Search results for: Robust Stability.

Authors: Randhir Singh Baghel, Joydip Dhar, Renu Jain

Abstract:

In this paper, for the understanding of the phytoplankton dynamics in marine ecosystem, a susceptible and an infected class of phytoplankton population is considered in spatiotemporal domain. Here, the susceptible phytoplankton is growing logistically and the growth of infected phytoplankton is due to the instantaneous Holling type-II infection response function. The dynamics are studied in terms of the local and global stabilities for the system and further explore the possibility of Hopf -bifurcation, taking the half saturation period as (i.e., ) the bifurcation parameter in temporal domain. It is also observe that the reaction diffusion system exhibits spatiotemporal chaos and pattern formation in phytoplankton dynamics, which is particularly important role play for the spatially extended phytoplankton system. Also the effect of the diffusion coefficient on the spatial system for both one and two dimensional case is obtained. Furthermore, we explore the higher-order stability analysis of the spatial phytoplankton system for both linear and no-linear system. Finally, few numerical simulations are carried out for pattern formation.

Keywords: Phytoplankton dynamics, Reaction-diffusion system, Local stability, Hopf-bifurcation, Global stability, Chaos, Pattern Formation, Higher-order stability analysis.

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Authors: M. Ahmadnezhad, M. Soltanpour

Abstract:

Electrohydraulic servo system have been used in industry in a wide number of applications. Its dynamics are highly nonlinear and also have large extent of model uncertainties and external disturbances. In this paper, a robust back-stepping control (RBSC) scheme is proposed to overcome the problem of disturbances and system uncertainties effectively and to improve the tracking performance of EHS systems. In order to implement the proposed control scheme, the system uncertainties in EHS systems are considered as total leakage coefficient and effective oil volume. In addition, in order to obtain the virtual controls for stabilizing system, the update rule for the system uncertainty term is induced by the Lyapunov control function (LCF). To verify the performance and robustness of the proposed control system, computer simulation of the proposed control system using Matlab/Simulink Software is executed. From the computer simulation, it was found that the RBSC system produces the desired tracking performance and has robustness to the disturbances and system uncertainties of EHS systems.

Keywords: Electro hydraulic servo system, back-stepping control, robust back-stepping control, Lyapunov redesign

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Authors: M. Ahmadnezhad, M. Soltanpour

Abstract:

Electrohydraulic servo system have been used in industry in a wide number of applications. Its dynamics are highly nonlinear and also have large extent of model uncertainties and external disturbances. In this paper, a robust back-stepping control (RBSC) scheme is proposed to overcome the problem of disturbances and system uncertainties effectively and to improve the tracking performance of EHS systems. In order to implement the proposed control scheme, the system uncertainties in EHS systems are considered as total leakage coefficient and effective oil volume. In addition, in order to obtain the virtual controls for stabilizing system, the update rule for the system uncertainty term is induced by the Lyapunov control function (LCF). To verify the performance and robustness of the proposed control system, computer simulation of the proposed control system using Matlab/Simulink Software is executed. From the computer simulation, it was found that the RBSC system produces the desired tracking performance and has robustness to the disturbances and system uncertainties of EHS systems.

Keywords: Electro hydraulic servo system, back-stepping control, robust back-stepping control, Lyapunov redesign.

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Authors: Mehrdad Ahmadi Kamarposhti, Mostafa Alinezhad

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One of the major causes of voltage instability is the reactive power limit of the system. Improving the system's reactive power handling capacity via Flexible AC transmission System (FACTS) devices is a remedy for prevention of voltage instability and hence voltage collapse. In this paper, the effects of SVC and STATCOM in Static Voltage Stability Margin Enhancement will be studied. AC and DC representations of SVC and STATCOM are used in the continuation power flow process in static voltage stability study. The IEEE-14 bus system is simulated to test the increasing loadability. It is found that these controllers significantly increase the loadability margin of power systems.

Keywords: SVC, STATCOM, Voltage Collapse, Maximum Loading Point.

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Authors: Daiming Wang

Abstract:

In this paper, by using Mawhin-s continuation theorem of coincidence degree and a method based on delay differential inequality, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of cellular neural networks with distributed delays and impulses on time scales. The results of this paper generalized previously known results.

Keywords: Periodic solutions, global exponential stability, coincidence degree, M-matrix.

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Authors: Fahim Kahlouche, Alaoua Bouaicha, Sihem Chaîbeddra, Sid-Ali Rafa, Abdelhamid Benouali

Abstract:

A designing of a structure requires its realization on rough or sloping ground. Besides the problem of the stability of the landslide, the behavior of the foundations that are bearing the structure is influenced by the destabilizing effect of the ground’s slope. This article focuses on the analysis of the slope stability exposed to loading by introducing the different factors influencing the slope’s behavior on the one hand, and on the influence of this slope on the foundation’s behavior on the other hand. This study is about the elastoplastic modelization using FLAC 2D. This software is based on the finite difference method, which is one of the older methods of numeric resolution of differential equations system with initial and boundary conditions. It was developed for the geotechnical simulation calculation. The aim of this simulation is to demonstrate the notable effect of shear modulus « G », cohesion « C », inclination angle (edge) « β », and distance between the foundation and the head of the slope on the stability of the slope as well as the stability of the foundation. In our simulation, the slope is constituted by homogenous ground. The foundation is considered as rigid/hard; therefore, the loading is made by the application of the vertical strengths on the nodes which represent the contact between the foundation and the ground. 

Keywords: Slope, shallow foundation, numeric method, FLAC 2D.

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Authors: S. Veera Ragavan, V. Ganapathy

Abstract:

Many environment specific methods and systems for Robot Navigation exist. However vast strides in the evolution of navigation technologies and system techniques create the need for a general unified framework that is scalable, modular and dynamic. In this paper a Unified Framework for a Robust Conflict-free Robot Navigation System that can be used for either a structured or unstructured and indoor or outdoor environments has been proposed. The fundamental design aspects and implementation issues encountered during the development of the module are discussed. The results of the deployment of three major peripheral modules of the framework namely the GSM based communication module, GIS Module and GPS module are reported in this paper.

Keywords: Localization, Sensor Fusion, Mapping, GIS, GPS, and Autonomous Mobile Robot Navigation.

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Authors: Cor M. Rops, Giaco C. Oosterbaan, Cees W.M. v/d Geld

Abstract:

Equipment miniaturisation offers several opportunities such as an increased surface-to-volume ratio and higher heat transfer coefficients. However, moving towards small-diameter channels demands extra attention to fouling, reliability and stable operation of the system. The present investigation explores possibilities to enhance the stability of the once-through micro evaporator by reducing its flow boiling induced pressure fluctuations. Experimental comparison shows that the measured reduction factor approaches a theoretically derived value. Pressure fluctuations are reduced by a factor of ten in the solid conical channel and a factor of 15 in the porous conical channel. This presumably leads to less backflow and therefore to a better flow control.

Keywords: Flow boiling, Operation stability, Microfluidics, Microchannels.

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Authors: J.H. Park, S. Lakshmanan, H.Y. Jung, S.M. Lee

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This paper is concerned with the delay-distributiondependent stability criteria for bidirectional associative memory (BAM) neural networks with time-varying delays. Based on the Lyapunov-Krasovskii functional and stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is derived to achieve the globally asymptotically mean square stable of the considered BAM neural networks. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, a numerical example and its simulation is given to demonstrate the usefulness and effectiveness of the proposed results.

Keywords: BAM neural networks, Probabilistic time-varying delays, Stability criteria.

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Authors: Saeed Safari Dolatabad, Rajab Choukan

Abstract:

Selection of maize (Zea mays) hybrids with wide adaptability across diverse farming environments is important, prior to recommending them to achieve a high rate of hybrid adoption. Grain yield of 14 maize hybrids, tested in a randomized completeblock design with four replicates across 22 environments in Iran, was analyzed using site regression (SREG) stability model. The biplot technique facilitates a visual evaluation of superior genotypes, which is useful for cultivar recommendation and mega-environment identification. The objectives of this study were (i) identification of suitable hybrids with both high mean performance and high stability (ii) to determine mega-environments for maize production in Iran. Biplot analysis identifies two mega-environments in this study. The first mega-environments included KRM, KSH, MGN, DZF A, KRJ, DRB, DZF B, SHZ B, and KHM, where G10 hybrid was the best performing hybrid. The second mega-environment included ESF B, ESF A, and SHZ A, where G4 hybrid was the best hybrid. According to the ideal-hybrid biplot, G10 hybrid was better than all other hybrids, followed by the G1 and G3 hybrids. These hybrids were identified as best hybrids that have high grain yield and high yield stability. GGE biplot analysis provided a framework for identifying the target testing locations that discriminates genotypes that are high yielding and stable.

Keywords: Zea mays L, GGE biplot, Multi-environment trials, Yield stability.

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Authors: M. Sedighizadeh, A. Rezazadeh

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A method has been developed for preparing load models for power flow and stability. The load modeling (LOADMOD) computer software transforms data on load class mix, composition, and characteristics into the from required for commonly–used power flow and transient stability simulation programs. Typical default data have been developed for load composition and characteristics. This paper defines LOADMOD software and describes the dynamic and static load modeling techniques used in this software and results of initial testing for BAKHTAR power system.

Keywords: Load Modelling, Static, Power Flow.

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Authors: Nurhani Kasuan, Zakariah Yusuf, Mohd Nasir Taib, Mohd Hezri Fazalul Rahiman, Nazurah Tajuddin, Mohd Azri Abdul Aziz

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This paper presents a hybrid fuzzy-PD plus PID (HFPP) controller and its application to steam distillation process for essential oil extraction system. Steam temperature is one of the most significant parameters that can influence the composition of essential oil yield. Due to parameter variations and changes in operation conditions during distillation, a robust steam temperature controller becomes nontrivial to avoid the degradation of essential oil quality. Initially, the PRBS input is triggered to the system and output of steam temperature is modeled using ARX model structure. The parameter estimation and tuning method is adopted by simulation using HFPP controller scheme. The effectiveness and robustness of proposed controller technique is validated by real time implementation to the system. The performance of HFPP using 25 and 49 fuzzy rules is compared. The experimental result demonstrates the proposed HFPP using 49 fuzzy rules achieves a better, consistent and robust controller compared to PID when considering the test on tracking the set point and the effects due to disturbance.

Keywords: Fuzzy Logic controller, steam temperature, steam distillation, real time control.

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Authors: Liqiong Liu, Shouming Zhong

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In this paper, the finite-time stabilization of a class of multi-state time delay of fractional-order system is proposed. First, we define finite-time stability with the fractional-order system. Second, by using Generalized Gronwall's approach and the methods of the inequality, we get some conditions of finite-time stability for the fractional system with multi-state delay. Finally, a numerical example is given to illustrate the result.

Keywords: Finite-time stabilization, fractional-order system, Gronwall inequality.

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

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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: Omid Borazjani, Alireza Rajabi, Mojtaba Saeedimoghadam, Khodakhast Isapour

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High Voltage Direct Current (HVDC) power transmission is employed to move large amounts of electric power. There are several possibilities to enhance the transient stability in a power system. One adequate option is by using the high controllability of the HVDC if HVDC is available in the system. This paper presents a control technique for HVDC to enhance the transient stability. The strategy controls the power through the HVDC to help make the system more transient stable during disturbances. Loss of synchronism is prevented by quickly producing sufficient decelerating energy to counteract accelerating energy gained during. In this study, the power flow in the HVDC link is modulated with the addition of an auxiliary signal to the current reference of the rectifier firing angle controller. This modulation control signal is derived from speed deviation signal of the generator utilizing a PD controller; the utilization of a PD controller is suitable because it has the property of fast response. The effectiveness of the proposed controller is demonstrated with a SMIB test system.

Keywords: HVDC, SMIB, Stability, Power System.

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Authors: Nurzaki Ikhsan, Ahmad Saifizul Abdullah, Rahizar Ramli

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One of the functions of the commercial heavy vehicle is to safely and efficiently transport goods and people. Due to its size and carrying capacity, it is important to study the vehicle dynamic stability during cornering. Study has shown that there are a number of overloaded heavy vehicles or permissible Gross Vehicle Weight (GVW) violations recorded at selected areas in Malaysia assigned by its type and category. Thus, the objective of this study is to investigate the correlation and effect of the GVW on heavy vehicle stability during cornering event using simulation. Various selected heavy vehicle types and category are simulated using IPG/Truck Maker® with different GVW and road condition (coefficient of friction of road surface), while the speed, driver characteristic, center of gravity of load and road geometry are constant. Based on the analysis, the relationship between GVW and lateral acceleration were established. As expected, on the same value of coefficient of friction, the maximum lateral acceleration would be increased as the GVW increases.

Keywords: Heavy Vehicle, Road Safety, Vehicle Stability, Lateral Acceleration, Gross Vehicle Weight.

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Authors: Xinhua Zhang, Kelin Li

Abstract:

In this paper, the problem of stability analysis for a class of impulsive stochastic fuzzy neural networks with timevarying delays and reaction-diffusion is considered. By utilizing suitable Lyapunov-Krasovskii funcational, the inequality technique and stochastic analysis technique, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive stochastic fuzzy cellular neural networks with time-varying delays and diffusion are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of fuzzy neural networks. An example is given to show the effectiveness of the obtained results.

Keywords: Exponential stability, stochastic fuzzy cellular neural networks, time-varying delays, impulses, reaction-diffusion terms.

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Authors: Chih-Hui Chiu, Chun-Hsien Lin

Abstract:

In this study, a robust intelligent backstepping tracking control (RIBTC) system combined with adaptive output recurrent cerebellar model articulation control (AORCMAC) and H∞ control technique is proposed for wheeled inverted pendulums (WIPs) real-time control with exact system dynamics unknown. Moreover, a robust H∞ controller is designed to attenuate the effect of the residual approximation errors and external disturbances with desired attenuation level. The experimental results indicate that the WIPs can stand upright stably when using the proposed RIBTC.

Keywords: Wheeled inverted pendulum, backsteppingtracking control, H∞ control, adaptive output recurrentcerebellar model articulation control.

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Authors: Xiang Zhang, Daohong Yang, Ziyuan Wu, Lei Li, Wanting Zhou

Abstract:

Visual Simultaneous Localization and Mapping (VSLAM) uses cameras to gather information in unknown environments to achieve simultaneous localization and mapping of the environment. This technology has a wide range of applications in autonomous driving, virtual reality, and other related fields. Currently, the research advancements related to VSLAM can maintain high accuracy in static environments. But in dynamic environments, the presence of moving objects in the scene can reduce the stability of the VSLAM system, leading to inaccurate localization and mapping, or even system failure. In this paper, a robust VSLAM method was proposed to effectively address the challenges in dynamic environments. We proposed a dynamic region removal scheme based on a semantic segmentation neural network and geometric constraints. Firstly, a semantic segmentation neural network is used to extract the prior active motion region, prior static region, and prior passive motion region in the environment. Then, the lightweight frame tracking module initializes the transform pose between the previous frame and the current frame on the prior static region. A motion consistency detection module based on multi-view geometry and scene flow is used to divide the environment into static regions and dynamic regions. Thus, the dynamic object region was successfully eliminated. Finally, only the static region is used for tracking thread. Our research is based on the ORBSLAM3 system, which is one of the most effective VSLAM systems available. We evaluated our method on the TUM RGB-D benchmark and the results demonstrate that the proposed VSLAM method improves the accuracy of the original ORBSLAM3 by 70%˜98.5% under a high dynamic environment.

Keywords: Dynamic scene, dynamic visual SLAM, semantic segmentation, scene flow, VSLAM.

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Authors: Abdelhakam A. Noreldien, Sakhr B. Abudarag, Muslim S. Eltoum, Salih O. Osman

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This paper presents an analytical study of Small Unmanned Aerial Vehicle (SUAV) dynamic stability derivatives. Simulating SUAV dynamics and analyzing its behavior at the earliest design stages is too important and more efficient design aspect. The approach suggested in this paper is using the wind tunnel experiment to collect the aerodynamic data and get the dynamic stability derivatives. AutoCAD Software was used to draw the case study (wildlife surveillance SUAV). The SUAV is scaled down to be 0.25% of the real SUAV dimensions and converted to a wind tunnel model. The model was tested in three different speeds for three different attitudes which are; pitch, roll and yaw. The wind tunnel results were then used to determine the case study stability derivative values, and hence it used to calculate the roots of the characteristic equation for both longitudinal and lateral motions. Finally, the characteristic equation roots were found and discussed in all possible cases.

Keywords: Model, simulating, SUAV, wind tunnel.

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Authors: S. Yaman, S. Rostami

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In this study, a black box modeling of the coupled-tank system is obtained by using fuzzy sets. The derived model is tested via adaptive neuro fuzzy inference system (ANFIS). In order to achieve a better control performance, the parameters of three different controller types, classical proportional integral controller (PID), fuzzy PID and function tuner method, are tuned by one of the evolutionary computation method, genetic algorithm. All tuned controllers are applied to the fuzzy model of the coupled-tank experimental setup and analyzed under the different reference input values. According to the results, it is seen that function tuner method demonstrates better robust control performance and guarantees the closed loop stability.

Keywords: Function tuner method, fuzzy modeling, fuzzy PID controller, genetic algorithm.

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Authors: Beata Jackowska-Zduniak

Abstract:

We formulate and analyze a mathematical model describing dynamics of the hypothalamus-pituitary-thyroid homoeostatic mechanism in endocrine system. We introduce to this system two types of couplings and delay. In our model, feedback controls the secretion of thyroid hormones and delay reflects time lags required for transportation of the hormones. The influence of delayed feedback on the stability behaviour of the system is discussed. Analytical results are illustrated by numerical examples of the model dynamics. This system of equations describes normal activity of the thyroid and also a couple of types of malfunctions (e.g. hyperthyroidism).

Keywords: Mathematical modeling, ordinary differential equations, endocrine system, stability analysis.

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Authors: Anuar Ishak

Abstract:

The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: Dual solutions, heat transfer, mixed convection, stability analysis.

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Authors: Sidshchadhaa Aumted, Shuhei Shiina, Hiroshi Takami

Abstract:

In this paper, we propose an advanced ILQ control for the buck-converter via two-degrees of freedom servo-system. Our presented strategy is based on Inverse Linear Quadratic (ILQ) servo-system controller without solving Riccati-s equation directly. The optimal controller of the current and voltage control system is designed. The stability and robust control are analyzed. A conscious and persistent effort has been made to improve ILQ control via two-degrees of freedom guarantees the optimal gains on the basis of polynomial pole assignment, which our results of the proposed strategy shows that the advanced ILQ control can be controlled independently the step response and the disturbance response by appending a feed-forward compensator.

Keywords: Optimal voltage control, inverse LQ design method, second order polynomial, two-degrees of freedom.

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Authors: M. Sallam, A. Ramadan, M. Fanni, M. Abdellatif

Abstract:

Time delay in bilateral teleoperation system was introduced as a sufficient reason to make the system unstable or certainly degrade the system performance. In this paper, simulations and experimental results of implementing p-like control scheme, under different ranges of variable time delay, will be presented to verify a certain criteria, which guarantee the system stability and position tracking. The system consists of two Phantom premium 1.5A devices. One of them acts as a master and the other acts as a slave. The study includes deriving the Phantom kinematic and dynamic model, establishing the link between the two Phantoms over Simulink in Matlab, and verifying the stability criteria with simulations and real experiments.

Keywords: bilateral teleoperation, Phantom premium 1.5, varying time delay

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Authors: D. Bala Bhaskar

Abstract:

An algorithm is proposed for the order reduction of large scale linear dynamic multi variable systems where the reduced order model denominator is obtained by using Stability equation method and numerator coefficients are obtained by using SRAM. The proposed algorithm produces a lower order model for an original stable high order multivariable system. The reduction procedure is easy to understand, efficient and computer oriented. To highlight the advantages of the approach, the algorithm is illustrated with the help of a numerical example and the results are compared with the other existing techniques in literature.

Keywords: Multi variable systems, order reduction, stability equation method, SRAM, time domain characteristics, ISE.

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Authors: David Jones, Richard McWilliam, Alan Purvis

Abstract:

Morphogenesis is the process that underpins the selforganised development and regeneration of biological systems. The ability to mimick morphogenesis in artificial systems has great potential for many engineering applications, including production of biological tissue, design of robust electronic systems and the co-ordination of parallel computing. Previous attempts to mimick these complex dynamics within artificial systems have relied upon the use of evolutionary algorithms that have limited their size and complexity. This paper will present some insight into the underlying dynamics of morphogenesis, then show how to, without the assistance of evolutionary algorithms, design cellular architectures that converge to complex patterns.

Keywords: Morphogenesis, regeneration, robustness, convergence, cellular automata.

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Authors: Hicham Serhoud, Djilani Benattous

Abstract:

In this paper present a sensorless maximum wind power extraction for variable speed constant frequency (VSCF) wind power generation systems with a doubly-fed induction generators (DFIG), to ensure stability and to impose the ideal feedback control solution despite of model uncertainties , using the principles of an active and reactive power controller (DPC) a robust sliding mode power control has been proposed to guarantees fast response times and precise control actions for control the active and reactive power independently. The simulation results in MATLAB/Simulink platform confirmed the good dynamic performance of power control approach for DFIGbased variable speed wind turbines.

Keywords: Doubly fed induction generator , sliding modecontrol, maximal wind energy capture, MRAS estimator

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Authors: Nor Hayati Ibrahim, Shamini Nair Achudan

Abstract:

This study was conducted in order to determine the physical properties and stability of mayonnaise-like emulsions as affected by modified yam starches. Native yam starch was modified via pre-gelatinization and cross-linking phosphorylation procedures. The emulsions (50% oil dispersed phase) were prepared with 0.3% native potato, native yam, pre-gelatinized yam and cross-linking phosphorylation yam starches. The droplet size of surface weighted mean diameter was found to be significantly (p < 0.05) lower in the sample with cross-linking phosphorylation yam starch as compared to other samples. Moreover, the viscosity of the sample with pregelatinized yam starch was observed to be higher than that of other samples. The phase separation stability was low in the freshly prepared and stored (45 days, 5°C) emulsions containing native yam starch. This study thus generally suggested that modified yam starches were more suitable (i.e. better physical properties and stability) to be used as stabilizers in a similar system i.e. light mayonnaises, rather than a native yam starch.

Keywords: Oil-in-water emulsions, low-fat mayonnaises, modified yam starches, droplet size distribution, viscosity.

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Authors: Dyah E. Herwindiati

Abstract:

A clustering is process to identify a homogeneous groups of object called as cluster. Clustering is one interesting topic on data mining. A group or class behaves similarly characteristics. This paper discusses a robust clustering process for data images with two reduction dimension approaches; i.e. the two dimensional principal component analysis (2DPCA) and principal component analysis (PCA). A standard approach to overcome this problem is dimension reduction, which transforms a high-dimensional data into a lower-dimensional space with limited loss of information. One of the most common forms of dimensionality reduction is the principal components analysis (PCA). The 2DPCA is often called a variant of principal component (PCA), the image matrices were directly treated as 2D matrices; they do not need to be transformed into a vector so that the covariance matrix of image can be constructed directly using the original image matrices. The decomposed classical covariance matrix is very sensitive to outlying observations. The objective of paper is to compare the performance of robust minimizing vector variance (MVV) in the two dimensional projection PCA (2DPCA) and the PCA for clustering on an arbitrary data image when outliers are hiden in the data set. The simulation aspects of robustness and the illustration of clustering images are discussed in the end of paper

Keywords: Breakdown point, Consistency, 2DPCA, PCA, Outlier, Vector Variance

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