Pub Date : 2015-05-15DOI: 10.4236/IJMNTA.2015.42008
O. Vukovic
Navier-Stokes equation has for a long time been considered as one of the greatest unsolved problems in three and more dimensions. This paper proposes a solution to the aforementioned equation on R3. It introduces results from the previous literature and it proves the existence and uniqueness of smooth solution. Firstly, the concept of turbulent solution is defined. It is proved that turbulent solutions become strong solutions after some time in Navier-Stokes set of equations. However, in order to define the turbulent solution, the decay or blow-up time of solution must be examined. Differential inequality is defined and it is proved that solution of Navier-Stokes equation exists in a finite time although it exhibits blow-up solutions. The equation is introduced that establishes the distance between the strong solutions of Navier-Stokes equation and heat equation. As it is demonstrated, as the time goes to infinity, the distance decreases to zero and the solution of heat equation is identical to the solution of N-S equation. As the solution of heat equation is defined in the heat-sphere, after its analysis, it is proved that as the time goes to infinity, solution converges to the stationary state. The solution has a finite τ time and it exists when τ → ∞ that implies that it exists and it is periodic. The aforementioned statement proves the existence and smoothness of solution of Navier-Stokes equation on R3 and represents a major breakthrough in fluid dynamics and turbulence analysis.
{"title":"Existence and Smoothness of Solution of Navier-Stokes Equation on R 3","authors":"O. Vukovic","doi":"10.4236/IJMNTA.2015.42008","DOIUrl":"https://doi.org/10.4236/IJMNTA.2015.42008","url":null,"abstract":"Navier-Stokes equation has for a long time been considered as one of the greatest unsolved problems in three and more dimensions. This paper proposes a solution to the aforementioned equation on R3. It introduces results from the previous literature and it proves the existence and uniqueness of smooth solution. Firstly, the concept of turbulent solution is defined. It is proved that turbulent solutions become strong solutions after some time in Navier-Stokes set of equations. However, in order to define the turbulent solution, the decay or blow-up time of solution must be examined. Differential inequality is defined and it is proved that solution of Navier-Stokes equation exists in a finite time although it exhibits blow-up solutions. The equation is introduced that establishes the distance between the strong solutions of Navier-Stokes equation and heat equation. As it is demonstrated, as the time goes to infinity, the distance decreases to zero and the solution of heat equation is identical to the solution of N-S equation. As the solution of heat equation is defined in the heat-sphere, after its analysis, it is proved that as the time goes to infinity, solution converges to the stationary state. The solution has a finite τ time and it exists when τ → ∞ that implies that it exists and it is periodic. The aforementioned statement proves the existence and smoothness of solution of Navier-Stokes equation on R3 and represents a major breakthrough in fluid dynamics and turbulence analysis.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"04 1","pages":"117-126"},"PeriodicalIF":0.0,"publicationDate":"2015-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70705779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-05-15DOI: 10.4236/IJMNTA.2015.42011
A. Aicha, Bnhamed Mouna, S. Lassâad
This paper discusses a comparative study of two modeling methods based on multimodel approach. The first is based on C-means clustering algorithm and the second is based on K-means clustering algorithm. The two methods are experimentally applied to an induction motor. The multimodel modeling consists in representing the IM through a finite number of local models. This number of models has to be initially fixed, for which a subtractive clustering is necessary. Then both C-means and K-means clustering are exploited to determine the clusters. These clusters will be then exploited on the basis of structural and parametric identification to determine the local models that are combined, finally, to form the multimodel. The experimental study is based on MATLAB/SIMULINK environment and a DSpace scheme with DS1104 controller board. Experimental results approve that the multimodel based on K-means clustering algorithm is the most efficient.
{"title":"Induction Motor Modeling Based on a Fuzzy Clustering Multi-Model—A Real-Time Validation","authors":"A. Aicha, Bnhamed Mouna, S. Lassâad","doi":"10.4236/IJMNTA.2015.42011","DOIUrl":"https://doi.org/10.4236/IJMNTA.2015.42011","url":null,"abstract":"This paper discusses a comparative study of two modeling methods based on multimodel approach. The first is based on C-means clustering algorithm and the second is based on K-means clustering algorithm. The two methods are experimentally applied to an induction motor. The multimodel modeling consists in representing the IM through a finite number of local models. This number of models has to be initially fixed, for which a subtractive clustering is necessary. Then both C-means and K-means clustering are exploited to determine the clusters. These clusters will be then exploited on the basis of structural and parametric identification to determine the local models that are combined, finally, to form the multimodel. The experimental study is based on MATLAB/SIMULINK environment and a DSpace scheme with DS1104 controller board. Experimental results approve that the multimodel based on K-means clustering algorithm is the most efficient.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"04 1","pages":"153-160"},"PeriodicalIF":0.0,"publicationDate":"2015-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70706376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-05-15DOI: 10.4236/IJMNTA.2015.42010
Liang Guo, Zhaoqin Yuan, Guoguang Lin
In this paper, firstly, some priori estimates are obtained for the existence and uniqueness of solutions of a nonlinear viscoelastic wave equation with strong damping, linear damping and source terms. Then we study the global attractors of the equation.
{"title":"The Global Attractors for a Nonlinear Viscoelastic Wave Equation with Strong Damping and Linear Damping and Source Terms","authors":"Liang Guo, Zhaoqin Yuan, Guoguang Lin","doi":"10.4236/IJMNTA.2015.42010","DOIUrl":"https://doi.org/10.4236/IJMNTA.2015.42010","url":null,"abstract":"In this paper, firstly, some priori estimates are obtained for the existence and uniqueness of solutions of a nonlinear viscoelastic wave equation with strong damping, linear damping and source terms. Then we study the global attractors of the equation.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"04 1","pages":"142-152"},"PeriodicalIF":0.0,"publicationDate":"2015-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70705883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-05-15DOI: 10.4236/IJMNTA.2015.42012
A. Aicha, B. Mouna, S. Lassâad
This paper studies the problem of diagnosis strategy for a doubly fed induction motor (DFIM) sensor faults. This strategy is based on unknown input proportional integral (PI) multiobserver. Thecontribution of this paper is on one hand the creation of a new DFIM model based on multi-model approach and, on the other hand, the synthesis of an adaptive PI multi-observer. The DFIM Volt per Hertz drive system behaves as a nonlinear complex system. It consists of a DFIM powered through a controlled PWM Voltage Source Inverter (VSI). The need of a sensorless drive requires soft sensors such as estimators or observers. In particular, an adaptive Proportional-Integral multi-observer is synthesized in order to estimate the DFIM’s outputs which are affected by different faults and to generate the different residual signals symptoms of sensor fault occurrence. The convergence of the estimation error is guaranteed by using the Lyapunov’s based theory. The proposed diagnosis approach is experimentally validated on a 1 kW Induction motor. Obtained simulation results confirm that the adaptive PI multiobserver consent to accomplish the detection, isolation and fault identification tasks with high dynamic performances.
{"title":"A DFIM Sensor Faults Multi-Model Diagnosis Approach Based on an Adaptive PI Multiobserver—Experimental Validation","authors":"A. Aicha, B. Mouna, S. Lassâad","doi":"10.4236/IJMNTA.2015.42012","DOIUrl":"https://doi.org/10.4236/IJMNTA.2015.42012","url":null,"abstract":"This paper studies the problem of diagnosis strategy for a doubly fed induction motor (DFIM) sensor faults. This strategy is based on unknown input proportional integral (PI) multiobserver. Thecontribution of this paper is on one hand the creation of a new DFIM model based on multi-model approach and, on the other hand, the synthesis of an adaptive PI multi-observer. The DFIM Volt per Hertz drive system behaves as a nonlinear complex system. It consists of a DFIM powered through a controlled PWM Voltage Source Inverter (VSI). The need of a sensorless drive requires soft sensors such as estimators or observers. In particular, an adaptive Proportional-Integral multi-observer is synthesized in order to estimate the DFIM’s outputs which are affected by different faults and to generate the different residual signals symptoms of sensor fault occurrence. The convergence of the estimation error is guaranteed by using the Lyapunov’s based theory. The proposed diagnosis approach is experimentally validated on a 1 kW Induction motor. Obtained simulation results confirm that the adaptive PI multiobserver consent to accomplish the detection, isolation and fault identification tasks with high dynamic performances.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"04 1","pages":"161-178"},"PeriodicalIF":0.0,"publicationDate":"2015-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70706413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-02-16DOI: 10.4236/IJMNTA.2015.41003
Baishun Liu
In conjunction with linear general integral control, this paper proposes a fire-new control design technique, named Equal ratio gain technique, and then develops two kinds of control design methods, that is, Decomposition and Synthetic methods, for a class of uncertain nonlinear system. By Routh’s stability criterion, we demonstrate that a canonical system matrix can be designed to be always Hurwitz as any row controller gains, or controller and its integrator gains increase with the same ratio. By solving Lyapunov equation, we demonstrate that as any row controller gains, or controller and its integrator gains of a canonical system matrix tend to infinity with the same ratio, if it is always Hurwitz, and then the same row solutions of Lyapunov equation all tend to zero. By Equal ratio gain technique and Lyapunov method, theorems to ensure semi-globally asymptotic stability are established in terms of some bounded information. Moreover, the striking robustness of linear general integral control and PID control is clearly illustrated by Equal ratio gain technique. Theoretical analysis, design example and simulation results showed that Equal ratio gain technique is a powerful tool to solve the control design problem of uncertain nonlinear system.
{"title":"Equal Ratio Gain Technique and Its Application in Linear General Integral Control","authors":"Baishun Liu","doi":"10.4236/IJMNTA.2015.41003","DOIUrl":"https://doi.org/10.4236/IJMNTA.2015.41003","url":null,"abstract":"In conjunction with linear general integral control, this paper proposes a fire-new control design technique, named Equal ratio gain technique, and then develops two kinds of control design methods, that is, Decomposition and Synthetic methods, for a class of uncertain nonlinear system. By Routh’s stability criterion, we demonstrate that a canonical system matrix can be designed to be always Hurwitz as any row controller gains, or controller and its integrator gains increase with the same ratio. By solving Lyapunov equation, we demonstrate that as any row controller gains, or controller and its integrator gains of a canonical system matrix tend to infinity with the same ratio, if it is always Hurwitz, and then the same row solutions of Lyapunov equation all tend to zero. By Equal ratio gain technique and Lyapunov method, theorems to ensure semi-globally asymptotic stability are established in terms of some bounded information. Moreover, the striking robustness of linear general integral control and PID control is clearly illustrated by Equal ratio gain technique. Theoretical analysis, design example and simulation results showed that Equal ratio gain technique is a powerful tool to solve the control design problem of uncertain nonlinear system.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"04 1","pages":"21-36"},"PeriodicalIF":0.0,"publicationDate":"2015-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70705599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-02-16DOI: 10.4236/IJMNTA.2015.41001
Mingjun Wang
In the paper, impulsive synchronization of two hyperchaotic Lu systems with different initial conditions is studied. The sufficient conditions on feedback strength and impulsive distances are established from two different angles to guarantee the synchronization. The relevant theoretical proofs are presented. Numerical simulations show the effectiveness of the methods.
{"title":"Impulsive Synchronization of Hyperchaotic Lü Systems with Two Methods","authors":"Mingjun Wang","doi":"10.4236/IJMNTA.2015.41001","DOIUrl":"https://doi.org/10.4236/IJMNTA.2015.41001","url":null,"abstract":"In the paper, impulsive synchronization of two hyperchaotic Lu systems \u0000with different initial conditions is studied. The sufficient conditions on \u0000feedback strength and impulsive distances are established from two different \u0000angles to guarantee the synchronization. The relevant theoretical proofs are \u0000presented. Numerical simulations show the effectiveness of the methods.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"04 1","pages":"1-9"},"PeriodicalIF":0.0,"publicationDate":"2015-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70705996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-02-16DOI: 10.4236/IJMNTA.2015.41004
M. Abdelrahman, E. Zahran, M. Khater
The exp(-φ(ξ))-expansion method is used as the first time to investigate the wave solution of a nonlinear dynamical system in a new double-Chain model of DNA and a diffusive predator-prey system. The proposed method also can be used for many other nonlinear evolution equations.
{"title":"The exp(-φ(ξ))-Expansion Method and Its Application for Solving Nonlinear Evolution Equations","authors":"M. Abdelrahman, E. Zahran, M. Khater","doi":"10.4236/IJMNTA.2015.41004","DOIUrl":"https://doi.org/10.4236/IJMNTA.2015.41004","url":null,"abstract":"The exp(-φ(ξ))-expansion method is used as the first time to investigate the wave solution of a nonlinear dynamical system in a new double-Chain model of DNA and a diffusive predator-prey system. The proposed method also can be used for many other nonlinear evolution equations.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"04 1","pages":"37-47"},"PeriodicalIF":0.0,"publicationDate":"2015-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4236/IJMNTA.2015.41004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70705712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-02-16DOI: 10.4236/IJMNTA.2015.41005
Jian Su, H. Fan, Weibing Feng, Hao Chen, Kaitai Li
In this paper, the boundary layer equations (abbreviation BLE) for exterior flow around an obstacle are established using semi-geodesic coordinate system (S-coordinate) based on the curved two dimensional surface of the obstacle. BLE are nonlinear partial differential equations on unknown normal viscous stress tensor and pressure on the obstacle and the existence of solution of BLE is proved. In addition a dimensional split method for dimensional three Navier-Stokes equations is established by applying several 2D-3C partial differential equations on two dimensional manifolds to approach 3D Navier-Stokes equations. The examples for the exterior flow around spheroid and ellipsoid are presents here.
{"title":"The Boundary Layer Equations and a Dimensional Split Method for Navier-Stokes Equations in Exterior Domain of a Spheroid and Ellipsoid","authors":"Jian Su, H. Fan, Weibing Feng, Hao Chen, Kaitai Li","doi":"10.4236/IJMNTA.2015.41005","DOIUrl":"https://doi.org/10.4236/IJMNTA.2015.41005","url":null,"abstract":"In this paper, the boundary layer equations (abbreviation BLE) for exterior flow around an obstacle are established using semi-geodesic coordinate system (S-coordinate) based on the curved two dimensional surface of the obstacle. BLE are nonlinear partial differential equations on unknown normal viscous stress tensor and pressure on the obstacle and the existence of solution of BLE is proved. In addition a dimensional split method for dimensional three Navier-Stokes equations is established by applying several 2D-3C partial differential equations on two dimensional manifolds to approach 3D Navier-Stokes equations. The examples for the exterior flow around spheroid and ellipsoid are presents here.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"4 1","pages":"48-87"},"PeriodicalIF":0.0,"publicationDate":"2015-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70706015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-02-16DOI: 10.4236/IJMNTA.2015.41006
Fidel Contreras López, Eusebio Tapia, F. Ongay, M. Agüero
The improved Boussinesq equation is solved with classical finite element method using the most basic Lagrange element k = 1, which leads us to a second order nonlinear ordinary differential equations system in time; this can be solved by any standard accurate numerical method for example Runge-Kutta-Fehlberg. The technique is validated with a typical example and a fourth order convergence in space is confirmed; the 1- and 2-soliton solutions are used to simulate wave travel, wave splitting and interaction; solution blow up is described graphically. The computer symbolic system MathLab is quite used for numerical simulation in this paper; the known results in the bibliography are confirmed.
{"title":"The k = 1 Finite Element Numerical Solution for the Improved Boussinesq Equation","authors":"Fidel Contreras López, Eusebio Tapia, F. Ongay, M. Agüero","doi":"10.4236/IJMNTA.2015.41006","DOIUrl":"https://doi.org/10.4236/IJMNTA.2015.41006","url":null,"abstract":"The improved Boussinesq equation is solved with classical finite element method using the most basic Lagrange element k = 1, which leads us to a second order nonlinear ordinary differential equations system in time; this can be solved by any standard accurate numerical method for example Runge-Kutta-Fehlberg. The technique is validated with a typical example and a fourth order convergence in space is confirmed; the 1- and 2-soliton solutions are used to simulate wave travel, wave splitting and interaction; solution blow up is described graphically. The computer symbolic system MathLab is quite used for numerical simulation in this paper; the known results in the bibliography are confirmed.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"04 1","pages":"88-99"},"PeriodicalIF":0.0,"publicationDate":"2015-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70705727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2014-11-07DOI: 10.4236/IJMNTA.2014.35021
M. Khlifi, B. Alshammari
In this paper modelling and analysis in autonomous mode of dual three-phase induction generator (DTPIG) with a new algorithm have been done. We develop the steady state model of a dual three-phase self-excited induction generator for stand-alone renewable generation dispensing with the segregating real and imaginary components of the complex impedance of the induction generator. The obtained admittance yields the adequate magnetizing reactance and the frequency. These two key parameters are then used to compute the self-excitation process requirements in terms of the prime mover speed, the capacitance and the load impedance on the one hand and to predict the generator steady state performance parameters on the other. Steady state performances and characteristics of different configurations are clearly examined and compared. The analytical results are found to be in good agreement with experimental results.
{"title":"Steady State Analysis of an Isolated Self-Excited Dual Three-Phase Induction Generator for Renewable Energy","authors":"M. Khlifi, B. Alshammari","doi":"10.4236/IJMNTA.2014.35021","DOIUrl":"https://doi.org/10.4236/IJMNTA.2014.35021","url":null,"abstract":"In this paper modelling and analysis in autonomous mode of dual three-phase induction generator (DTPIG) with a new algorithm have been done. We develop the steady state model of a dual three-phase self-excited induction generator for stand-alone renewable generation dispensing with the segregating real and imaginary components of the complex impedance of the induction generator. The obtained admittance yields the adequate magnetizing reactance and the frequency. These two key parameters are then used to compute the self-excitation process requirements in terms of the prime mover speed, the capacitance and the load impedance on the one hand and to predict the generator steady state performance parameters on the other. Steady state performances and characteristics of different configurations are clearly examined and compared. The analytical results are found to be in good agreement with experimental results.","PeriodicalId":69680,"journal":{"name":"现代非线性理论与应用(英文)","volume":"42 1","pages":"191-198"},"PeriodicalIF":0.0,"publicationDate":"2014-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70705469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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