Search results for: Linear system of equations
10096 Optimization of Slider Crank Mechanism Using Design of Experiments and Multi-Linear Regression
Authors: Galal Elkobrosy, Amr M. Abdelrazek, Bassuny M. Elsouhily, Mohamed E. Khidr
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Crank shaft length, connecting rod length, crank angle, engine rpm, cylinder bore, mass of piston and compression ratio are the inputs that can control the performance of the slider crank mechanism and then its efficiency. Several combinations of these seven inputs are used and compared. The throughput engine torque predicted by the simulation is analyzed through two different regression models, with and without interaction terms, developed according to multi-linear regression using LU decomposition to solve system of algebraic equations. These models are validated. A regression model in seven inputs including their interaction terms lowered the polynomial degree from 3rd degree to 1st degree and suggested valid predictions and stable explanations.
Keywords: Design of experiments, regression analysis, SI Engine, statistical modeling.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 120110095 Optimal Control Strategies for Speed Control of Permanent-Magnet Synchronous Motor Drives
Authors: Roozbeh Molavi, Davood A. Khaburi
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The permanent magnet synchronous motor (PMSM) is very useful in many applications. Vector control of PMSM is popular kind of its control. In this paper, at first an optimal vector control for PMSM is designed and then results are compared with conventional vector control. Then, it is assumed that the measurements are noisy and linear quadratic Gaussian (LQG) methodology is used to filter the noises. The results of noisy optimal vector control and filtered optimal vector control are compared to each other. Nonlinearity of PMSM and existence of inverter in its control circuit caused that the system is nonlinear and time-variant. With deriving average model, the system is changed to nonlinear time-invariant and then the nonlinear system is converted to linear system by linearization of model around average values. This model is used to optimize vector control then two optimal vector controls are compared to each other. Simulation results show that the performance and robustness to noise of the control system has been highly improved.Keywords: Kalman filter, Linear quadratic Gaussian (LQG), Linear quadratic regulator (LQR), Permanent-Magnet synchronousmotor (PMSM).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 296610094 On Problem of Parameters Identification of Dynamic Object
Authors: Kamil Aida-zade, C. Ardil
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In this paper, some problem formulations of dynamic object parameters recovery described by non-autonomous system of ordinary differential equations with multipoint unshared edge conditions are investigated. Depending on the number of additional conditions the problem is reduced to an algebraic equations system or to a problem of quadratic programming. With this purpose the paper offers a new scheme of the edge conditions transfer method called by conditions shift. The method permits to get rid from differential links and multipoint unshared initially-edge conditions. The advantage of the proposed approach is concluded by capabilities of reduction of a parametric identification problem to essential simple problems of the solution of an algebraic system or quadratic programming.Keywords: dynamic objects, ordinary differential equations, multipoint unshared edge conditions, quadratic programming, conditions shift
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 142610093 Modeling And Analysis of Simple Open Cycle Gas Turbine Using Graph Networks
Authors: Naresh Yadav, I.A. Khan, Sandeep Grover
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This paper presents a unified approach based graph theory and system theory postulates for the modeling and analysis of Simple open cycle Gas turbine system. In the present paper, the simple open cycle gas turbine system has been modeled up to its subsystem level and system variables have been identified to develop the process subgraphs. The theorems and algorithms of the graph theory have been used to represent behavioural properties of the system like rate of heat and work transfers rates, pressure drops and temperature drops in the involved processes of the system. The processes have been represented as edges of the process subgraphs and their limits as the vertices of the process subgraphs. The system across variables and through variables has been used to develop terminal equations of the process subgraphs of the system. The set of equations developed for vertices and edges of network graph are used to solve the system for its process variables.Keywords: Simple open cycle gas turbine, Graph theoretic approach, process subgraphs, gas turbines system modeling, systemtheory
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 257910092 A Necessary Condition for the Existence of Chaos in Fractional Order Delay Differential Equations
Authors: Sachin Bhalekar
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In this paper we propose a necessary condition for the existence of chaos in delay differential equations of fractional order. To explain the proposed theory, we discuss fractional order Liu system and financial system involving delay.
Keywords: Caputo derivative, delay, stability, chaos.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 262510091 Numerical Modeling of Natural Convection on Various Configuration of Rectangular Fin Arrays on Vertical Base Plates
Authors: H.R.Goshayeshi, M.Fahim inia, M.M.Naserian
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In this research, the laminar heat transfer of natural convection on vertical surfaces has been investigated. Most of the studies on natural convection have been considered constantly whereas velocity and temperature domain, do not change with time, transient one are used a lot. Governing equations are solved using a finite volume approach. The convective terms are discretized using the power-law scheme, whereas for diffusive terms the central difference is employed. Coupling between the velocity and pressure is made with SIMPLE algorithm. The resultant system of discretized linear algebraic equations is solved with an alternating direction implicit scheme. Then a configuration of rectangular fins is put in different ways on the surface and heat transfer of natural convection on these surfaces without sliding is studied and finally optimization is done.
Keywords: Natural convection, vertical surfaces, SIMPLE algorithm, Rectangular fins.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 151410090 An Efficient Computational Algorithm for Solving the Nonlinear Lane-Emden Type Equations
Authors: Gholamreza Hojjati, Kourosh Parand
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In this paper we propose a class of second derivative multistep methods for solving some well-known classes of Lane- Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-Emden type equations.
Keywords: Lane-Emden type equations, nonlinear ODE, stiff problems, multistep methods, astrophysics.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 312410089 Equations of Pulse Propagation in Three-Layer Structure of As2S3 Chalcogenide Plasmonic Nano-Waveguides
Authors: Leila Motamed-Jahromi, Mohsen Hatami, Alireza Keshavarz
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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, propagation equation, plasmonic waveguide.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 123110088 New Laguerre-s Type Method for Solving of a Polynomial Equations Systems
Authors: Oleksandr Poliakov, Yevgen Pashkov, Marina Kolesova, Olena Chepenyuk, Mykhaylo Kalinin, Vadym Kramar
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In this paper we present a substantiation of a new Laguerre-s type iterative method for solving of a nonlinear polynomial equations systems with real coefficients. The problems of its implementation, including relating to the structural choice of initial approximations, were considered. Test examples demonstrate the effectiveness of the method at the solving of many practical problems solving.Keywords: Iterative method, Laguerre's method, Newton's method, polynomial equation, system of equations
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 144210087 Optimum Parameter of a Viscous Damper for Seismic and Wind Vibration
Authors: Soltani Amir, Hu Jiaxin
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Determination of optimal parameters of a passive control system device is the primary objective of this study. Expanding upon the use of control devices in wind and earthquake hazard reduction has led to development of various control systems. The advantage of non-linearity characteristics in a passive control device and the optimal control method using LQR algorithm are explained in this study. Finally, this paper introduces a simple approach to determine optimum parameters of a nonlinear viscous damper for vibration control of structures. A MATLAB program is used to produce the dynamic motion of the structure considering the stiffness matrix of the SDOF frame and the non-linear damping effect. This study concluded that the proposed system (variable damping system) has better performance in system response control than a linear damping system. Also, according to the energy dissipation graph, the total energy loss is greater in non-linear damping system than other systems.
Keywords: Passive Control System, Damping Devices, Viscous Dampers, Control Algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 354210086 Stabilization of the Lorenz Chaotic Equations by Fuzzy Controller
Authors: Behrooz Rezaie, Zahra Rahmani Cherati, Mohammad Reza Jahed Motlagh, Mohammad Farrokhi
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In this paper, a fuzzy controller is designed for stabilization of the Lorenz chaotic equations. A simple Mamdani inference method is used for this purpose. This method is very simple and applicable for complex chaotic systems and it can be implemented easily. The stability of close loop system is investigated by the Lyapunov stabilization criterion. A Lyapunov function is introduced and the global stability is proven. Finally, the effectiveness of this method is illustrated by simulation results and it is shown that the performance of the system is improved.Keywords: Chaotic system, Fuzzy control, Lorenz equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 197810085 Improved Asymptotic Stability Criteria for Uncertain Neutral Systems with Time-varying Discrete Delays
Authors: Changchun Shen, Shouming Zhong
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This paper investigates the robust stability of uncertain neutral system with time-varying delay. By using Lyapunov method and linear matrix inequality technology, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs), which can be easy to check the robust stability of the considered systems. Numerical examples are given to indicate significant improvements over some existing results.
Keywords: Neutral system, linear matrix inequalities, Lyapunov, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 145610084 Boundary-Element-Based Finite Element Methods for Helmholtz and Maxwell Equations on General Polyhedral Meshes
Authors: Dylan M. Copeland
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We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.
Keywords: Boundary elements, finite elements, Helmholtz equation, Maxwell equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 168410083 A High Order Theory for Functionally Graded Shell
Authors: V. V. Zozulya
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New theory for functionally graded (FG) shell based on expansion of the equations of elasticity for functionally graded materials (GFMs) into Legendre polynomials series has been developed. Stress and strain tensors, vectors of displacements, traction and body forces have been expanded into Legendre polynomials series in a thickness coordinate. In the same way functions that describe functionally graded relations has been also expanded. Thereby all equations of elasticity including Hook-s law have been transformed to corresponding equations for Fourier coefficients. Then system of differential equations in term of displacements and boundary conditions for Fourier coefficients has been obtained. Cases of the first and second approximations have been considered in more details. For obtained boundary-value problems solution finite element (FE) has been used of Numerical calculations have been done with Comsol Multiphysics and Matlab.
Keywords: Shell, FEM, FGM, legendre polynomial.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 154210082 Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations
Authors: Fuziyah Ishak, Siti Norazura Ahmad
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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.
Keywords: Accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 159310081 The Validity Range of LSDP Robust Controller by Exploiting the Gap Metric Theory
Authors: Ali Ameur Haj Salah, Tarek Garna, Hassani Messaoud
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This paper attempts to define the validity domain of LSDP (Loop Shaping Design Procedure) controller system, by determining the suitable uncertainty region, so that linear system be stable. Indeed the LSDP controller cannot provide stability for any perturbed system. For this, we will use the gap metric tool that is introduced into the control literature for studying robustness properties of feedback systems with uncertainty. A 2nd order electric linear system example is given to define the validity domain of LSDP controller and effectiveness gap metric.
Keywords: LSDP, Gap metric, Robust Control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 147010080 Simplex Method for Fuzzy Variable Linear Programming Problems
Authors: S.H. Nasseri, E. Ardil
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Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.
Keywords: Fuzzy variable linear programming, fuzzy number, ranking function, simplex method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 329810079 Using Finite Element Method for Determination of Poles Number in Optimal Design of Linear Motor
Authors: Abdolamir Nekoubin
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One of Effective parameters on the performance of linear induction motors is number of poles which must be selected and optimized to increase power efficiency and motor performance significantly. In this paper a double-sided linear induction motor with different poles number by using MAXWELL3D software is designed and with finite element method is analyzed electromagnetically. Then for dynamic simulation, linear motor by using MATLAB software is simulated. The results show that by adding poles number, system time response is increased and motor after more time reaches to steady state. Also propulsion force of motor is increased.
Keywords: Linear motor, poles number, finite element method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 215110078 The Pell Equation x2 − (k2 − k)y2 = 2t
Authors: Ahmet Tekcan
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Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k2 - k. In the first section we give some preliminaries from Pell equations x2 - dy2 = 1 and x2 - dy2 = N, where N be any fixed positive integer. In the second section, we consider the integer solutions of Pell equations x2 - dy2 = 1 and x2 - dy2 = 2t. We give a method for the solutions of these equations. Further we derive recurrence relations on the solutions of these equationsKeywords: Pell equation, solutions of Pell equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 142310077 Economic Dispatch Fuzzy Linear Regression and Optimization
Authors: A. K. Al-Othman
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This study presents a new approach based on Tanaka's fuzzy linear regression (FLP) algorithm to solve well-known power system economic load dispatch problem (ELD). Tanaka's fuzzy linear regression (FLP) formulation will be employed to compute the optimal solution of optimization problem after linearization. The unknowns are expressed as fuzzy numbers with a triangular membership function that has middle and spread value reflected on the unknowns. The proposed fuzzy model is formulated as a linear optimization problem, where the objective is to minimize the sum of the spread of the unknowns, subject to double inequality constraints. Linear programming technique is employed to obtain the middle and the symmetric spread for every unknown (power generation level). Simulation results of the proposed approach will be compared with those reported in literature.Keywords: Economic Dispatch, Fuzzy Linear Regression (FLP)and Optimization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 225010076 Some Results on Parallel Alternating Methods
Authors: Guangbin Wang, Fuping Tan
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In this paper, we investigate two parallel alternating methods for solving the system of linear equations Ax = b and give convergence theorems for the parallel alternating methods when the coefficient matrix is a nonsingular H-matrix. Furthermore, we give one example to show our results.
Keywords: Nonsingular H-matrix, parallel alternating method, convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 106910075 Some Third Order Methods for Solving Systems of Nonlinear Equations
Authors: Janak Raj Sharma, Rajni Sharma
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Based on Traub-s methods for solving nonlinear equation f(x) = 0, we develop two families of third-order methods for solving system of nonlinear equations F(x) = 0. The families include well-known existing methods as special cases. The stability is corroborated by numerical results. Comparison with well-known methods shows that the present methods are robust. These higher order methods may be very useful in the numerical applications requiring high precision in their computations because these methods yield a clear reduction in number of iterations.Keywords: Nonlinear equations and systems, Newton's method, fixed point iteration, order of convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 215310074 Conditions on Blind Source Separability of Linear FIR-MIMO Systems with Binary Inputs
Authors: Jiashan Tang
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In this note, we investigate the blind source separability of linear FIR-MIMO systems. The concept of semi-reversibility of a system is presented. It is shown that for a semi-reversible system, if the input signals belong to a binary alphabet, then the source data can be blindly separated. One sufficient condition for a system to be semi-reversible is obtained. It is also shown that the proposed criteria is weaker than that in the literature which requires that the channel matrix is irreducible/invertible or reversible.
Keywords: Blind source separable, FIR-MIMO system, Binary input, Bezout equality.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 126910073 Constructing Distinct Kinds of Solutions for the Time-Dependent Coefficients Coupled Klein-Gordon-Schrödinger Equation
Authors: Anupma Bansal
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We seek exact solutions of the coupled Klein-Gordon-Schrödinger equation with variable coefficients with the aid of Lie classical approach. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of coupled Klein-Gordon-Schrödinger equations involving some special functions such as Airy wave functions, Bessel functions, Mathieu functions etc.
Keywords: Klein-Gordon-Schödinger Equation, Lie Classical Method, Exact Solutions
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 448510072 Approximation Approach to Linear Filtering Problem with Correlated Noise
Authors: Hong Son Hoang, Remy Baraille
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The (sub)-optimal soolution of linear filtering problem with correlated noises is considered. The special recursive form of the class of filters and criteria for selecting the best estimator are the essential elements of the design method. The properties of the proposed filter are studied. In particular, for Markovian observation noise, the approximate filter becomes an optimal Gevers-Kailath filter subject to a special choice of the parameter in the class of given linear recursive filters.Keywords: Linear dynamical system, filtering, minimum meansquare filter, correlated noise
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 133310071 TS Fuzzy Controller to Stochastic Systems
Authors: Joabe Silva, Ginalber Serra
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This paper proposes the analysis and design of robust fuzzy control to Stochastic Parametrics Uncertaint Linear systems. This system type to be controlled is partitioned into several linear sub-models, in terms of transfer function, forming a convex polytope, similar to LPV (Linear Parameters Varying) system. Once defined the linear sub-models of the plant, these are organized into fuzzy Takagi- Sugeno (TS) structure. From the Parallel Distributed Compensation (PDC) strategy, a mathematical formulation is defined in the frequency domain, based on the gain and phase margins specifications, to obtain robust PI sub-controllers in accordance to the Takagi- Sugeno fuzzy model of the plant. The main results of the paper are based on the robust stability conditions with the proposal of one Axiom and two Theorems.Keywords: Fuzzy Systems; Robust Stability, Stochastic Control, Stochastic Process
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 165810070 A Study of Hamilton-Jacobi-Bellman Equation Systems Arising in Differential Game Models of Changing Society
Authors: Weihua Ruan, Kuan-Chou Chen
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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: Differential games, Hamilton-Jacobi-Bellman equations, infinite horizon, political-economy models.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 101210069 Prediction of the Total Decay Heat from Fast Neutron Fission of 235U and 239Pu
Authors: Sherif. S. Nafee, Ameer. K. Al-Ramady, Salem. A. Shaheen
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The analytical prediction of the decay heat results from the fast neutron fission of actinides was initiated under a project, 10-MAT1134-3, funded by king Abdulaziz City of Science and Technology (KASCT), Long-Term Comprehensive National Plan for Science, Technology and Innovations, managed by a team from King Abdulaziz University (KAU), Saudi Arabia, and supervised by Argonne National Laboratory (ANL) has collaborated with KAU's team to assist in the computational analysis. In this paper, the numerical solution of coupled linear differential equations that describe the decays and buildups of minor fission product MFA, has been used to predict the total decay heat and its components from the fast neutron fission of 235U and 239Pu. The reliability of the present approach is illustrated via systematic comparisons with the measurements reported by the University of Tokyo, in YAYOI reactor.Keywords: Decay heat, fast neutron fission, and Numerical Solution of Linear Differential Equations.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 143910068 Numerical Solving of General Fuzzy Linear Systems by Huang's Method
Authors: S. J. Hosseini Ghoncheh, M. Paripour
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In this paper the Huang-s method for solving a m×n fuzzy linear system when, m≤ n, is considered. The method in detail is discussed and illustrated by solving some numerical examples.
Keywords: Fuzzy number, fuzzy linear systems, Huang's method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 124410067 Automatic Iterative Methods for the Multivariate Solution of Nonlinear Algebraic Equations
Authors: Rafat Alshorman, Safwan Al-Shara', I. Obeidat
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Most real world systems express themselves formally as a set of nonlinear algebraic equations. As applications grow, the size and complexity of these equations also increase. In this work, we highlight the key concepts in using the homotopy analysis method as a methodology used to construct efficient iteration formulas for nonlinear equations solving. The proposed method is experimentally characterized according to a set of determined parameters which affect the systems. The experimental results show the potential and limitations of the new method and imply directions for future work.Keywords: Nonlinear Algebraic Equations, Iterative Methods, Homotopy Analysis Method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1869