Search results for: Stabilization processes

Authors: Li Jie, Zhang Wei

Abstract:

In this paper, the problem of posture stabilization for a kinematic model of differential drive robots is studied. A more complex model of the kinematics of differential drive robots is used for the design of stabilizing control. This model is formulated in terms of the physical parameters of the system such as the radius of the wheels, and velocity of the wheels are the control inputs of it. In this paper, the framework of Lyapunov-based control design has been used to solve posture stabilization problem for the comprehensive model of differential drive robots. The results of the simulations show that the devised controller successfully solves the posture regulation problem. Finally, robustness and performance of the controller have been studied under system parameter uncertainty.

Keywords: Differential drive robots, nonlinear control, Lyapunov-based control design, posture regulation.

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Authors: A. Hasanpour, M. Farhadi, K.Sedighi, H.R.Ashorynejad

Abstract:

A numerical study of flow in a horizontally channel partially filled with a porous screen with non-uniform inlet has been performed by lattice Boltzmann method (LBM). The flow in porous layer has been simulated by the Brinkman-Forchheimer model. Numerical solutions have been obtained for variable porosity models and the effects of Darcy number and porosity have been studied in detail. It is found that the flow stabilization is reliant on the Darcy number. Also the results show that the stabilization of flow field and heat transfer is depended to Darcy number. Distribution of stream field becomes more stable by decreasing Darcy number. Results illustrate that the effect of variable porosity is significant just in the region of the solid boundary. In addition, difference between constant and variable porosity models is decreased by decreasing the Darcy number.

Keywords: Lattice Boltzmann Method, Porous Media, Variable Porosity, Flow Stabilization

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Authors: Attitude Stabilization of Satellites Using Random Dither Quantization

Abstract:

Recently, the effectiveness of random dither quantization method for linear feedback control systems has been shown in several papers. However, the random dither quantization method has not yet been applied to nonlinear feedback control systems. The objective of this paper is to verify the effectiveness of random dither quantization method for nonlinear feedback control systems. For this purpose, we consider the attitude stabilization problem of satellites using discrete-level actuators. Namely, this paper provides a control method based on the random dither quantization method for stabilizing the attitude of satellites using discrete-level actuators.

Keywords: Quantized control, nonlinear systems, random dither quantization.

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Authors: Sameh A. S. Alariqi

Abstract:

Food is widely packaged with plastic materials to prevent microbial contamination and spoilage. Ionizing radiation is widely used to sterilize the food-packaging materials. Sterilization by γ-radiation causes degradation such as embrittlement, stiffening, softening, discoloration, odour generation, and decrease in molecular weight. Many antioxidants can prevent γ-degradation but most of them are toxic. The migration of antioxidants to its environment gives rise to major concerns in case of food packaging plastics. In this attempt, we have aimed to utilize synergistic mixtures of stabilizers which are approved for food-contact applications. Ethylene-propylene-diene terpolymer has been melt-mixed with hindered amine stabilizers (HAS), phenolic antioxidants and organophosphites (hydroperoxide decomposer). Results were discussed by comparing the stabilizing efficiency of mixtures with and without phenol system. Among phenol containing systems where we mostly observed discoloration due to the oxidation of hindered phenol, the combination of secondary HAS, tertiary HAS, organo-phosphite and hindered phenol exhibited improved stabilization efficiency than single or binary additive systems. The mixture of secondary HAS and tertiary HAS, has shown antagonistic effect of stabilization. However, the combination of organo-phosphite with secondary HAS, tertiary HAS and phenol antioxidants have been found to give synergistic even at higher doses of Gamma-irradiation. The effects have been explained through the interaction between the stabilizers. After γ-irradiation, the consumption of oligomeric stabilizer significantly depends on the components of stabilization mixture. The effect of the organo-phosphite antioxidant on the overall stability has been discussed.

Keywords: Ethylene-propylene-diene terpolymer, Synergistic mixtures, Gamma-sterilization and stabilization.

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Authors: Safae El Alaoui, Mohamed Ouzahra

Abstract:

In this work, we investigate the exponential stability of a linear system described by x˙ (t) = Ax(t) − ρBx(t). Here, A generates a semigroup S(t) on a Hilbert space, the operator B is supposed to be of Desch-Schappacher type, which makes the investigation more interesting in many applications. The case of Miyadera-Voigt perturbations is also considered. Sufficient conditions are formulated in terms of admissibility and observability inequalities and the approach is based on some energy estimates. Finally, the obtained results are applied to prove the uniform exponential stabilization of bilinear partial differential equations.

Keywords: Exponential stabilization, unbounded operator, Desch-Schappacher, Miyadera-Voigt operator.

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Authors: Brahim Brahmi, Mohammed Hamza Laraki, Mohammad Habibur Rahman, Islam M. Rasedul, M. Assad Uz-Zaman

Abstract:

The humanoid robot, specifically the NAO robot must be able to provide a highly dynamic performance on the soccer field. Maintaining the balance of the humanoid robot during the required motion is considered as one of a challenging problems especially when the robot is subject to external disturbances, as contact with other robots. In this paper, a dynamic controller is proposed in order to ensure a robust walking (stabilization) and to improve the dynamic balance of the robot during its contact with the environment (external disturbances). The generation of the trajectory of the center of mass (CoM) is done by a model predictive controller (MPC) conjoined with zero moment point (ZMP) technique. Taking into account the properties of the rotational dynamics of the whole-body system, a modified previous control mixed with feedback control is employed to manage the angular momentum and the CoM’s acceleration, respectively. This latter is dedicated to provide a robust gait of the robot in the presence of the external disturbances. Simulation results are presented to show the feasibility of the proposed strategy.

Keywords: Preview control, walking, stabilization, humanoid robot.

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Authors: Mahdi Yaghobi, Mohammad Haeri

Abstract:

The current methods of predictive controllers are utilized for those processes in which the rate of output variations is not high. For such processes, therefore, stability can be achieved by implementing the constrained predictive controller or applying infinite prediction horizon. When the rate of the output growth is high (e.g. for unstable nonminimum phase process) the stabilization seems to be problematic. In order to avoid this, it is suggested to change the method in the way that: first, the prediction error growth should be decreased at the early stage of the prediction horizon, and second, the rate of the error variation should be penalized. The growth of the error is decreased through adjusting its weighting coefficients in the cost function. Reduction in the error variation is possible by adding the first order derivate of the error into the cost function. By studying different examples it is shown that using these two remedies together, the closed-loop stability of unstable nonminimum phase process can be achieved.

Keywords: GPC, Stability, Varying Weighting Coefficients.

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Authors: Ju H. Park, S.M. Lee

Abstract:

In this paper, we propose a robust controller design method for discrete-time systems with sector-bounded nonlinearities and time-varying delay. Based on the Lyapunov theory, delaydependent stabilization criteria are obtained in terms of linear matrix inequalities (LMIs) by constructing the new Lyapunov-Krasovskii functional and using some inequalities. A robust state feedback controller is designed by LMI framework and a reciprocally convex combination technique. The effectiveness of the proposed method is verified throughout a numerical example.

Keywords: Lur'e systems, Time-delay, Stabilization, LMIs.

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Authors: Guilhem Baccialone, Nicolas Delaunay, Juan-Diego Gonzales, Céline Leclercq, Adrien Leroux, Santa Pallier

Abstract:

This paper presents the software conception of a quadrotor UAV, named SKYWATCHER, which is able to follow a target. This capacity can at a long turn time permit to follow another drone and combine their performance in order to military missions for example.

From a low-cost architecture constructed by five students we implemented a software and added a camera to create a visual servoing. This project demonstrates the possibility to associate the technology of stabilization and the technology of visual enslavement.

Keywords: Quadrotor, visual servoing, student project, image processing, Unmanned Aerial Vehicles, stabilization.

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Authors: Madihah Mohd Saudi, Andrea J Cullen, Mike E Woodward

Abstract:

This paper presents a new STAKCERT KDD processes for worm detection. The enhancement introduced in the data-preprocessing resulted in the formation of a new STAKCERT model for worm detection. In this paper we explained in detail how all the processes involved in the STAKCERT KDD processes are applied within the STAKCERT model for worm detection. Based on the experiment conducted, the STAKCERT model yielded a 98.13% accuracy rate for worm detection by integrating the STAKCERT KDD processes.

Keywords: data mining, incident response, KDD processes, security metrics and worm detection.

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Authors: A. Thabet, G. B. H. Frej, M. Boutayeb

Abstract:

This paper presents a design of dynamic feedback control based on observer for a class of large scale Lipschitz nonlinear systems. The use of Differential Mean Value Theorem (DMVT) is to introduce a general condition on the nonlinear functions. To ensure asymptotic stability, sufficient conditions are expressed in terms of linear matrix inequalities (LMIs). High performances are shown through real time implementation with ARDUINO Duemilanove board to the one-link flexible joint robot.

Keywords: Feedback stabilization, DMVT, Lipschitz nonlinear systems, nonlinear observer, real time implementation.

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Authors: Lianglin Xiong, Shouming Zhong, Mao Ye

Abstract:

This paper addresses the stabilization issues for a class of uncertain switched neutral systems with nonlinear perturbations. Based on new classes of piecewise Lyapunov functionals, the stability assumption on all the main operators or the convex combination of coefficient matrices is avoid, and a new switching rule is introduced to stabilize the neutral systems. The switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. Finally, three simulation examples are given to demonstrate the significant improvements over the existing results.

Keywords: Switched neutral system, piecewise Lyapunov functional, nonlinear perturbation, Lyapunov-Metzler linear matrix inequality.

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Authors: A. S. Soğancı

Abstract:

Expansive soils are often encountered in many parts of the world, especially in arid and semi-arid fields. Such kind of soils, generally including active clay minerals in low water content, enlarge in volume by absorbing the water through the surface and cause a great harm to the light structures such as channel coating, roads and airports. The expansive soils were encountered on the path of Apa-Hotamış conveyance channel belonging to the State Hydraulic Works in the region of Konya. In the research done in this area, it is predicted that the soil has a swollen nature and the soil should be filled with proper granular equipments by digging the ground to 50-60 cm. In this study, for purpose of helping the other research to be done in the same area, it is thought that instead of replacing swollen soil with the granular soil, by stabilizing it with polypropylene fiber and using it its original place decreases effect of swelling percent, in this way the cost will be decreased. Therefore, laboratory tests were conducted to study the effects of polypropylene fiber on swelling characteristics of expansive soil. Test results indicated that inclusion of fiber reduced swell percent of expansive soil. As the fiber content increased, the unconfined compressive strength was increased. Finally, it can be said that stabilization of expansive soils with polypropylene fiber is an effective method.

Keywords: Expansive soils, polypropylene fiber, stabilization, swelling percent.

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Authors: Liqiong Liu, Shouming Zhong

Abstract:

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: Youngseok Kim, Chul Park, Jonghwa Yi, Sangsik Choi

Abstract:

The 2-MHz Side Scan SONAR (SSS) attached to the boat for inspection of underwater structures is affected by shaking. It is difficult to determine the exact scale of damage of structure. In this study, a motion sensor is attached to the inside of the 2-MHz SSS to get roll, pitch, and yaw direction data, and developed the image stabilization tool to correct the sonar image. We checked that reliable data can be obtained with an average error rate of 1.99% between the measured value and the actual distance through experiment. It is possible to get the accurate sonar data to inspect damage in underwater structure.

Keywords: Image stabilization, motion sensor, safety inspection, sonar image, underwater structure.

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Authors: Takao Sakakura, Kazunori Fujimoto

Abstract:

This paper proposes an analytical method for the dynamics of generating firms- alliance networks along with business phases. Dynamics in network developments have previously been discussed in the research areas of organizational strategy rather than in the areas of regional cluster, where the static properties of the networks are often discussed. The analytical method introduces the concept of business phases into innovation processes and uses relationships called prior experiences; this idea was developed in organizational strategy to investigate the state of networks from the viewpoints of tradeoffs between link stabilization and node exploration. This paper also discusses the results of the analytical method using five cases of the network developments of firms. The idea of Embeddedness helps interpret the backgrounds of the analytical results. The analytical method is useful for policymakers of regional clusters to establish concrete evaluation targets and a viewpoint for comparisons of policy programs.

Keywords: Regional Clusters, Alliance Networks, Innovation Processes, Prior Experiences, Embeddedness.

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Authors: Amin Eisazadeh, Khairul Anuar Kassim, Hadi Nur

Abstract:

The expansive nature of soils containing high amounts of clay minerals can be altered through chemical stabilization, resulting in a material suitable for construction purposes. The primary objective of this investigation was to study the changes induced in the molecular structure of phosphoric acid stabilized bentonite and lateritic soil using Nuclear Magnetic Resonance (NMR) and Fourier Transform Infrared (FTIR) spectroscopy. Based on the obtained data, it was found that a surface alteration mechanism was the main reason responsible for the improvement of treated soils. Furthermore, the results indicated that the Al present in the octahedral layer of clay minerals were more amenable to chemical attacks and also partly responsible for the formation of new products.

Keywords: Bentonite, Laterite clay, Molecularcharacterization, Phosphoric acid, Stabilization

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Authors: G. Petruzzelli, F. Pedron, M. Grifoni, A. Pera, I. Rosellini, B. Pezzarossa

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The addition of lime as Ca(OH)2 to sewage sludge to destroy pathogens (Escherichia coli), was evaluated also in relation to heavy metal bioavailability. The obtained results show that the use of calcium hydroxide at the dose of 3% effectively destroyed pathogens ensuring the stability at high pH values over long period and the duration of the sewage sludge stabilization. In general, lime addition decreased the total extractability of heavy metals indicating a reduced bioavailability of these elements. This is particularly important for a safe utilization in agricultural soils to reduce the possible transfer of heavy metals to the food chain.

Keywords: Biological sludge, Ca(OH)2, copper, pathogens, sanitation, zinc.

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Authors: Irina E. Sukovataya, Oleg S. Sutormin, Valentina A. Kratasyuk

Abstract:

Effect of viscosity of media on kinetic parameters of the coupled enzyme system NADH:FMN-oxidoreductase–luciferase was investigated with addition of organic solvents (glycerol and sucrose), because bioluminescent enzyme systems based on bacterial luciferases offer a unique and general tool for analysis of the many analytes and enzymes in the environment, research and clinical laboratories and other fields. The possibility of stabilization and increase of activity of the coupled enzyme system NADH:FMN-oxidoreductase–luciferase activity in vicious aqueous-organic mixtures have been shown.

Keywords: The coupled enzyme system of bioluminescence bacteria NAD(P)H:FMN-oxidoreductase–luciferase, glycerol, stabilization of enzymes, sucrose.

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Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon

Abstract:

The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler Plate Equation, Numerical Simulations, Stability, Energy Decay, Finite Difference Method.

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Authors: G. M. Ayininuola, A. O. Sogunro

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Most failures of soil have been attributed to poor shear strength. Consequently, the present paper investigated the suitability of cattle bone ash as a possible additive to improve the shear strength of soils. Four soil samples were collected and stabilized with prepared bone ash in proportions of 3%, 5%, 7%, 10%, 15% and 20% by dry weight. Chemical analyses of the bone ash; followed by classification, compaction, and triaxial shear tests of the treated soil samples were conducted. Results obtained showed that bone ash contained high proportion of calcium oxide and phosphate. Addition of bone ash to soil samples led to increase in soil shear strengths within the range of 22.40% to 105.18% over the strengths of the respective control tests. Conversely, all samples attained maximum shear strengths at 7% bone ash stabilization. The use of bone ash as an additive will therefore improve the shear strength of soils; however, using bone ash quantities in excess of 7% may not yield ample results.

Keywords: Bone ash, Shear strength, Stabilization, Soil.

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Authors: Naveed Ahmed, Gunar Matthies

Abstract:

We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numerical results which shows that the cGP(k) and dG(k)- methods are accurate of order k +1, respectively, in the whole time interval. Moreover, the cGP(k)-method is superconvergent of order 2k and dG(k)-method is of order 2k +1 at the discrete time points. Furthermore, the dependence of the results on the choice of the stabilization parameter are discussed and compared.

Keywords: Convection-diffusion-reaction equations, stabilized finite elements, discontinuous Galerkin, continuous Galerkin-Petrov.

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Authors: Jorge Cardoso

Abstract:

Workflow Management Systems (WfMS) alloworganizations to streamline and automate business processes and reengineer their structure. One important requirement for this type of system is the management and computation of the Quality of Service(QoS) of processes and workflows. Currently, a range of Web processes and workflow languages exist. Each language can be characterized by the set of patterns they support. Developing andimplementing a suitable and generic algorithm to compute the QoSof processes that have been designed using different languages is a difficult task. This is because some patterns are specific to particular process languages and new patterns may be introduced in future versions of a language. In this paper, we describe an adaptive algorithm implemented to cope with these two problems. The algorithm is called adaptive since it can be dynamically changed as the patterns of a process language also change.

Keywords: quality of service, web processes, workflows, web services

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Authors: Nazira Kakulia

Abstract:

The analysis of transformation of institutional changes outlines two important characteristics. These are: the speed of the changes and their sequence. Successful transformation must be carried out in three different stages; On the first stage, macroeconomic stabilization must be achieved with the help of fiscal and monetary tools. Two-tier banking system should be established and the active functions of central bank should be replaced by the passive ones (reserve requirements and refinancing rate), together with the involvement growth of private sector. Fiscal policy by itself here means the creation of tax system which must replace previously existing direct state revenues; the share of subsidies in the state expenses must be reduced also. The second stage begins after reaching the macroeconomic stabilization at a time of change of formal institutes which must stimulate the private business. Corporate legislation creates a competitive environment at the market and the privatization of state companies takes place. Bankruptcy and contract law is created. he third stage is the most extended one, which means the formation of all state structures that is necessary for the further proper functioning of a market economy. These three stages about the cycle period of political and social transformation and the hierarchy of changes can also be grouped by the different methodology: on the first and the most short-term stage the transfer of power takes place. On the second stage institutions corresponding to new goal are created. The last phase of transformation is extended in time and it includes the infrastructural, socio-cultural and socio-structural changes. The main goal of this research is to explore and identify the features of such kind of models.

Keywords: Competitive, environment, fiscal policy, macro-economic stabilization.

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Authors: Magdi M. E. Zumrawi, Nehla Mansour

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This paper aims to assess the efficiency of using geogrid reinforcement for subgrade stabilization. The literature of applying geogrid reinforcement technique for pavements built on soft subgrades and the previous experiences were reviewed. Laboratory tests were conducted on soil reinforced with geogrids in one or several layers. The soil specimens were compacted in four layers with or without geogrid sheets. The California Bearing Ratio (CBR) test, in soaking condition, was performed on natural soil and soil-geogrid specimens. The test results revealed that the CBR value is much affected by the geogrid sheet location and the number of sheets used in the soil specimen. When a geogrid sheet was placed at the 1^st layer of the soil, there was an increment of 26% in the CBR value. Moreover, the CBR value was significantly increased by 62% when geogrid sheets were placed at all four layers. The high CBR value is attributed to interface friction and interlock involved in the geogrid/ soil interactions. It could be concluded that geogrid reinforcement is successful and more economical technique.

Keywords: Geogrid, reinforcement, stabilization, subgrade.

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Authors: Dilavar Khan, Z. Ahmad

Abstract:

Riprap is mostly used to prevent erosion by flows down the steep slopes in river engineering. A total of 53 stability tests performed on angular riprap with a median stone size ranging from 15 to 278 mm and slope ranging from 1 to 40% are used in this study. The existing equations for the prediction of medium size of angular stones are checked for their accuracy using the available data. Predictions of median size using these equations are not satisfactory and results show deviation by more than ±20% from the observed values. A multivariable power regression analysis is performed to propose a new equation relating the median size with unit discharge, bed slope, riprap thickness and coefficient of uniformity. The proposed relationship satisfactorily predicts the median angular stone size with ±20% error. Further, the required size of the rounded stone is more than the angular stone for the same unit discharge and the ratio increases with unit discharge and also with embankment slope of the riprap.

Keywords: Angularity, Gradation, Riprap, Stabilization

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Authors: A. Puras Trueba, J. R. Llata García

Abstract:

A nonlinear optimal controller with a fuzzy gain scheduler has been designed and applied to a Line-Of-Sight (LOS) stabilization system. Use of Linear Quadratic Regulator (LQR) theory is an optimal and simple manner of solving many control engineering problems. However, this method cannot be utilized directly for multigimbal LOS systems since they are nonlinear in nature. To adapt LQ controllers to nonlinear systems at least a linearization of the model plant is required. When the linearized model is only valid within the vicinity of an operating point a gain scheduler is required. Therefore, a Takagi-Sugeno Fuzzy Inference System gain scheduler has been implemented, which keeps the asymptotic stability performance provided by the optimal feedback gain approach. The simulation results illustrate that the proposed controller is capable of overcoming disturbances and maintaining a satisfactory tracking performance.

Keywords: Fuzzy Gain-Scheduling, Gimbal, Line-Of-SightStabilization, LQR, Optimal Control

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Authors: Katarzyna Mleczko

Abstract:

Processes of production of innovative medical tools have interdisciplinary character. They consist of direct and indirect close cooperation of specialists of different scientific branches. The Knowledge they have seems to be important for undertaken design, construction and manufacturing processes. The Knowledge exchange between participants of these processes is therefore crucial for the final result, which are innovative medical products. The paper draws attention to the necessity of feedback from the end user to the designer / manufacturer of medical tools which will allow for more accurate understanding of user needs. The study describes prerequisites of production processes of innovative medical (surgical) tools including participants and category of knowledge resources occurring in these processes. They are the result of research in selected Polish organizations involved in the production of medical instruments and are the basis for further work on the development of knowledge sharing model in interdisciplinary teams geographically dispersed.

Keywords: Interdisciplinary production processes, knowledge exchange, knowledge sharing, medical tools, user-centered design.

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Authors: Aziz Sezgin

Abstract:

We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.

Keywords: Backstepping, boundary control, 2-D, 3-D, n-D heat equation, distributed parameter systems.

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Authors: Rasaki O. Olanrewaju

Abstract:

The driven processes of Wiener and Lévy are known self-standing Gaussian-Markov processes for fitting non-linear dynamical Vasciek model. In this paper, a coincidental Gaussian density stationarity condition and autocorrelation function of the two driven processes were established. This led to the conflation of Wiener and Lévy processes so as to investigate the efficiency of estimates incorporated into the one-dimensional Vasciek model that was estimated via the Maximum Likelihood (ML) technique. The conditional laws of drift, diffusion and stationarity process was ascertained for the individual Wiener and Lévy processes as well as the commingle of the two processes for a fixed effect and Autoregressive like Vasciek model when subjected to financial series; exchange rate of Naira-CFA Franc. In addition, the model performance error of the sub-merged driven process was miniature compared to the self-standing driven process of Wiener and Lévy.

Keywords: Wiener process, Lévy process, Vasciek model, drift, diffusion, Gaussian density stationary.

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