Search results for: nonlinear dynamical system

Authors: Magdi. M. Nabi, Ding-Li Yu

Abstract:

Control of a semi-batch polymerization reactor using an adaptive radial basis function (RBF) neural network method is investigated in this paper. A neural network inverse model is used to estimate the valve position of the reactor; this method can identify the controlled system with the RBF neural network identifier. The weights of the adaptive PID controller are timely adjusted based on the identification of the plant and self-learning capability of RBFNN. A PID controller is used in the feedback control to regulate the actual temperature by compensating the neural network inverse model output. Simulation results show that the proposed control has strong adaptability, robustness and satisfactory control performance and the nonlinear system is achieved.

Keywords: Chylla-Haase polymerization reactor, RBF neural networks, feed-forward, feedback control

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Authors: Gamal F.Attia

Abstract:

The baselines are the distances and lengths of the chords between projections of the positions of the laser stations on the reference ellipsoid. For the satellite geodesy, it is very important to determine the optimal length of orbital arc along which laser measurements are to be carried out. It is clear that for the dynamical methods long arcs (one month or more) are to be used. According to which more errors of modeling of different physical forces such as earth's gravitational field, air drag, solar radiation pressure, and others that may influence the accuracy of the estimation of the satellites position, at the same time the measured errors con be almost completely excluded and high stability in determination of relative coordinate system can be achieved. It is possible to diminish the influence of the errors of modeling by using short-arcs of the satellite orbit (several revolutions or days), but the station's coordinates estimated by different arcs con differ from each other by a larger quantity than statistical zero. Under the semidynamical ‘short arc’ method one or several passes of the satellite in one of simultaneous visibility from both ends of the chord is known and the estimated parameter in this case is the length of the chord. The comparison of the same baselines calculated with long and short arcs methods shows a good agreement and even speaks in favor of the last one. In this paper the Short Arc technique has been explained and 3 baselines have been determined using the ‘short arc’ method.

Keywords: baselines, short arc, dynamical, gravitational field

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Authors: Muna Alghabshi, Edmana Krishnan

Abstract:

A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method.

Keywords: Jacobi elliptic function, mapping methods, nonlinear Schrodinger Equation, tanh method

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Authors: Younghoo Choi, Yong Jun, Jinkoo Kim

Abstract:

In this study seismic performance of typical reinforced concrete staggered wall system structures was evaluated through nonlinear static and incremental dynamic analyses. To this end, and 15-story SWS structures were designed and were analyzed to obtain their nonlinear force-displacement relationships. The analysis results showed that the 5-story SWS structures failed due to yielding of columns and walls located in the lower stories, whereas in the 15-story structures plastic hinges were more widely distributed throughout the stories.

Keywords: staggered wall systems, reinforced concrete, seismic performance

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Authors: Mahmood Khalghollah, Mohammad Tavallaeinejad, Mohammad Eghtesad

Abstract:

The method of Controlled Lagrangian is an energy shaping control technique for under actuated Lagrangian systems. Energy shaping control design methods are appealing as they retain the underlying nonlinear dynamics and can provide stability results that hold over larger domain than can be obtained using linear design and analysis. In the present study, controlled lagrangian is employed for designing a controller in an under actuated rotating flexible plate system. In the system of rotating flexible plate, due to its nonlinear characteristics and coupled dynamics of rigid and flexible components, controller design is a known challenge. In this paper, controller objectives are considered to be vibration reduction of flexible component and position control of the tip of the plate. To achieve the goals, a method based on both kinetic and potential energy shaping is introduced. The stability of the closed-loop system is investigated and proved around its equilibrium points. Moreover, the proposed controller is shown to be robust against disturbance and plant uncertainties.

Keywords: controlled lagrangian, underactuated system, flexible rotating plate, disturbance

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Authors: Ju-Young Hwang, Hyo-Gyoung Kwak

Abstract:

This paper introduces a numerical analysis method for reinforced-concrete (RC) structures exposed to fire and compares the result with experimental results. The proposed analysis method for RC structure under the high temperature consists of two procedures. First step is to decide the temperature distribution across the section through the heat transfer analysis by using the time-temperature curve. After determination of the temperature distribution, the nonlinear analysis is followed. By considering material and geometrical nonlinearity with the temperature distribution, nonlinear analysis predicts the behavior of RC structure under the fire by the exposed time. The proposed method is validated by the comparison with the experimental results. Finally, prediction model to describe the status of after-cooling concrete can also be introduced based on the results of additional experiment. The product of this study is expected to be embedded for smart structure monitoring system against fire in u-City.

Keywords: RC, high temperature, after-cooling analysis, nonlinear analysis

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Authors: Weihua Ruan, Kuan-Chou Chen

Abstract:

This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.

Keywords: Hamilton-Jacobi-Bellman equations, infinite-horizon differential games, continuous and discrete state variables, political-economy models

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Authors: Mezghiche Kamel

Abstract:

We present solitary wave solutions for the perturbed nonlinear Schrodinger (PNLS) equation describing propagation of femtosecond light pulses through the fiber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe W shaped of solitons and their properties.

Keywords: fiber bragg grating, nonlinear-coupled mode equations, w shaped of solitons, PNLS

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Authors: Hassan Al Salman

Abstract:

We consider a nonlinear parabolic cross diffusion model arising in applied mathematics. A fully practical piecewise linear finite element approximation of the model is studied. By using entropy-type inequalities and compactness arguments, existence of a global weak solution is proved. Providing further regularity of the solution of the model, some uniqueness results and error estimates are established. Finally, some numerical experiments are performed.

Keywords: cross diffusion model, entropy-type inequality, finite element approximation, numerical analysis

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Authors: Sergio Haram Sarmiento, Arcady Ponosov

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Based on appropriate multivariate statistical methodology, we suggest a generic framework for efficient parameter estimation for ordinary differential equations and the corresponding nonlinear models. In this framework classical linear regression strategies is refined into a nonlinear regression by a locally linear modelling technique (known as metamodelling). The approach identifies those latent variables of the given model that accumulate most information about it among all approximations of the same dimension. The method is applied to several benchmark problems, in particular, to the so-called ”power-law systems”, being non-linear differential equations typically used in Biochemical System Theory.

Keywords: principal component analysis, generalized law of mass action, parameter estimation, metamodels

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Authors: A. Zerarka, W. Djoudi

Abstract:

The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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Authors: K. N. S. Kasi Viswanadham

Abstract:

Coupled system of second order linear and nonlinear boundary value problems occur in various fields of Science and Engineering. In the formulation of the problem, any one of 81 possible types of boundary conditions may occur. These 81 possible boundary conditions are written as a combination of four boundary conditions. To solve a coupled system of boundary value problem with these converted boundary conditions, a collocation method with cubic B-splines as basis functions has been developed. In the collocation method, the mesh points of the space variable domain have been selected as the collocation points. The basis functions have been redefined into a new set of basis functions which in number match with the number of mesh points in the space variable domain. The solution of a non-linear boundary value problem has been obtained as the limit of a sequence of solutions of linear boundary value problems generated by quasilinearization technique. Several linear and nonlinear boundary value problems are presented to test the efficiency of the proposed method and found that numerical results obtained by the present method are in good agreement with the exact solutions available in the literature.

Keywords: collocation method, coupled system, cubic b-splines, mesh points

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Authors: M. Y. Waziri, M. A. Aliyu

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The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method.

Keywords: mulit-step Broyden, nonlinear systems of equations, computational efficiency, iterate

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Authors: Madhu Aneja, Sapna Sharma

Abstract:

Thermal conductivity of ordinary heat transfer fluids is not adequate to meet today’s cooling rate requirements. Nanoparticles have been shown to increase the thermal conductivity and convective heat transfer to the base fluids. One of the possible mechanisms for anomalous increase in the thermal conductivity of nanofluids is the Brownian motions of the nanoparticles in the basefluid. In this paper, the natural convection of incompressible nanofluid over a nonlinear stretching sheet in the presence of magnetic field is studied. The flow and heat transfer induced by stretching sheets is important in the study of extrusion processes and is a subject of considerable interest in the contemporary literature. Appropriate similarity variables are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary (similarity) differential equations. For computational purpose, Finite Element Method is used. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo – Klienstreuer – Li) correlation. In this model effect of Brownian motion on thermal conductivity is considered. The effect of important parameter i.e. nonlinear parameter, volume fraction, Hartmann number, heat source parameter is studied on velocity and temperature. Skin friction and heat transfer coefficients are also calculated for concerned parameters.

Keywords: Brownian motion, convection, finite element method, magnetic field, nanofluid, stretching sheet

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Authors: Abderraouf Gaaloul, Faouzi Msahli

Abstract:

The use of standard sliding mode controller, usually, leads to the appearing of an undesirable chattering phenomenon affecting the control signal. Such problem can be overcome using a higher-order sliding mode controller (HOSMC) which preserves the main properties of the standard sliding mode and deliberately increases the control smoothness. In this paper, we propose a new HOSMC for a class of uncertain multi-input multi-output nonlinear systems. Based on high gain and integral sliding mode paradigms, the established control scheme removes theoretically the chattering phenomenon and provides the stability of the control system. Numerical simulations are developed to show the effectiveness of the proposed controller when applied to solve a control problem of two water levels into a quadruple-tank process.

Keywords: nonlinear systems, sliding mode control, high gain, higher order

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

Abstract:

In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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Authors: Taha Benarbia, Kay W. Axhausen, Anugrah Ilahi

Abstract:

Electric car sharing system as ecologic transportation increasing in the world. The complexity of managing electric car sharing systems, especially one-way trips and battery autonomy have direct influence to on supply and demand of system. One must be able to precisely model the demand and supply of these systems to better operate electric car sharing and estimate its effect on mobility management and the accessibility that it provides in urban areas. In this context, our work focus to develop performances optimization model of the system based on discrete event simulation and stochastic Petri net. The objective is to search optimal decisions and management parameters of the system in order to fulfil at best demand while minimizing undesirable situations. In this paper, we present new model of electric cars sharing with relocation based on monitoring system. The proposed approach also help to precise the influence of battery charging level on the behaviour of system as important decision parameter of this complex and dynamical system.

Keywords: electric car-sharing systems, smart mobility, Petri nets modelling, discrete event simulation

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Authors: Kanica Goel, Nilam

Abstract:

Infectious diseases are a leading cause of death worldwide and hence a great challenge for every nation. Thus, it becomes utmost essential to prevent and reduce the spread of infectious disease among humans. Mathematical models help to better understand the transmission dynamics and spread of infections. For this purpose, in the present article, we have proposed a nonlinear time-delayed SVIRS (Susceptible-Vaccinated-Infected-Recovered-Susceptible) mathematical model with nonlinear type incidence rate and nonlinear type treatment rate. Analytical study of the model shows that model exhibits two types of equilibrium points, namely, disease-free equilibrium and endemic equilibrium. Further, for the long-term behavior of the model, stability of the model is discussed with the help of basic reproduction number R₀ and we showed that disease-free equilibrium is locally asymptotically stable if the basic reproduction number R₀ is less than one and unstable if the basic reproduction number R₀ is greater than one for the time lag τ≥0. Furthermore, when basic reproduction number R₀ is one, using center manifold theory and Casillo-Chavez and Song theorem, we showed that the model undergoes transcritical bifurcation. Moreover, numerical simulations are being carried out using MATLAB 2012b to illustrate the theoretical results.

Keywords: nonlinear incidence rate, nonlinear treatment rate, stability, time delayed SVIRS epidemic model

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Authors: Mohammadsadegh Zanganehfar

Abstract:

Since the modernism, movement, and appearance of modern architecture, an aggressive desire for a general design theory in the theoretical works of architects in the form of books and essays emerges. Since Robert Venturi and Denise Scott Brown’s published complexity and contradiction in architecture in 1966, the discourse of complexity and volumetric composition has been an important and controversial issue in the discipline. Ever since various theories and essays were involved in this discourse, this paper attempt to identify chaos theory as a scientific model of complexity and its relation to architecture design theory by conducting a qualitative analysis and multidisciplinary critical approach through architecture and basic sciences resources. As a result, we identify chaotic architecture as the correlation of chaos theory and architecture as an independent nonlinear design theory with specific characteristics and properties.

Keywords: architecture complexity, chaos theory, fractals, nonlinear dynamic systems, nonlinear ontology

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Authors: Leila Motamed-Jahromi, Mohsen Hatami, Alireza Keshavarz

Abstract:

This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As₂S₃ chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.

Keywords: nonlinear optics, plasmonic waveguide, chalcogenide, propagation equation

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Authors: Nini Johana Marín Rodríguez, William Fernando Oquendo Patino

Abstract:

In this work, we model a coupled system where we explore the effects of steady and random behavior on a linear system like an extension of the classic Strogatz model. This is exemplified by modeling a couple love dynamics as a linear system of two coupled differential equations and studying its stability for four types of lovers chosen as CC='Cautious- Cautious', OO='Only other feelings', OP='Opposites' and RR='Romeo the Robot'. We explore the effects of, first, introducing saturation, and second, adding a random variation to one of the CC-type lover, which will shape his character by trying to model how its variability influences the dynamics between love and hate in couple in a long run relationship. This work could also be useful to model other kind of systems where interactions can be modeled as linear systems with external or internal random influence. We found the final results are not easy to predict and a strong dependence on initial conditions appear, which a signature of chaos.

Keywords: differential equations, dynamical systems, linear system, love dynamics

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Authors: Ju-young Hwang, Hyo-Gyoung Kwak, Hong Jae Yim

Abstract:

This paper introduces a numerical analysis method for reinforced-concrete (RC) structures exposed to fire and compares the result with experimental results. The proposed analysis method for RC structure under the high temperature consists of two procedures. First step is to decide the temperature distribution across the section through the heat transfer analysis by using the time-temperature curve. After determination of the temperature distribution, the nonlinear analysis is followed. By considering material and geometrical non-linearity with the temperature distribution, nonlinear analysis predicts the behavior of RC structure under the fire by the exposed time. The proposed method is validated by the comparison with the experimental results. Finally, Prediction model to describe the status of after-cooling concrete can also be introduced based on the results of additional experiment. The product of this study is expected to be embedded for smart structure monitoring system against fire in u-City.

Keywords: RC structures, heat transfer analysis, nonlinear analysis, after-cooling concrete model

Procedia PDF Downloads 345

Authors: Ebrahim Hassan Kapeel, Ahmed Mohsen Kamel, Hossan Hendy, Yehia Z. Elhalwagy

Abstract:

Interest in autopilot design has been raised intensely as a result of recent advancements in Unmanned Aerial vehicles (UAVs). Due to the enormous number of applications that UAVs can achieve, the number of applied control theories used for them has increased in recent years. These small fixed-wing UAVs are suffering high non-linearity, sensitivity to disturbances, and coupling effects between their channels. In this work, the nonlinear dynamic inversion (NDI) control lawisdesigned for a nonlinear small fixed-wing UAV model. The NDI is preferable for varied operating conditions, there is no need for a scheduling controller. Moreover, it’s applicable for high angles of attack. For the designed flight controller validation, a nonlinear Modified PI-D controller is performed with our model. A comparative study between both controllers is achieved to evaluate the NDI performance. Simulation results and analysis are proposed to illustrate the effectiveness of the designed controller based on NDI.

Keywords: UAV dynamic model, attitude control, nonlinear PID, dynamic inversion

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Authors: Qiuling Xie, Shanliang Zhu, Zongdi Sun

Abstract:

In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.

Keywords: grey relational degree, multiple linear regression, membership function, nonlinear programming

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Authors: Masood Roohi, Amir Taghavipour

Abstract:

This paper describes a strategy to develop an energy management system (EMS) for a charge-sustaining power-split hybrid electric vehicle. This kind of hybrid electric vehicles (HEVs) benefit from the advantages of both parallel and series architecture. However, it gets relatively more complicated to manage power flow between the battery and the engine optimally. The applied strategy in this paper is based on nonlinear model predictive control approach. First of all, an appropriate control-oriented model which was accurate enough and simple was derived. Towards utilization of this controller in real-time, the problem was solved off-line for a vast area of reference signals and initial conditions and stored the computed manipulated variables inside look-up tables. Look-up tables take a little amount of memory. Also, the computational load dramatically decreased, because to find required manipulated variables the controller just needed a simple interpolation between tables.

Keywords: hybrid electric vehicles, energy management system, nonlinear model predictive control, real-time

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Authors: Ali Raheli, Rahim Habibifar, Behzad Mohammadi-Alasti, Mahdi Abbasgholipour

Abstract:

This paper presents vibration behavior of a FGM micro-beam and its pull-in instability under a nonlinear electrostatic pressure. An exponential function has been applied to show the continuous gradation of the properties along thickness. Nonlinear integro-differential-electro-mechanical equation based on Euler–Bernoulli beam theory has been derived. The governing equation in the static analysis has been solved using Step-by-Step Linearization Method and Finite Difference Method. Fixed points or equilibrium positions and singular points have been shown in the state control space. In order to find the response to a step DC voltage, the nonlinear equation of motion has been solved using Galerkin-based reduced-order model and time histories and phase portrait for different applied voltages have been shown. The effects of electrostatic pressure on stability of FGM micro-beams having various amounts of the ceramic constituent have been investigated.

Keywords: FGM, MEMS, nonlinear vibration, electrical, dynamic pull-in voltage

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Authors: K. Karuppasamy

Abstract:

In this paper analysis of an infinite beam resting on multilayer tensionless extensible geosynthetic reinforced granular fill - poor soil system overlying soft soil strata under moving the load with constant velocity is presented. The beam is subjected to a concentrated load moving with constant velocity. The upper reinforced granular bed is modeled by a rough membrane embedded in Pasternak shear layer overlying a series of compressible nonlinear Winkler springs representing the underlying the very poor soil. The multilayer tensionless extensible geosynthetic layer has been assumed to deform such that at the interface the geosynthetic and the soil have some deformation. Nonlinear behavior of granular fill and the very poor soil has been considered in the analysis by means of hyperbolic constitutive relationships. Governing differential equations of the soil foundation system have been obtained and solved with the help of appropriate boundary conditions. The solution has been obtained by employing finite difference method by means of Gauss-Siedel iterative scheme. Detailed parametric study has been conducted to study the influence of various parameters on the response of soil – foundation system under consideration by means of deflection and bending moment in the beam and tension mobilized in the geosynthetic layer. These parameters include the magnitude of applied load, the velocity of the load, damping, the ultimate resistance of the poor soil and granular fill layer. The range of values of parameters has been considered as per Indian Railways conditions. This study clearly observed that the comparisons of multilayer tensionless extensible geosynthetic reinforcement with poor foundation soil and magnitude of applied load, relative compressibility of granular fill and ultimate resistance of poor soil has significant influence on the response of soil – foundation system. However, for the considered range of velocity, the response has been found to be insensitive towards velocity. The ultimate resistance of granular fill layer has also been found to have no significant influence on the response of the system.

Keywords: infinite beams, multilayer tensionless extensible geosynthetic, granular layer, moving load and nonlinear behavior of poor soil

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Authors: Ebrahim H. Kapeel, Ahmed M. Kamel, Hossam Hendy, Yehia Z. Elhalwagy

Abstract:

Interest in autopilot design has been raised intensely as a result of recent advancements in Unmanned Aerial vehicles (UAVs). Due to the enormous number of applications that UAVs can achieve, the number of applied control theories used for them has increased in recent years. These small fixed-wing UAVs are suffering high non-linearity, sensitivity to disturbances, and coupling effects between their channels. In this work, the nonlinear dynamic inversion (NDI) control law is designed for a nonlinear small fixed-wing UAV model. The NDI is preferable for varied operating conditions, there is no need for a scheduling controller. Moreover, it’s applicable for high angles of attack. For the designed flight controller validation, a nonlinear Modified PI-D controller is performed with our model. A comparative study between both controllers is achieved to evaluate the NDI performance. Simulation results and analysis are proposed to illustrate the effectiveness of the designed controller based on NDI.

Keywords: attitude control, nonlinear PID, dynamic inversion

Procedia PDF Downloads 86

Authors: Jairo Aparecido Martins, Estaner Claro Romão

Abstract:

This paper presents the static and cyclic stresses in combination with fatigue analysis resultant of loads applied on the friction discs usually utilized on industrial clutches. The material chosen to simulate the friction discs under load is aluminum. The numerical simulation was done by software COMSOL^TM Multiphysics. The results obtained for static loads showed enough stiffness for both geometries and the material utilized. On the other hand, in the fatigue standpoint, failure is clearly verified, what demonstrates the importance of both approaches, mainly dynamical analysis. The results and the conclusion are based on the stresses on disc, counted stress cycles, and fatigue usage factor.

Keywords: aluminum, industrial clutch, static and dynamic loading, numerical simulation

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Authors: Hisham M. Soliman, Hassan Yousef

Abstract:

This manuscript presents new results on design saturated power system stabilizers (PSS) to assign system poles within a desired region for achieving good dynamic performance. The regional pole placement is accomplished against model uncertainties caused by different load conditions. The design is based on a sufficient condition in the form of linear matrix inequalities (LMI) which forces the saturated nonlinear controller to lie within the linear zone. The controller effectiveness is demonstrated on a single machine infinite bus system.

Keywords: power system stabilizer, saturated control, robust control, regional pole placement, linear matrix inequality (LMI)

Procedia PDF Downloads 548