Search results for: nonlinear analytical model

Authors: K. Melouk, M. Dellakrachai

Abstract:

Analytical formula for the optical gain based on a simple parabolic-band by introducing theoretical expressions for the quantized energy is presented. The model used in this treatment take into account the effects of intraband relaxation. It is shown, as a result, that the gain for the TE mode is larger than that for TM mode and the presence of acceptor impurity increase the peak gain.

Keywords: Laser, quantum well, semiconductor, InGaAsP.

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Authors: Fotis N. Koumboulis, Michael G. Skarpetis, Maria P. Tzamtzi

Abstract:

The problem of robust disturbance rejection (RDR) using a proportional state feedback controller is studied for the case of Left Invertible MIMO generalized state space linear systems with nonlinear uncertain structure. Sufficient conditions for the problem to have a solution are established. The set of all proportional feedback controllers solving the problem subject to these conditions is analytically determined.

Keywords: System theory, uncertain systems, robust control, singular systems.

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Authors: Amr Abdel Azim Ali, G. A. Elsheikh, Moutaz Hegazy

Abstract:

This paper presents verification of a modeling and simulation for a Spacecraft (SC) attitude and orbit control system. Detailed formulation of coupled SC orbital and attitude equations of motion is performed in order to achieve accepted accuracy to meet the requirements of multitargets tracking and orbit correction complex modes. Correction of the target parameter based on the estimated state vector during shooting time to enhance pointing accuracy is considered. Time-optimal nonlinear feedback control technique was used in order to take full advantage of the maximum torques that the controller can deliver. This simulation provides options for visualizing SC trajectory and attitude in a 3D environment by including an interface with V-Realm Builder and VR Sink in Simulink/MATLAB. Verification data confirms the simulation results, ensuring that the model and the proposed control law can be used successfully for large and fast tracking and is robust enough to keep the pointing accuracy within the desired limits with considerable uncertainty in inertia and control torque.

Keywords: Attitude and orbit control, time-optimal nonlinear feedback control, modeling and simulation, pointing accuracy, maximum torques.

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Authors: Fengxia Zheng

Abstract:

By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

Keywords: Fractional differential equation, boundary value problem, positive solution, existence and uniqueness, fixed point theorem, mixed monotone operator.

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Authors: Hyun-Woo Cho

Abstract:

Detection of incipient abnormal events is important to improve safety and reliability of machine operations and reduce losses caused by failures. Improper set-ups or aligning of parts often leads to severe problems in many machines. The construction of prediction models for predicting faulty conditions is quite essential in making decisions on when to perform machine maintenance. This paper presents a multivariate calibration monitoring approach based on the statistical analysis of machine measurement data. The calibration model is used to predict two faulty conditions from historical reference data. This approach utilizes genetic algorithms (GA) based variable selection, and we evaluate the predictive performance of several prediction methods using real data. The results shows that the calibration model based on supervised probabilistic principal component analysis (SPPCA) yielded best performance in this work. By adopting a proper variable selection scheme in calibration models, the prediction performance can be improved by excluding non-informative variables from their model building steps.

Keywords: Prediction, operation monitoring, on-line data, nonlinear statistical methods, empirical model.

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Authors: Mihai Caramihai, Irina Severin

Abstract:

Bioprocesses are appreciated as difficult to control because their dynamic behavior is highly nonlinear and time varying, in particular, when they are operating in fed batch mode. The research objective of this study was to develop an appropriate control method for a complex bioprocess and to implement it on a laboratory plant. Hence, an intelligent control structure has been designed in order to produce biomass and to maximize the specific growth rate.

Keywords: Fed batch bioprocess, mass-balance model, fuzzy control

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Authors: Vijay Kumar Kukreja, Ravneet Kaur

Abstract:

In this paper, one dimensional advection diffusion model is analyzed using finite difference method based on Crank-Nicolson scheme. A practical problem of filter cake washing of chemical engineering is analyzed. The model is converted into dimensionless form. For the grid Ω × ω = [0, 1] × [0, T], the Crank-Nicolson spatial derivative scheme is used in space domain and forward difference scheme is used in time domain. The scheme is found to be unconditionally convergent, stable, first order accurate in time and second order accurate in space domain. For a test problem, numerical results are compared with the analytical ones for different values of parameter.

Keywords: Consistency, Crank-Nicolson scheme, Gerschgorin circle, Lax-Richtmyer theorem, Peclet number, stability.

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Authors: Sana Bouzaida, Anis Sakly, Faouzi M'Sahli

Abstract:

In this paper, a TSK-type Neuro-fuzzy Inference System that combines the features of fuzzy sets and neural networks has been applied for the identification of MIMO systems. The procedure of adapting parameters in TSK model employs a Shuffled Frog Leaping Algorithm (SFLA) which is inspired from the memetic evolution of a group of frogs when seeking for food. To demonstrate the accuracy and effectiveness of the proposed controller, two nonlinear systems have been considered as the MIMO plant, and results have been compared with other learning methods based on Particle Swarm Optimization algorithm (PSO) and Genetic Algorithm (GA).

Keywords: Identification, Shuffled frog Leaping Algorithm (SFLA), TSK-type neuro-fuzzy model.

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Authors: Ag. S. Abd. Hamid, S. K. Lee, J. Dayou, R. Yusoff, F. Sulaiman

Abstract:

The mixture between two fluids of different salinity has been proven to capable of producing electricity in an ocean salinity energy conversion system known as hydrocratic generator. The system relies on the difference between the salinity of the incoming fresh water and the surrounding sea water in the generator. In this investigation, additional parameter is introduced which is the temperature difference between the two fluids; hence the system is known as Ocean Salinity and Temperature Energy Conversion System (OSTEC). The investigation is divided into two papers. This first paper of Part 1 presents the theoretical formulation by considering the effect of fluid dynamic viscosity known as Viscosity Model and later compares with the conventional formulation which is Density Model. The dynamic viscosity model is used to predict the dynamic of the fluids in the system which in turns gives the analytical formulation of the potential power output that can be harvested. 

Keywords: Buoyancy, density, frictional head loss, kinetic power, viscosity.

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Authors: Jiashang Jiang, Yongxin Yuan

Abstract:

In this paper we develop an efficient numerical method for the finite-element model updating of damped gyroscopic systems based on incomplete complex modal measured data. It is assumed that the analytical mass and stiffness matrices are correct and only the damping and gyroscopic matrices need to be updated. By solving a constrained optimization problem, the optimal corrected symmetric damping matrix and skew-symmetric gyroscopic matrix complied with the required eigenvalue equation are found under a weighted Frobenius norm sense.

Keywords: Model updating, damped gyroscopic system, partially prescribed spectral information.

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Authors: T. Cornelius, G. Secilmis

Abstract:

When dealing with safety in structures, the connections between structural components play an important role. Robustness of a structure as a whole depends both on the load- bearing capacity of the structural component and on the structures capacity to resist total failure, even though a local failure occurs in a component or a connection between components. To avoid progressive collapse it is necessary to be able to carry out a design for connections. A connection may be executed with anchors to withstand local failure of the connection in structures built with prefabricated components. For the design of these anchors, a model is developed for connections in structures performed in prefabricated autoclaved aerated concrete components. The design model takes into account the effect of anchors placed close to the edge, which may result in splitting failure. Further the model is developed to consider the effect of reinforcement diameter and anchor depth. The model is analytical and theoretically derived assuming a static equilibrium stress distribution along the anchor. The theory is compared to laboratory test, including the relevant parameters and the model is refined and theoretically argued analyzing the observed test results. The method presented can be used to improve safety in structures or even optimize the design of the connections

Keywords: Robustness, anchors, connections, aircrete, prefabricated components.

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Authors: Dmitry A. Mikoyelov

Abstract:

The paper presents a set of guidelines for analysis of industrial embedded distributed systems and introduces a mathematical model derived from these guidelines. In this study, the author examines a set of modern communication technologies that are or possibly can be used to build communication links between the subsystems of a distributed embedded system. An investigation of these guidelines results in a algorithm for analysis of specific use cases of target technologies. A goal of the paper acts as an important base for ongoing research on comparison of communication technologies. The author describes the principles of the model and presents results of the test calculations. Practical implementation of target technologies and empirical experiment data are based on a practical experience during the design and test of specific distributed systems in Latvian market.

Keywords: Distributed embedded system, analytical model, communication technology.

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Authors: M. Mohebbi, K. Shakeri

Abstract:

The effect of different combinations of response feedback on the performance of active control system on nonlinear frames has been studied in this paper. To this end different feedback combinations including displacement, velocity, acceleration and full response feedback have been utilized in controlling the response of an eight story bilinear hysteretic frame which has been subjected to a white noise excitation and controlled by eight actuators which could fully control the frame. For active control of nonlinear frame Newmark nonlinear instantaneous optimal control algorithm has been used which a diagonal matrix has been selected for weighting matrices in performance index. For optimal design of active control system while the objective has been to reduce the maximum drift to below the yielding level, Distributed Genetic Algorithm (DGA) has been used to determine the proper set of weighting matrices. The criteria to assess the effect of each combination of response feedback have been the minimum required control force to reduce the maximum drift to below the yielding drift. The results of numerical simulation show that the performance of active control system is dependent on the type of response feedback where the velocity feedback is more effective in designing optimal control system in comparison with displacement and acceleration feedback. Also using full feedback of response in controller design leads to minimum control force amongst other combinations. Also the distributed genetic algorithm shows acceptable convergence speed in solving the optimization problem of designing active control systems.

Keywords: Active control, Distributed genetic algorithms, Response feedback, Weighting matrices.

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Authors: Elie H. Karam, Antoine B. Abche

Abstract:

It is known that the heart interacts with and adapts to its venous and arterial loading conditions. Various experimental studies and modeling approaches have been developed to investigate the underlying mechanisms. This paper presents a model of the left ventricle derived based on nonlinear stress-length myocardial characteristics integrated over truncated ellipsoidal geometry, and second-order dynamic mechanism for the excitation-contraction coupling system. The results of the model presented here describe the effects of the viscoelastic damping element of the electromechanical coupling system on the hemodynamic response. Different heart rates are considered to study the pacing effects on the performance of the left-ventricle against constant preload and afterload conditions under various damping conditions. The results indicate that the pacing process of the left ventricle has to take into account, among other things, the viscoelastic damping conditions of the myofilament excitation-contraction process.

Keywords: Myocardial sarcomere, cardiac pump, excitationcontraction coupling, viscoelasicity

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Authors: R. Z. R. R. Rosdin, N. M. Ali, S. W. Harun, H. Arof

Abstract:

We have experimentally demonstrated bright-dark pulses in a nonlinear polarization rotation (NPR) based mode-locked Erbium-doped fiber laser (EDFL) with a long cavity configuration. Bright–dark pulses could be achieved when the laser works in the passively mode-locking regime and the net group velocity dispersion is quite anomalous. The EDFL starts to generate a bright pulse train with degenerated dark pulse at the mode-locking threshold pump power of 35.09 mW by manipulating the polarization states of the laser oscillation modes using a polarization controller (PC). A split bright–dark pulse is generated when further increasing the pump power up to 37.95 mW. Stable bright pulses with no obvious evidence of a dark pulse can also be generated when further adjusting PC and increasing the pump power up to 52.19 mW. At higher pump power of 54.96 mW, a new form of bright-dark pulse emission was successfully identified with the repetition rate of 29 kHz. The bright and dark pulses have a duration of 795.5 ns and 640 ns, respectively.

Keywords: Erbium-doped fiber laser, Nonlinear polarization rotation, bright-dark pulse.

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Authors: S.H. Mirtalaie, M.A. Hajabasi

Abstract:

In this paper, an analytical approach is used to study the coupled lateral-torsional vibrations of laminated composite beam. It is known that in such structures due to the fibers orientation in various layers, any lateral displacement will produce a twisting moment. This phenomenon is modeled by the bending-twisting material coupling rigidity and its main feature is the coupling of lateral and torsional vibrations. In addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies. Then, the governing differential equations are derived using the Hamilton-s principle and the mathematical model matches the Timoshenko beam model when neglecting the effect of bending-twisting rigidity. The equations of motion which form a system of three coupled PDEs are solved analytically to study the free vibrations of the beam in lateral and rotational modes due to the bending, as well as the torsional mode caused by twisting. The analytic solution is carried out in three steps: 1) assuming synchronous motion for the kinematic variables which are the lateral, rotational and torsional displacements, 2) solving the ensuing eigenvalue problem which contains three coupled second order ODEs and 3) imposing different boundary conditions related to combinations of simply, clamped and free end conditions. The resulting natural frequencies and mode shapes are compared with similar results in the literature and good agreement is achieved.

Keywords: Free vibration, laminated composite beam, material coupling, state space.

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Authors: O. Poleshchuk, E.Komarov

Abstract:

This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: Interval type-2 fuzzy sets, fuzzy regression, weighted interval.

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Authors: Gilberto Gonzalez-A, Dunia Nuñez-P

Abstract:

Bond graph models of an electrical transformer including the nonlinear saturation are presented. The transformer using electrical and magnetic circuits are modelled. These models determine the relation between self and mutual inductances, and the leakage and magnetizing inductances of power transformers with two windings using the properties of a bond graph. The equivalence between electrical and magnetic variables is given. The modelling and analysis using this methodology to three phase power transformers can be extended.

Keywords: Bond graph, electrical transformer, magnetic circuits, nonlinear saturation.

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Authors: Mihai Caramihai Ana A Chirvase, Irina Severin

Abstract:

Bioprocesses are appreciated as difficult to control because their dynamic behavior is highly nonlinear and time varying, in particular, when they are operating in fed batch mode. The research objective of this study was to develop an appropriate control method for a complex bioprocess and to implement it on a laboratory plant. Hence, an intelligent control structure has been designed in order to produce biomass and to maximize the specific growth rate.

Keywords: Fed batch bioprocess, mass-balance model, fuzzy control.

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Authors: Labar Hocine, Dgeghader Yacine, Kelaiaia Mounia Samira, Bounaya Kamel

Abstract:

To maximise furnace production it-s necessary to optimise furnace control, with the objectives of achieving maximum power input into the melting process, minimum network distortion and power-off time, without compromise on quality and safety. This can be achieved with on the one hand by an appropriate electrode control and on the other hand by a minimum of AC transformer switching. Electrical arc is a stochastic process; witch is the principal cause of power quality problems, including voltages dips, harmonic distortion, unbalance loads and flicker. So it is difficult to make an appropriate model for an Electrical Arc Furnace (EAF). The factors that effect EAF operation are the melting or refining materials, melting stage, electrode position (arc length), electrode arm control and short circuit power of the feeder. So arc voltages, current and power are defined as a nonlinear function of the arc length. In this article we propose our own empirical function of the EAF and model, for the mean stages of the melting process, thanks to the measurements in the steel factory.

Keywords: Modelling, electrical arc, melting, power, EAF, steel.

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Authors: Manisha Chaudhary, Joydip Dhar, Govind Prasad Sahu

Abstract:

A mathematical model is proposed considering the forest biomass density B(t), density of wood based industries W(t) and density of synthetic industries S(t). It is assumed that the forest biomass grows logistically in the absence of wood based industries, but depletion of forestry biomass is due to presence of wood based industries. The growth of wood based industries depends on B(t), while S(t) grows at a constant rate, independent of B(t). Further there is a competition between W(t) and S(t) according to market demand. The proposed model has four ecologically feasible steady states, namely, E1: forest biomass free and wood industries free equilibrium; E2: wood industries free equilibrium and two coexisting equilibria E∗1 , E∗2 . Behavior of the system near all feasible equilibria is analyzed using the stability theory of differential equations. In the proposed model, the natural depletion rate h1 is a crucial parameter and system exhibits Hopf-bifurcation about the non-trivial equilibrium with respect to h1. The analytical results are verified using numerical simulation.

Keywords: A mathematical model, Competition between wood based and synthetic industries, Hopf-bifurcation, Stability analysis.

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Authors: Daniel Y. Abebe, Sijeong Jeong, Jaehyouk Choi

Abstract:

The use of eccentrically braced frame (EBF) is increasing day by day as EBF possesses high elastic stiffness, stable inelastic response under cyclic lateral loading, and excellent ductility and energy dissipation capacity. The ductility and energy dissipation capacity of EBF depends on the active link beams. Recently, there are two types EBFs; these are conventional EBFs and EBFs with replaceable links. The conventional EBF has a disadvantage during maintenance in post-earthquake. The concept of removable active link beam in EBF is developed to overcome the limitation of the conventional EBF in post-earthquake. In this study, a replaceable link with reduced web section is introduced and design equations are suggested. In addition, nonlinear finite element analysis was conducted in order to evaluate the proposed links.

Keywords: EBFs, replaceable link, earthquake disaster, reduced section.

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Authors: Abdulrahman Abdulrahman

Abstract:

A side weir is a hydraulic structure set into the side of a channel. This structure is used for water level control in channels, to divert flow from a main channel into a side channel when the water level in the main channel exceeds a specific limit and as storm overflows from urban sewerage system. Computation of water surface over the side weirs is essential to determine the flow rate of the side weir. Analytical solutions for water surface profile along rectangular side weir are available only for the special cases of rectangular and trapezoidal channels considering constant specific energy. In this paper, a rectangular side weir located in a combined (trapezoidal with exponential) channel was considered. Expanding binominal series of integer and fraction powers and the using of reduction formula of cosine function integrals, a general analytical formula was obtained for water surface profile along a side weir in a combined (trapezoidal with exponential) channel. Since triangular, rectangular, trapezoidal and parabolic cross-sections are special cases of the combined cross section, the derived formula, is applicable to triangular, rectangular, trapezoidal cross-sections as analytical solution and semi-analytical solution to parabolic cross-section with maximum relative error smaller than 0.76%. The proposed solution should be a useful engineering tool for the evaluation and design of side weirs in open channel.

Keywords: Analytical solution, combined channel, exponential channel, side weirs, trapezoidal channel, water surface profile.

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Authors: R. Khaniki, M.B. Menhaj, H. Eliasi

Abstract:

This paper describes the application of a model predictive controller to the problem of batch reactor temperature control. Although a great deal of work has been done to improve reactor throughput using batch sequence control, the control of the actual reactor temperature remains a difficult problem for many operators of these processes. Temperature control is important as many chemical reactions are sensitive to temperature for formation of desired products. This controller consist of two part (1) a nonlinear control method GLC (Global Linearizing Control) to create a linear model of system and (2) a Model predictive controller used to obtain optimal input control sequence. The temperature of reactor is tuned to track a predetermined temperature trajectory that applied to the batch reactor. To do so two input signals, electrical powers and the flow of coolant in the coil are used. Simulation results show that the proposed controller has a remarkable performance for tracking reference trajectory while at the same time it is robust against noise imposed to system output.

Keywords: Generalized Predictive Control (GPC), TemperatureControl, Global Linearizing Control (GLC), Batch Reactor.

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Authors: R. Khaniki, M.B. Menhaj, H. Eliasi

Abstract:

This paper describes the application of a model predictive controller to the problem of batch reactor temperature control. Although a great deal of work has been done to improve reactor throughput using batch sequence control, the control of the actual reactor temperature remains a difficult problem for many operators of these processes. Temperature control is important as many chemical reactions are sensitive to temperature for formation of desired products. This controller consist of two part (1) a nonlinear control method GLC (Global Linearizing Control) to create a linear model of system and (2) a Model predictive controller used to obtain optimal input control sequence. The temperature of reactor is tuned to track a predetermined temperature trajectory that applied to the batch reactor. To do so two input signals, electrical powers and the flow of coolant in the coil are used. Simulation results show that the proposed controller has a remarkable performance for tracking reference trajectory while at the same time it is robust against noise imposed to system output.

Keywords: Generalized Predictive Control (GPC), TemperatureControl, Global Linearizing Control (GLC), Batch Reactor.

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Authors: Snehal R. Pathak, Sachin S. Munnoli

Abstract:

Evaluation of dynamic earth pressure on retaining wall is a topic of primary importance. In present paper, dynamic active earth pressure and displacement of flexible cantilever retaining wall has been evaluated analytically using 2-DOF mass-spring-dashpot model by incorporating both wall and backfill properties. The effect of wall flexibility on dynamic active earth pressure and wall displacement are studied and presented in graphical form. The obtained results are then compared with the various conventional methods, experimental analysis and also with PLAXIS analysis. It is observed that the dynamic active earth pressure decreases with increase in the wall flexibility while wall displacement increases linearly with flexibility of the wall. The results obtained by proposed 2-DOF analytical model are found to be more realistic and economical.

Keywords: Earth pressure, earthquake, 2-DOF model, plaxis, wall movement, retaining walls.

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Authors: Mohamed Amine Ben Henni, Taher Hassaine Daouadji, Boussad Abbes, Yu Ming Li, Fazilay Abbes

Abstract:

The reinforcement and repair of concrete structures by bonding composite materials have become relatively common operations. Different types of composite materials can be used: carbon fiber reinforced polymer (CFRP), glass fiber reinforced polymer (GFRP) as well as functionally graded material (FGM). The development of analytical and numerical models describing the mechanical behavior of structures in civil engineering reinforced by composite materials is necessary. These models will enable engineers to select, design, and size adequate reinforcements for the various types of damaged structures. This study focuses on the free vibration behavior of orthotropic laminated composite plates using a refined shear deformation theory. In these models, the distribution of transverse shear stresses is considered as parabolic satisfying the zero-shear stress condition on the top and bottom surfaces of the plates without using shear correction factors. In this analysis, the equation of motion for simply supported thick laminated rectangular plates is obtained by using the Hamilton’s principle. The accuracy of the developed model is demonstrated by comparing our results with solutions derived from other higher order models and with data found in the literature. Besides, a finite-element analysis is used to calculate the natural frequencies of laminated composite plates and is compared with those obtained by the analytical approach.

Keywords: Composites materials, laminated composite plate, shear deformation theory of plates, finite element analysis, free vibration.

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Authors: Anuj K. Sharma, Amit Sharma, Kulbhushan Agnihotri

Abstract:

In this work, we propose and analyze a model of Phytoplankton-Zooplankton interaction with harvesting considering that some species are exploited commercially for food. Criteria for local stability, instability and global stability are derived and some threshold harvesting levels are explored to maintain the population at an appropriate equilibrium level even if the species are exploited continuously.Further,biological and bionomic equilibria of the system are obtained and an optimal harvesting policy is also analysed using the Pantryagin’s Maximum Principle.Finally analytical findings are also supported by some numerical simulations.

Keywords: Phytoplankton-Zooplankton, Global stability, Bionomic Equilibrium, Pontrying-Maximum Principal.

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Authors: J. Geiser, R. Röhle

Abstract:

In this paper we present discretization and decomposition methods for a multi-component transport model of a chemical vapor deposition (CVD) process. CVD processes are used to manufacture deposition layers or bulk materials. In our transport model we simulate the deposition of thin layers. The microscopic model is based on the heavy particles, which are derived by approximately solving a linearized multicomponent Boltzmann equation. For the drift-process of the particles we propose diffusionreaction equations as well as for the effects of heat conduction. We concentrate on solving the diffusion-reaction equation with analytical and numerical methods. For the chemical processes, modelled with reaction equations, we propose decomposition methods and decouple the multi-component models to simpler systems of differential equations. In the numerical experiments we present the computational results of our proposed models.

Keywords: Chemical reactions, chemical vapor deposition, convection-diffusion-reaction equations, decomposition methods, multi-component transport.

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Authors: Aref Aasi, Sadegh Mehdi Aghaei, Balaji Panchapakesan

Abstract:

This work aims to evaluate the free and forced vibration of a beam with two end joints subjected to a concentrated moving mass and a load using the Euler-Bernoulli method. The natural frequency is calculated for different locations of the concentrated mass and load on the beam. The analytical results are verified by the experimental data. The variations of natural frequency as a function of the location of the mass, the effect of the forced frequency on the vibrational amplitude, and the displacement amplitude versus time are investigated. It is discovered that as the concentrated mass moves toward the center of the beam, the natural frequency of the beam and the relative error between experimental and analytical data decreases. There is a close resemblance between analytical data and experimental observations.

Keywords: Euler-Bernoulli beam, natural frequency, forced vibration, experimental setup.

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