interaction. Automatic analysis of human facial expression is still a challenging problem with many applications. In this paper, we propose neuro-fuzzy based automatic facial expression recognition system to recognize the human facial expressions like happy, fear, sad, angry, disgust and surprise. Initially facial image is segmented into three regions from which the uniform Local Binary Pattern (LBP) texture features distributions are extracted and represented as a histogram descriptor. The facial expressions are recognized using Multiple Adaptive Neuro Fuzzy Inference System (MANFIS). The proposed system designed and tested with JAFFE face database. The proposed model reports 94.29% of classification accuracy.

Keywords: Adaptive neuro-fuzzy inference system, Facialexpression, Local binary pattern, Uniform Histogram

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Authors: Sara Mohtashami, Habib Rajabi Mashhadi

Abstract:

With the growth of electricity generation from gas energy gas pipeline reliability can substantially impact the electric generation. A physical disruption to pipeline or to a compressor station can interrupt the flow of gas or reduce the pressure and lead to loss of multiple gas-fired electric generators, which could dramatically reduce the supplied power and threaten the power system security. Gas pressure drops during peak loading time on pipeline system, is a common problem in network with no enough transportation capacity which limits gas transportation and causes many problem for thermal domain power systems in supplying their demand. For a feasible generation scheduling planning in networks with no sufficient gas transportation capacity, it is required to consider gas pipeline constraints in solving the optimization problem and evaluate the impacts of gas consumption in power plants on gas pipelines operating condition. This paper studies about operating of gas fired power plants in critical conditions when the demand of gas and electricity peak together. An integrated model of gas and electric model is used to consider the gas pipeline constraints in the economic dispatch problem of gas-fueled thermal generator units.

Keywords:

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Authors: Raida El Mansouri, Elhillali Kerkouche, Allaoua Chaoui

Abstract:

The Petri net tool INA is a well known tool by the Petri net community. However, it lacks a graphical environment to cerate and analyse INA models. Building a modelling tool for the design and analysis from scratch (for INA tool for example) is generally a prohibitive task. Meta-Modelling approach is useful to deal with such problems since it allows the modelling of the formalisms themselves. In this paper, we propose an approach based on the combined use of Meta-modelling and Graph Grammars to automatically generate a visual modelling tool for INA for analysis purposes. In our approach, the UML Class diagram formalism is used to define a meta-model of INA models. The meta-modelling tool ATOM3 is used to generate a visual modelling tool according to the proposed INA meta-model. We have also proposed a graph grammar to automatically generate INA description of the graphically specified Petri net models. This allows the user to avoid the errors when this description is done manually. Then the INA tool is used to perform the simulation and the analysis of the resulted INA description. Our environment is illustrated through an example.

Keywords: INA, Meta-modelling, Graph Grammars, AToM3, Automatic Code Generation.

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Authors: Rajesh Kumar, Roopali Dogra, Puneet Aggarwal

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Based on a survey conducted for second and third year students of the electrical engineering department at Maharishi Markandeshwar University, India, it was found that around 92% of students felt that it would be better to introduce a virtual environment for laboratory experiments. Hence, a need was felt to perform modern pedagogy techniques for students which consist of a virtual environment using MATLAB/Simulink. In this paper, a virtual environment for the speed control of a DC motor is performed using MATLAB/Simulink. The various speed control methods for the DC motor include the field resistance control method and armature voltage control method. The performance analysis of the DC motor is hence analyzed.

Keywords: Pedagogy techniques, speed control, virtual environment, DC motor, field control, voltage control.

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Authors: Zulkeflee Kusin, Mohamad Shanudin Zakaria

Abstract:

Hierarchical Mobile IPv6 (HMIPv6) was designed to support IP micro-mobility management in the Next Generation Networks (NGN) framework. The main design behind this protocol is the usage of Mobility Anchor Point (MAP) located at any level router of network to support hierarchical mobility management. However, the distance MAP selection in HMIPv6 causes MAP overloaded and increase frequent binding update as the network grows. Therefore, to address the issue in designing MAP selection scheme, we propose a dynamic load control mechanism integrates with a speed detection mechanism (DMS-DLC). From the experimental results we obtain that the proposed scheme gives better distribution in MAP load and increase handover speed.

Keywords: Dynamic load control, HMIPv6, Mobility AnchorPoint, MAP selection scheme

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Authors: N. Z. Azlan, H. Yamaura

Abstract:

The experimental study of position control of a light weight and small size robotic finger during non-contact motion is presented in this paper. The finger possesses fingertip pinching and self adaptive grasping capabilities, and is made of a seven bar linkage mechanism with a slider in the middle phalanx. The control system is tested under the Proportional Integral Derivative (PID) control algorithm and Recursive Least Square (RLS) based Feedback Error Learning (FEL) control scheme to overcome the uncertainties present in the plant. The experiments conducted in Matlab Simulink and xPC Target environments show that the overall control strategy is efficient in controlling the finger movement.

Keywords: Anthropomorphic finger, position control, feedback error learning, experimental study

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Authors: T. Narongrit, K-L. Areerak, K-N. Areerak

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This paper presents the comparison study of current control techniques for shunt active power filter. The hysteresis current control, the delta modulation control and the carrier-based PWM control are considered in the paper. The synchronous detection method is used to calculate the reference currents for shunt active power filter. The simulation results show that the carrier-based PWM control technique provides the minimum %THD value of the source currents compared with other comparable techniques after compensation. However, the %THD values of all three techniques can follow the IEEE std.519-1992.

Keywords: hysteresis current control, delta modulation current control, pulse width modulation control, shunt active power filter, synchronous detection.

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Authors: F.Katlane, M.S.Naceur, M.A.Loghmari

Abstract:

Automatic methods of detecting changes through satellite imaging are the object of growing interest, especially beca²use of numerous applications linked to analysis of the Earth’s surface or the environment (monitoring vegetation, updating maps, risk management, etc...). This work implemented spatial analysis techniques by using images with different spatial and spectral resolutions on different dates. The work was based on the principle of control charts in order to set the upper and lower limits beyond which a change would be noted. Later, the a contrario approach was used. This was done by testing different thresholds for which the difference calculated between two pixels was significant. Finally, labeled images were considered, giving a particularly low difference which meant that the number of “false changes” could be estimated according to a given limit.

Keywords: multi-scale, a contrario approach, significantthresholds, change detection.

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Authors: Wang Zhan-Xi, Zhang Yi-Ming, Chen Hang, Wang Gang

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Manual polishing has problems such as high labor intensity, low production efficiency and difficulty in guaranteeing the consistency of polishing quality. The use of robot polishing instead of manual polishing can effectively avoid these problems. Polishing force directly affects the quality of polishing, so accurate tracking and control of polishing force is one of the most important conditions for improving the accuracy of robot polishing. The traditional force control strategy is difficult to adapt to the strong coupling of force control and position control during the robot polishing process. Therefore, based on the analysis of force-based impedance control and position-based impedance control, this paper proposed a type of adaptive controller. Based on force feedback control of active compliance control, the controller can adaptively estimate the stiffness and position of the external environment and eliminate the steady-state force error produced by traditional impedance control. The simulation results of the model show that the adaptive controller has good adaptability to changing environmental positions and environmental stiffness, and can accurately track and control polishing force.

Keywords: robot polishing, force feedback, impedance control, adaptive control

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Authors: N. Popovich, P. Yan

Abstract:

In this paper, the process of obtaining Q and R matrices for optimal pitch aircraft control system has been described. Since the innovation of optimal control method, the determination of Q and R matrices for such system has not been fully specified. The value of Q and R for optimal pitch aircraft control application, have been simulated and calculated. The suitable results for Q and R have been observed through the performance index (PI). If the PI is small “enough", we would say the Q & R values are suitable for that certain type of optimal control system. Moreover, for the same value of PI, we could have different Q and R sets. Due to the rule-free determination of Q and R matrices, a specific method is brought to find out the rough value of Q and R referring to rather small value of PI.

Keywords: Aircraft, control, digital, optimal, Q and R matrices

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Authors: Ming-Hui Lee, Shou-Jen Hsu

Abstract:

This study presents an active vibration control technique to reduce the earthquake responses of a retained structural system. The proposed technique is a synthesis of the adaptive input estimation method (AIEM) and linear quadratic Gaussian (LQG) controller. The AIEM can estimate an unknown system input online. The LQG controller offers optimal control forces to suppress wall-structural system vibration. The numerical results show robust performance in the active vibration control technique.

Keywords: Active vibration control, AIEM, LQG, Optimal control

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Authors: Jolly Shah, S.S.Rattan, B.C.Nakra

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Automatic control of the robotic manipulator involves study of kinematics and dynamics as a major issue. This paper involves the forward and inverse kinematics of 2-DOF robotic manipulator with revolute joints. In this study the Denavit- Hartenberg (D-H) model is used to model robot links and joints. Also forward and inverse kinematics solution has been achieved using Artificial Neural Networks for 2-DOF robotic manipulator. It shows that by using artificial neural network the solution we get is faster, acceptable and has zero error.

Keywords: Artificial Neural Network, Forward Kinematics, Inverse Kinematics, Robotic Manipulator

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Authors: Toshiyuki Satoh, Hiroki Hara, Naoki Saito, Jun-ya Nagase, Norihiko Saga

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This paper addresses a control system design for a table drive system based on the disturbance observer (DOB)-based predictive functional critical control (PFCC). To empower the previously developed DOB-based PFC to handle constraints on controlled outputs, we propose to take a critical control approach. To this end, we derive the transfer function representation of the PFC controller and yield a detailed design procedure. The effectiveness of the proposed method is confirmed through an experimental evaluation.

Keywords: Critical control, disturbance observer, mechatronics, motion control, predictive functional control, table drive systems.

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Authors: Dongliang Wang, Jun Han, Dianfu Ma, Xianqi Zhao

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Avionics software is safe-critical embedded software and its architecture is evolving from traditional federated architectures to Integrated Modular Avionics (IMA) to improve resource usability. ARINC 653 (Avionics Application Standard Software Interface) is a software specification for space and time partitioning in Safety-critical avionics Real-time operating systems. Arinc653 uses two-level scheduling strategies, but current modeling tools only apply to simple problems of Arinc653 two-level scheduling, which only contain time property. In avionics industry, we are always manually allocating tasks and calculating the timing table of a real-time system to ensure it-s running as we design. In this paper we represent an automatically generating strategy which applies to the two scheduling problems with dependent constraints in Arinc653 partition run-time environment. It provides the functionality of automatic generation from the task and partition models to scheduling policy through allocating the tasks to the partitions while following the constraints, and then we design a simulating mechanism to check whether our policy is schedulable or not

Keywords: Arinc653, scheduling, task allocation, simulation.

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Authors: Gwanghee Heo, Geonhyeok Bang, Chunggil Kim, Chinok Lee

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This paper attempts to develop a wireless feedback control system as a primary step eventually toward a bio-inspired structure system where inanimate structure behaves like a life form autonomously. It is a standalone wireless control system which is supposed to measure externally caused structural responses, analyze structural state from acquired data, and take its own action on the basis of the analysis with an embedded logic. For an experimental examination of its effectiveness, we applied it on a model of two-span bridge and performed a wireless control test. Experimental tests have been conducted for comparison on both the wireless and the wired system under the conditions of Un-control, Passive-off, Passive-on, and Lyapunov control algorithm. By proving the congruence of the test result of the wireless feedback control system with the wired control system, its control performance was proven to be effective. Besides, it was found to be economical in energy consumption and also autonomous by means of a command algorithm embedded into it, which proves its basic capacity as a bio-inspired system.

Keywords: Structural vibration control, wireless system, MR damper, feedback control, embedded system.

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Authors: Geoffrey J. Blanford, Christoph Weissbart

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The prospects for the European power sector indicate that it has to almost fully decarbonize in order to reach the economy-wide target of CO₂-emission reduction. We apply the EU-REGEN model to explain the penetration of RES from an economic perspective, their spatial distribution, and the complementary role of conventional generation technologies. Furthermore, we identify economic consequences of national energy and climate targets. Our study shows that onshore wind power will be the most crucial generation technology for the future European power sector. Its geographic distribution is driven by resource quality. Gas power will be the major conventional generation technology for backing-up wind power. Moreover, a complete phase out of coal power proves to be not economically optimal. The paper demonstrates that existing national targets have a negative impact, especially on the German region with higher prices and lower revenues. The remaining regions profit are hardly affected. We encourage an EU-wide coordination on the expansion of wind power with harmonized policies. Yet, this requires profitable market structures for both, RES and conventional generation technologies.

Keywords: European decarbonization pathway, power market investment, public policies, technology choice.

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Authors: Maamar Ali Saud Al Tobi, Geraint Bevan, K. P. Ramachandran, Peter Wallace, David Harrison

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Centrifugal pumps are complex machines which can experience different types of fault. Condition monitoring can be used in centrifugal pump fault detection through vibration analysis for mechanical and hydraulic forces. Vibration analysis methods have the potential to be combined with artificial intelligence systems where an automatic diagnostic method can be approached. An automatic fault diagnosis approach could be a good option to minimize human error and to provide a precise machine fault classification. This work aims to introduce an approach to centrifugal pump fault diagnosis based on artificial intelligence and genetic algorithm systems. An overview of the future works, research methodology and proposed experimental setup is presented and discussed. The expected results and outcomes based on the experimental work are illustrated.

Keywords: Centrifugal pump setup, vibration analysis, artificial intelligence, genetic algorithm.

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Authors: Y. Areepong

Abstract:

The main goal of this paper is to study Statistical Process Control (SPC) with Exponentially Weighted Moving Average (EWMA) control chart when observations are serially-correlated. The characteristic of control chart is Average Run Length (ARL) which is the average number of samples taken before an action signal is given. Ideally, an acceptable ARL of in-control process should be enough large, so-called (ARL₀). Otherwise it should be small when the process is out-of-control, so-called Average of Delay Time (ARL₁) or a mean of true alarm. We find explicit formulas of ARL for EWMA control chart for Seasonal Autoregressive and Moving Average processes (SARMA) with Exponential white noise. The results of ARL obtained from explicit formula and Integral equation are in good agreement. In particular, this formulas for evaluating (ARL₀) and (ARL₁) be able to get a set of optimal parameters which depend on smoothing parameter (λ) and width of control limit (H) for designing EWMA chart with minimum of (ARL₁).

Keywords: Average Run Length1, Optimal parameters, Exponentially Weighted Moving Average (EWMA) control chart.

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Authors: Ching-Shoei Chiang, Sheng-Hsin Tsai, James Chen

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The PH curve can be constructed by given parameters, but the shape of the curve is not so easy to image from the value of the parameters. On the contract, Bézier curve can be constructed by the control polygon, and from the control polygon, we can image the figure of the curve. In this paper, we want to use the hodograph of Bézier curve to construct PH curve by selecting part of the control vectors, and produce other control vectors, so the property of PH curve exists.

Keywords: PH curve, hodograph, Bézier curve.

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