Search results for: Non-linear equation
1623 Evaluation of Linear and Geometrically Nonlinear Static and Dynamic Analysis of Thin Shells by Flat Shell Finite Elements
Authors: Djamel Boutagouga, Kamel Djeghaba
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The choice of finite element to use in order to predict nonlinear static or dynamic response of complex structures becomes an important factor. Then, the main goal of this research work is to focus a study on the effect of the in-plane rotational degrees of freedom in linear and geometrically non linear static and dynamic analysis of thin shell structures by flat shell finite elements. In this purpose: First, simple triangular and quadrilateral flat shell finite elements are implemented in an incremental formulation based on the updated lagrangian corotational description for geometrically nonlinear analysis. The triangular element is a combination of DKT and CST elements, while the quadrilateral is a combination of DKQ and the bilinear quadrilateral membrane element. In both elements, the sixth degree of freedom is handled via introducing fictitious stiffness. Secondly, in the same code, the sixth degrees of freedom in these elements is handled differently where the in-plane rotational d.o.f is considered as an effective d.o.f in the in-plane filed interpolation. Our goal is to compare resulting shell elements. Third, the analysis is enlarged to dynamic linear analysis by direct integration using Newmark-s implicit method. Finally, the linear dynamic analysis is extended to geometrically nonlinear dynamic analysis where Newmark-s method is used to integrate equations of motion and the Newton-Raphson method is employed for iterating within each time step increment until equilibrium is achieved. The obtained results demonstrate the effectiveness and robustness of the interpolation of the in-plane rotational d.o.f. and present deficiencies of using fictitious stiffness in dynamic linear and nonlinear analysis.Keywords: Flat shell, dynamic analysis, nonlinear, Newmark, drilling rotation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 29071622 Power Series Solution to Sliding Velocity in Three-Dimensional Multibody Systems with Impact and Friction
Authors: Hesham A. Elkaranshawy, Amr M. Abdelrazek, Hosam M. Ezzat
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The system of ordinary nonlinear differential equations describing sliding velocity during impact with friction for a three-dimensional rigid-multibody system is developed. No analytical solutions have been obtained before for this highly nonlinear system. Hence, a power series solution is proposed. Since the validity of this solution is limited to its convergence zone, a suitable time step is chosen and at the end of it a new series solution is constructed. For a case study, the trajectory of the sliding velocity using the proposed method is built using 6 time steps, which coincides with a Runge- Kutta solution using 38 time steps.Keywords: Impact with friction, nonlinear ordinary differential equations, power series solutions, rough collision.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19011621 State Feedback Speed Controller for Turbocharged Diesel Engine and Its Robustness
Authors: Dileep Malkhede, Bhartendu Seth
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In this paper, the full state feedback controllers capable of regulating and tracking the speed trajectory are presented. A fourth order nonlinear mean value model of a 448 kW turbocharged diesel engine published earlier is used for the purpose. For designing controllers, the nonlinear model is linearized and represented in state-space form. Full state feedback controllers capable of meeting varying speed demands of drivers are presented. Main focus here is to investigate sensitivity of the controller to the perturbations in the parameters of the original nonlinear model. Suggested controller is shown to be highly insensitive to the parameter variations. This indicates that the controller is likely perform with same accuracy even after significant wear and tear of engine due to its use for years.Keywords: Diesel engine model, Engine speed control, State feedback controller, Controller robustness.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22071620 Simulation of Multiphase Flows Using a Modified Upwind-Splitting Scheme
Authors: David J. Robbins, R. Stewart Cant, Lynn F. Gladden
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A robust AUSM+ upwind discretisation scheme has been developed to simulate multiphase flow using consistent spatial discretisation schemes and a modified low-Mach number diffusion term. The impact of the selection of an interfacial pressure model has also been investigated. Three representative test cases have been simulated to evaluate the accuracy of the commonly-used stiffenedgas equation of state with respect to the IAPWS-IF97 equation of state for water. The algorithm demonstrates a combination of robustness and accuracy over a range of flow conditions, with the stiffened-gas equation tending to overestimate liquid temperature and density profiles.
Keywords: Multiphase flow, AUSM+ scheme, liquid EOS, low Mach number models
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20381619 Aeroelastic Analysis of Engine Nacelle Strake Considering Geometric Nonlinear Behavior
Authors: N. Manoj
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The aeroelastic behavior of engine nacelle strake when subjected to unsteady aerodynamic flows is investigated in this paper. Geometric nonlinear characteristics and modal parameters of nacelle strake are studied when it is under dynamic loading condition. Here, an N-S based Finite Volume solver is coupled with Finite Element (FE) based nonlinear structural solver to investigate the nonlinear characteristics of nacelle strake over a range of dynamic pressures at various phases of flight like takeoff, climb, and cruise conditions. The combination of high fidelity models for both aerodynamics and structural dynamics is used to predict the nonlinearities of strake (chine). The methodology adopted for present aeroelastic analysis is partitioned-based time domain coupled CFD and CSD solvers and it is validated by the consideration of experimental and numerical comparison of aeroelastic data for a cropped delta wing model which has a proven record. The present strake geometry is derived from theoretical formulation. The amplitude and frequency obtained from the coupled solver at various dynamic pressures is discussed, which gives a better understanding of its impact on aerodynamic design-sizing of strake.
Keywords: Aeroelasticity, finite volume, geometric nonlinearity, limit cycle oscillations, strake.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12571618 Digital Image Encryption Scheme using Chaotic Sequences with a Nonlinear Function
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In this study, a system of encryption based on chaotic sequences is described. The system is used for encrypting digital image data for the purpose of secure image transmission. An image secure communication scheme based on Logistic map chaotic sequences with a nonlinear function is proposed in this paper. Encryption and decryption keys are obtained by one-dimensional Logistic map that generates secret key for the input of the nonlinear function. Receiver can recover the information using the received signal and identical key sequences through the inverse system technique. The results of computer simulations indicate that the transmitted source image can be correctly and reliably recovered by using proposed scheme even under the noisy channel. The performance of the system will be discussed through evaluating the quality of recovered image with and without channel noise.Keywords: Digital image, Image encryption, Secure communication
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22251617 Solution of Two-Point Nonlinear Boundary Problems Using Taylor Series Approximation and the Ying Buzu Shu Algorithm
Authors: U. C. Amadi, N. A. Udoh
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One of the major challenges faced in solving initial and boundary problems is how to find approximate solutions with minimal deviation from the exact solution without so much rigor and complications. The Taylor series method provides a simple way of obtaining an infinite series which converges to the exact solution for initial value problems and this method of solution is somewhat limited for a two point boundary problem since the infinite series has to be truncated to include the boundary conditions. In this paper, the Ying Buzu Shu algorithm is used to solve a two point boundary nonlinear diffusion problem for the fourth and sixth order solution and compare their relative error and rate of convergence to the exact solution.
Keywords: Ying Buzu Shu, nonlinear boundary problem, Taylor series algorithm, infinite series.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4381616 Effect of Concrete Nonlinear Parameters on the Seismic Response of Concrete Gravity Dams
Authors: Z. Heirany, M. Ghaemian
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Behavior of dams against the seismic loads has been studied by many researchers. Most of them proposed new numerical methods to investigate the dam safety. In this paper, to study the effect of nonlinear parameters of concrete in gravity dams, a twodimensional approach was used including the finite element method, staggered method and smeared crack approach. Effective parameters in the models are physical properties of concrete such as modulus of elasticity, tensile strength and specific fracture energy. Two different models were used in foundation (mass-less and massed) in order to determine the seismic response of concrete gravity dams. Results show that when the nonlinear analysis includes the dam- foundation interaction, the foundation-s mass, flexibility and radiation damping are important in gravity dam-s response.Keywords: Numerical methods; concrete gravity dams; finiteelement method; boundary condition
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23251615 Analysis of EEG Signals Using Wavelet Entropy and Approximate Entropy: A Case Study on Depression Patients
Authors: Subha D. Puthankattil, Paul K. Joseph
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Analyzing brain signals of the patients suffering from the state of depression may lead to interesting observations in the signal parameters that is quite different from a normal control. The present study adopts two different methods: Time frequency domain and nonlinear method for the analysis of EEG signals acquired from depression patients and age and sex matched normal controls. The time frequency domain analysis is realized using wavelet entropy and approximate entropy is employed for the nonlinear method of analysis. The ability of the signal processing technique and the nonlinear method in differentiating the physiological aspects of the brain state are revealed using Wavelet entropy and Approximate entropy.
Keywords: EEG, Depression, Wavelet entropy, Approximate entropy, Relative Wavelet energy, Multiresolution decomposition.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 36261614 About the Instability Modes of Current Sheet in Wide Range of Frequencies
Authors: V. V. Lyahov, V. M. Neshchadim
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We offer a new technique for research of stability of current sheaths in space plasma taking into account the effect of polarization. At the beginning, the found perturbation of the distribution function is used for calculation of the dielectric permeability tensor, which simulates inhomogeneous medium of a current sheath. Further, we in the usual manner solve the system of Maxwell's equations closed with the material equation. The amplitudes of Fourier perturbations are considered to be exponentially decaying through the current sheath thickness. The dispersion equation follows from the nontrivial solution requirement for perturbations of the electromagnetic field. The resulting dispersion equation allows one to study the temporal and spatial characteristics of instability modes of the current sheath (within the limits of the proposed model) over a wide frequency range, including low frequencies.
Keywords: Current sheath, distribution function, effect of polarization, instability modes, low frequencies, perturbation of electromagnetic field dispersion equation, space plasma, tensor of dielectric permeability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16461613 Positive Solutions for Systems of Nonlinear Third-Order Differential Equations with p-Laplacian
Authors: Li Xiguang
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In this paper, by constructing a special set and utilizing fixed point theory, we study the existence and multiplicity of the positive solutions for systems of nonlinear third-order differential equations with p-laplacian, which improve and generalize the result of related paper.Keywords: p-Laplacian, cone, fixed point theorem, positive solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5821612 A Comparison of Recent Methods for Solving a Model 1D Convection Diffusion Equation
Authors: Ashvin Gopaul, Jayrani Cheeneebash, Kamleshsing Baurhoo
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In this paper we study some numerical methods to solve a model one-dimensional convection–diffusion equation. The semi-discretisation of the space variable results into a system of ordinary differential equations and the solution of the latter involves the evaluation of a matrix exponent. Since the calculation of this term is computationally expensive, we study some methods based on Krylov subspace and on Restrictive Taylor series approximation respectively. We also consider the Chebyshev Pseudospectral collocation method to do the spatial discretisation and we present the numerical solution obtained by these methods.
Keywords: Chebyshev Pseudospectral collocation method, convection-diffusion equation, restrictive Taylor approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16671611 Nonoscillation Criteria for Nonlinear Delay Dynamic Systems on Time Scales
Authors: Xinli Zhang
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In this paper, we consider the nonlinear delay dynamic system xΔ(t) = p(t)f1(y(t)), yΔ(t) = −q(t)f2(x(t − τ )). We obtain some necessary and sufficient conditions for the existence of nonoscillatory solutions with special asymptotic properties of the system. We generalize the known results in the literature. One example is given to illustrate the results.
Keywords: Dynamic system, oscillation, time scales, two-dimensional.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12841610 Sliding Mode Control of Autonomous Underwater Vehicles
Authors: Ahmad Forouzan Tabar, Mohammad Azadi, Alireza Alesaadi
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This paper describes a sliding mode controller for autonomous underwater vehicles (AUVs). The dynamic of AUV model is highly nonlinear because of many factors, such as hydrodynamic drag, damping, and lift forces, Coriolis and centripetal forces, gravity and buoyancy forces, as well as forces from thruster. To address these difficulties, a nonlinear sliding mode controller is designed to approximate the nonlinear dynamics of AUV and improve trajectory tracking. Moreover, the proposed controller can profoundly attenuate the effects of uncertainties and external disturbances in the closed-loop system. Using the Lyapunov theory the boundedness of AUV tracking errors and the stability of the proposed control system are also guaranteed. Numerical simulation studies of an AUV are included to illustrate the effectiveness of the presented approach.
Keywords: Lyapunov stability, autonomous underwater vehicle (AUV), sliding mode controller, electronics engineering.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25811609 Alternating Implicit Block FDTD Method For Scalar Wave Equation
Authors: N. M. Nusi, M. Othman, M. Suleiman, F. Ismail, N. Alias
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In this paper, an alternating implicit block method for solving two dimensional scalar wave equation is presented. The new method consist of two stages for each time step implemented in alternating directions which are very simple in computation. To increase the speed of computation, a group of adjacent points is computed simultaneously. It is shown that the presented method increase the maximum time step size and more accurate than the conventional finite difference time domain (FDTD) method and other existing method of natural ordering.Keywords: FDTD, Scalar wave equation, alternating direction implicit (ADI), alternating group explicit (AGE), asymmetric approximation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18901608 Numerical Solution for Elliptical Crack with Developing Cusps Subject to Shear Loading
Authors: Nik Mohd Asri Nik Long, Koo Lee Feng, Zainidin K. Eshkuvatov, A. A. Khaldjigitov
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This paper study the behavior of the solution at the crack edges for an elliptical crack with developing cusps, Ω in the plane elasticity subjected to shear loading. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over Ω and it is then transformed into a similar equation over a circular region, D, using conformal mapping. An appropriate collocation points are chosen on the region D to reduce the hypersingular integral equation into a system of linear equations with (2N+1)(N+1) unknown coefficients, which will later be used in the determination of shear stress intensity factors and maximum shear stress intensity. Numerical solution for the considered problem are compared with the existing asymptotic solution, and displayed graphically. Our results give a very good agreement to the existing asymptotic solutions.
Keywords: Elliptical crack, stress intensity factors, hyper singular integral equation, shear loading, conformal mapping.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16881607 Optimal Feedback Linearization Control of PEM Fuel Cell
Authors: E. Shahsavari, R. Ghasemi, A. Akramizadeh
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This paper presents a new method to design nonlinear feedback linearization controller for PEMFCs (Polymer Electrolyte Membrane Fuel Cells). A nonlinear controller is designed based on nonlinear model to prolong the stack life of PEMFCs. Since it is known that large deviations between hydrogen and oxygen partial pressures can cause severe membrane damage in the fuel cell, feedback linearization is applied to the PEMFC system so that the deviation can be kept as small as possible during disturbances or load variations. To obtain an accurate feedback linearization controller, tuning the linear parameters are always important. So in proposed study NSGA (Non-Dominated Sorting Genetic Algorithm)-II method was used to tune the designed controller in aim to decrease the controller tracking error. The simulation result showed that the proposed method tuned the controller efficiently.
Keywords: Feedback Linearization controller, NSGA, Optimal Control, PEMFC.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22391606 Radiation Damage as Nonlinear Evolution of Complex System
Authors: Pavlo Selyshchev
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Irradiated material is a typical example of a complex system with nonlinear coupling between its elements. During irradiation the radiation damage is developed and this development has bifurcations and qualitatively different kinds of behavior. The accumulation of primary defects in irradiated crystals is considered in frame work of nonlinear evolution of complex system. The thermo-concentration nonlinear feedback is carried out as a mechanism of self-oscillation development. It is shown that there are two ways of the defect density evolution under stationary irradiation. The first is the accumulation of defects; defect density monotonically grows and tends to its stationary state for some system parameters. Another way that takes place for opportune parameters is the development of self-oscillations of the defect density. The stationary state, its stability and type are found. The bifurcation values of parameters (environment temperature, defect generation rate, etc.) are obtained. The frequency of the selfoscillation and the conditions of their development is found and rated. It is shown that defect density, heat fluxes and temperature during self-oscillations can reach much higher values than the expected steady-state values. It can lead to a change of typical operation and an accident, e.g. for nuclear equipment.Keywords: Irradiation, Primary Defects, Solids, Self-oscillation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17261605 Finite Element Approximation of the Heat Equation under Axisymmetry Assumption
Authors: Raphael Zanella
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This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit time marching. The code is verified by space and time convergence tests using a manufactured solution. An example problem is solved with an axisymmetric formulation and with a 3D formulation. Both formulations lead to the same result but the code based on the axisymmetric formulation is mush faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest of using an axisymmetric formulation when it is possible.
Keywords: Axisymmetric problem, continuous finite elements, heat equation, weak formulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3341604 Multivariable System Reduction Using Stability Equation Method and SRAM
Authors: D. Bala Bhaskar
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An algorithm is proposed for the order reduction of large scale linear dynamic multi variable systems where the reduced order model denominator is obtained by using Stability equation method and numerator coefficients are obtained by using SRAM. The proposed algorithm produces a lower order model for an original stable high order multivariable system. The reduction procedure is easy to understand, efficient and computer oriented. To highlight the advantages of the approach, the algorithm is illustrated with the help of a numerical example and the results are compared with the other existing techniques in literature.
Keywords: Multi variable systems, order reduction, stability equation method, SRAM, time domain characteristics, ISE.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7131603 Chua’s Circuit Regulation Using a Nonlinear Adaptive Feedback Technique
Authors: Abolhassan Razminia, Mohammad-Ali Sadrnia
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Chua’s circuit is one of the most important electronic devices that are used for Chaos and Bifurcation studies. A central role of secure communication is devoted to it. Since the adaptive control is used vastly in the linear systems control, here we introduce a new trend of application of adaptive method in the chaos controlling field. In this paper, we try to derive a new adaptive control scheme for Chua’s circuit controlling because control of chaos is often very important in practical operations. The novelty of this approach is for sake of its robustness against the external perturbations which is simulated as an additive noise in all measured states and can be generalized to other chaotic systems. Our approach is based on Lyapunov analysis and the adaptation law is considered for the feedback gain. Because of this, we have named it NAFT (Nonlinear Adaptive Feedback Technique). At last, simulations show the capability of the presented technique for Chua’s circuit.
Keywords: Chaos, adaptive control, nonlinear control, Chua's circuit.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20531602 Solitary Wave Solutions for Burgers-Fisher type Equations with Variable Coefficients
Authors: Amit Goyal, Alka, Rama Gupta, C. Nagaraja Kumar
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We have solved the Burgers-Fisher (BF) type equations, with time-dependent coefficients of convection and reaction terms, by using the auxiliary equation method. A class of solitary wave solutions are obtained, and some of which are derived for the first time. We have studied the effect of variable coefficients on physical parameters (amplitude and velocity) of solitary wave solutions. In some cases, the BF equations could be solved for arbitrary timedependent coefficient of convection term.Keywords: Solitary wave solution, Variable coefficient Burgers- Fisher equation, Auxiliary equation method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16181601 Solving One-dimensional Hyperbolic Telegraph Equation Using Cubic B-spline Quasi-interpolation
Authors: Marzieh Dosti, Alireza Nazemi
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In this paper, the telegraph equation is solved numerically by cubic B-spline quasi-interpolation .We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement. The results of numerical experiments are presented, and are compared with analytical solutions by calculating errors L2 and L∞ norms to confirm the good accuracy of the presented scheme.
Keywords: Cubic B-spline, quasi-interpolation, collocation method, second-order hyperbolic telegraph equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27851600 The Differential Transform Method for Advection-Diffusion Problems
Authors: M. F. Patricio, P. M. Rosa
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In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.
Keywords: Method of Lines, Differential Transform Method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17331599 Comparative Analysis of DTC Based Switched Reluctance Motor Drive Using Torque Equation and FEA Models
Authors: P. Srinivas, P. V. N. Prasad
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Since torque ripple is the main cause of noise and vibrations, the performance of Switched Reluctance Motor (SRM) can be improved by minimizing its torque ripple using a novel control technique called Direct Torque Control (DTC). In DTC technique, torque is controlled directly through control of magnitude of the flux and change in speed of the stator flux vector. The flux and torque are maintained within set hysteresis bands.
The DTC of SRM is analyzed by two methods. In one method, the actual torque is computed by conducting Finite Element Analysis (FEA) on the design specifications of the motor. In the other method, the torque is computed by Simplified Torque Equation. The variation of peak current, average current, torque ripple and speed settling time with Simplified Torque Equation model is compared with FEA based model.
Keywords: Direct Toque Control, Simplified Torque Equation, Finite Element Analysis, Torque Ripple.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 34941598 Schrödinger Equation with Position-Dependent Mass: Staggered Mass Distributions
Authors: J. J. Peña, J. Morales, J. García-Ravelo, L. Arcos-Díaz
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The Point canonical transformation method is applied for solving the Schrödinger equation with position-dependent mass. This class of problem has been solved for continuous mass distributions. In this work, a staggered mass distribution for the case of a free particle in an infinite square well potential has been proposed. The continuity conditions as well as normalization for the wave function are also considered. The proposal can be used for dealing with other kind of staggered mass distributions in the Schrödinger equation with different quantum potentials.
Keywords: Free particle, point canonical transformation method, position-dependent mass, staggered mass distribution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15561597 Fuzzy Rules Emulated Network Adaptive Controller with Unfixed Learning Rate for a Class of Unknown Discrete-time Nonlinear Systems
Authors: Chidentree Treesatayapun
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A direct adaptive controller for a class of unknown nonlinear discrete-time systems is presented in this article. The proposed controller is constructed by fuzzy rules emulated network (FREN). With its simple structure, the human knowledge about the plant is transferred to be if-then rules for setting the network. These adjustable parameters inside FREN are tuned by the learning mechanism with time varying step size or learning rate. The variation of learning rate is introduced by main theorem to improve the system performance and stabilization. Furthermore, the boundary of adjustable parameters is guaranteed through the on-line learning and membership functions properties. The validation of the theoretical findings is represented by some illustrated examples.
Keywords: Neuro-Fuzzy, learning algorithm, nonlinear discrete time.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14191596 Design of Nonlinear Robust Control in a Class of Structurally Stable Functions
Authors: V. Ten
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An approach of design of stable of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers. Theoretical part presents an analysis of designed nonlinear second-order control systems. As more important the integrators in series, canonical controllable form and Jordan forms are considered. The analysis resumes that due to added controllers systems become stable and insensitive to any disturbance of parameters. Experimental part presents MATLAB simulation of design of control systems of epidemic spread, aircrafts angular motion and submarine depth. The results of simulation confirm the efficiency of offered method of design. KeywordsCatastrophes, robust control, simulation, uncertain parameters.
Keywords: Catastrophes, robust control, simulation, uncertain parameters.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12841595 Research on the Correlation of the Fluctuating Density Gradient of the Compressible Flows
Authors: Yasuo Obikane
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This work is to study a roll of the fluctuating density gradient in the compressible flows for the computational fluid dynamics (CFD). A new anisotropy tensor with the fluctuating density gradient is introduced, and is used for an invariant modeling technique to model the turbulent density gradient correlation equation derived from the continuity equation. The modeling equation is decomposed into three groups: group proportional to the mean velocity, and that proportional to the mean strain rate, and that proportional to the mean density. The characteristics of the correlation in a wake are extracted from the results by the two dimensional direct simulation, and shows the strong correlation with the vorticity in the wake near the body. Thus, it can be concluded that the correlation of the density gradient is a significant parameter to describe the quick generation of the turbulent property in the compressible flows.Keywords: Turbulence Modeling , Density Gradient Correlation, Compressible
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14331594 Identification of a PWA Model of a Batch Reactor for Model Predictive Control
Authors: Gorazd Karer, Igor Skrjanc, Borut Zupancic
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The complex hybrid and nonlinear nature of many processes that are met in practice causes problems with both structure modelling and parameter identification; therefore, obtaining a model that is suitable for MPC is often a difficult task. The basic idea of this paper is to present an identification method for a piecewise affine (PWA) model based on a fuzzy clustering algorithm. First we introduce the PWA model. Next, we tackle the identification method. We treat the fuzzy clustering algorithm, deal with the projections of the fuzzy clusters into the input space of the PWA model and explain the estimation of the parameters of the PWA model by means of a modified least-squares method. Furthermore, we verify the usability of the proposed identification approach on a hybrid nonlinear batch reactor example. The result suggest that the batch reactor can be efficiently identified and thus formulated as a PWA model, which can eventually be used for model predictive control purposes.
Keywords: Batch reactor, fuzzy clustering, hybrid systems, identification, nonlinear systems, PWA systems.
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