Search results for: state space equations

Authors: İres İskender, Ahmet Karaarslan

Abstract:

In this study, the performance of a high-frequency arc welding machine including a two-switch inverter is analyzed. The control of the system is achieved using two different control techniques i- fuzzy logic control (FLC) ii- state space averaging based sliding control. Fuzzy logic control does not need accurate mathematical model of a plant and can be used in nonlinear applications. The second method needs the mathematical model of the system. In this method the state space equations of the system are derived for two different “on" and “off" states of the switches. The derived state equations are combined with the sliding control rule considering the duty-cycle of the converter. The performance of the system is analyzed by simulating the system using SIMULINK tool box of MATLAB. The simulation results show that fuzzy logic controller is more robust and less sensitive to parameter variations.

Keywords: Fuzzy logic, arc welding, sliding state space control, PWM, current control.

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for the boundary value problem of second-order singular differential equations in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular equation.

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Authors: Arti Vaish, Harish Parthasarathy

Abstract:

The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.

Keywords: General theory of relativity, electromagnetism, metric tensor, Maxwells equations, test functions, finite element method.

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Authors: M. M. Fateh, A. Izadbakhsh

Abstract:

A robust control approach is proposed for a high speed manipulator using a hybrid computed torque control approach in the state space. The high-speed manipulator is driven by permanent magnet dc motors to track a trajectory in the joint space in the presence of disturbances. Tracking problem is analyzed in the state space where the completed models are considered for actuators. The proposed control approach can guarantee the stability and a satisfactory tracking performance. A two-link elbow manipulator driven by electrical actuators is simulated and results are shown to satisfy conditions under technical specifications.

Keywords: Computed torque, manipulator, robust control, state space.

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Authors: Lv Yuhua

Abstract:

In this paper, by establishing a new comparison result, we investigate the existence of positive solutions for initial value problems of nonlinear systems of second order integro-differential equations in Banach space.We improve and generalize some results  (see[5,6]), and the results is new even in finite dimensional spaces.

Keywords: Systems of integro-differential equations, monotone iterative method, comparison result, cone.

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Authors: Belkacem Meziane

Abstract:

The original 3D Lorenz-Haken equations -which describe laser dynamics- are converted into 2-second-order differential equations out of which the so far missing mathematics is extracted. Leaning on high-order trigonometry, important outcomes are pulled out: A fundamental result attributes chaos to forbidden periodic solutions, inside some precisely delimited region of the control parameter space that governs self-pulsing.

Keywords: chaos, Lorenz-Haken equations, laser dynamics, nonlinearities

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Authors: Tamal Bose, Zhurun Zhang, Miloje Radenkovic, Ojas Chauhan

Abstract:

In this paper, a novel approach is presented for designing multiplier-free state-space digital filters. The multiplier-free design is obtained by finding power-of-2 coefficients and also quantizing the state variables to power-of-2 numbers. Expressions for the noise variance are derived for the quantized state vector and the output of the filter. A “structuretransformation matrix" is incorporated in these expressions. It is shown that quantization effects can be minimized by properly designing the structure-transformation matrix. Simulation results are very promising and illustrate the design algorithm.

Keywords: Digital filters, minimum noise, multiplier-free, quantization, state-space.

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Authors: Nader Ghareeb, R¨udiger Schmidt

Abstract:

Minimizing the weight in flexible structures means reducing material and costs as well. However, these structures could become prone to vibrations. Attenuating these vibrations has become a pivotal engineering problem that shifted the focus of many research endeavors. One technique to do that is to design and implement an active control system. This system is mainly composed of a vibrating structure, a sensor to perceive the vibrations, an actuator to counteract the influence of disturbances, and finally a controller to generate the appropriate control signals. In this work, two different techniques are explored to create two different mathematical models of an active control system. The first model is a finite element model with a reduced number of nodes and it is called a super-element. The second model is in the form of state-space representation, i.e. a set of partial differential equations. The damping coefficients are calculated and incorporated into both models. The effectiveness of these models is demonstrated when the system is excited by its first natural frequency and an active control strategy is developed and implemented to attenuate the resulting vibrations. Results from both modeling techniques are presented and compared.

Keywords: Finite element analysis, super-element, state-space model.

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Authors: Sachin Kumar, Y. K. Gupta, J. R. Sharma

Abstract:

In the present article, a new class of solutions of Einstein field equations is investigated for a spherically symmetric space-time when the source of gravitation is a perfect fluid. All the solutions have been derived by making some suitable arrangements in the field equations. The solutions so obtained have been seen to describe Schwarzschild interior solutions. Most of the solutions are subjected to the reality conditions. As far as the authors are aware the solutions are new.

Keywords: Einstein's equations, General Relativity, PerfectFluid, Spherical symmetric.

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Authors: Malika Yaici, Kamel Hariche, Tim Clarke

Abstract:

The relationship between eigenstructure (eigenvalues and eigenvectors) and latent structure (latent roots and latent vectors) is established. In control theory eigenstructure is associated with the state space description of a dynamic multi-variable system and a latent structure is associated with its matrix fraction description. Beginning with block controller and block observer state space forms and moving on to any general state space form, we develop the identities that relate eigenvectors and latent vectors in either direction. Numerical examples illustrate this result. A brief discussion of the potential of these identities in linear control system design follows. Additionally, we present a consequent result: a quick and easy method to solve the polynomial eigenvalue problem for regular matrix polynomials.

Keywords: Eigenvalues/Eigenvectors, Latent values/vectors, Matrix fraction description, State space description.

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Authors: N. A. Samat, D. F. Percy

Abstract:

The main aim of this study is to describe and introduce a method of numerical analysis in obtaining approximate solutions for the SIR-SI differential equations (susceptible-infectiverecovered for human populations; susceptible-infective for vector populations) that represent a model for dengue disease transmission. Firstly, we describe the ordinary differential equations for the SIR-SI disease transmission models. Then, we introduce the numerical analysis of solutions of this continuous time, discrete space SIR-SI model by simplifying the continuous time scale to a densely populated, discrete time scale. This is followed by the application of this numerical analysis of solutions of the SIR-SI differential equations to the estimation of relative risk using continuous time, discrete space dengue data of Kuala Lumpur, Malaysia. Finally, we present the results of the analysis, comparing and displaying the results in graphs, table and maps. Results of the numerical analysis of solutions that we implemented offers a useful and potentially superior model for estimating relative risks based on continuous time, discrete space data for vector borne infectious diseases specifically for dengue disease. 

Keywords: Dengue disease, disease mapping, numerical analysis, SIR-SI differential equations.

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Authors: Yang Liu, Jinfeng Wang, Hong Li, Wei Gao, Siriguleng He

Abstract:

A new numerical scheme based on the H1-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. And the proposed method dose not requires the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.

Keywords: Pseudo-hyperbolic equations, splitting system, H1-Galerkin mixed method, error estimates.

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Authors: Inese Bula

Abstract:

Symbolic dynamics studies dynamical systems on the basis of the symbol sequences obtained for a suitable partition of the state space. This approach exploits the property that system dynamics reduce to a shift operation in symbol space. This shift operator is a chaotic mapping. In this article we show that in the symbol space exist other chaotic mappings.

Keywords: Infinite symbol space, prefix metric, chaotic mapping, generator function, jump mapping.

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Authors: Kholod M. Abu-Alnaja

Abstract:

In this work, we derive two numerical schemes for solving a class of nonlinear partial differential equations. The first method is of second order accuracy in space and time directions, the scheme is unconditionally stable using Von Neumann stability analysis, the scheme produced a nonlinear block system where Newton-s method is used to solve it. The second method is of fourth order accuracy in space and second order in time. The method is unconditionally stable and Newton's method is used to solve the nonlinear block system obtained. The exact single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitary waves for different parameters are also discussed.

Keywords: Crank-Nicolson Scheme, Douglas Scheme, Partial Differential Equations

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Authors: Abdullah E. Al-Mazrooei

Abstract:

In this paper, we present a new kind of the bilinear systems in the form of state space model. The evolution of this system depends on the product of state vector by its self. The well known Lotak Volterra and Lorenz models are special cases of this new model. We also present here a generalization of Kalman filter which is suitable to work with the new bilinear model. An application to real measurements is introduced to illustrate the efficiency of the proposed algorithm.

Keywords: Bilinear systems, state space model, Kalman filter.

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Authors: Cheng-Chieh Chiang, Yi-Chia Chan, Greg C. Lee

Abstract:

This paper proposes a video-based framework for face recognition to identify which faces appear in a video sequence. Our basic idea is like a tracking task - to track a selection of person candidates over time according to the observing visual features of face images in video frames. Hence, we employ the state-space model to formulate video-based face recognition by dividing this problem into two parts: the likelihood and the transition measures. The likelihood measure is to recognize whose face is currently being observed in video frames, for which two-dimensional linear discriminant analysis is employed. The transition measure estimates the probability of changing from an incorrect recognition at the previous stage to the correct person at the current stage. Moreover, extra nodes associated with head nodes are incorporated into our proposed state-space model. The experimental results are also provided to demonstrate the robustness and efficiency of our proposed approach.

Keywords: 2DLDA, face recognition, state-space model, likelihood measure, transition measure.

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Authors: Giovanni Incerti

Abstract:

In this paper the vibration of a synchronous belt drive during start-up is analyzed and discussed. Besides considering the belt elasticity, the model here proposed also takes into consideration the electromagnetic response of the DC motor. The solution of the motion equations is obtained by means of the modal analysis in state space, which allows to obtain the decoupling of all equations, without introducing the hypothesis of proportional damping. The mathematical model of the transmission and the solution algorithms have been implemented within a computing software that allows the user to simulate the dynamics of the system and to evaluate the effects due to the elasticity of the belt branches and to the electromagnetic behavior of the DC motor. In order to show the details of the calculation procedure, the paper presents a case study developed with the aid of the above-mentioned software.

Keywords: Belt drive, Vibrations, Startup, DC motor.

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Authors: Xiguang Li

Abstract:

In this paper , by using fixed point theorem , upper and lower solution-s method and monotone iterative technique , we prove the existence of maximum and minimum solutions of differential equations with delay , which improved and generalize the result of related paper.

Keywords: Banach space, boundary value problem, differential equation, delay.

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

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Authors: N. M. Singh, Jayant Dubey, Ghanshyam Laddha

Abstract:

State Dependent Riccati Equation (SDRE) approach is a modification of the well studied LQR method. It has the capability of being applied to control nonlinear systems. In this paper the technique has been applied to control the single inverted pendulum (SIP) which represents a rich class of nonlinear underactuated systems. SIP modeling is based on Euler-Lagrange equations. A procedure is developed for judicious selection of weighting parameters and constraint handling. The controller designed by SDRE technique here gives better results than existing controllers designed by energy based techniques.

Keywords: State Dependent Riccati Equation (SDRE), Single Inverted Pendulum (SIP), Linear Quadratic Regulator (LQR)

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Authors: D. Mehdizadeh, M. Rahimian, M. Eskandari-Ghadi

Abstract:

This article is concerned with the determination of the static interaction of a vertically loaded rigid circular disc embedded at the interface of a horizontal layer sandwiched in between two different transversely isotropic half-spaces called as tri-material full-space. The axes of symmetry of different regions are assumed to be normal to the horizontal interfaces and parallel to the movement direction. With the use of a potential function method, and by implementing Hankel integral transforms in the radial direction, the government partial differential equation for the solely scalar potential function is transformed to an ordinary 4th order differential equation, and the mixed boundary conditions are transformed into a pair of integral equations called dual integral equations, which can be reduced to a Fredholm integral equation of the second kind, which is solved analytically. Then, the displacements and stresses are given in the form of improper line integrals, which is due to inverse Hankel integral transforms. It is shown that the present solutions are in exact agreement with the existing solutions for a homogeneous full-space with transversely isotropic material. To confirm the accuracy of the numerical evaluation of the integrals involved, the numerical results are compared with the solutions exists for the homogeneous full-space. Then, some different cases with different degrees of material anisotropy are compared to portray the effect of degree of anisotropy.

 

Keywords: Transversely isotropic, rigid disc, elasticity, dual integral equations, tri-material full-space.

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Authors: Saleh A. Al-Jufout

Abstract:

This paper presents a procedure of forming the mathematical model of radial electric power systems for simulation of both transient and steady-state conditions. The research idea has been based on nodal voltages technique and on differentiation of Kirchhoff's current law (KCL) applied to each non-reference node of the radial system, the result of which the nodal voltages has been calculated by solving a system of algebraic equations. Currents of the electric power system components have been determined by solving their respective differential equations. Transforming the three-phase coordinate system into Cartesian coordinate system in the model decreased the overall number of equations by one third. The use of Cartesian coordinate system does not ignore the DC component during transient conditions, but restricts the model's implementation for symmetrical modes of operation only. An example of the input data for a four-bus radial electric power system has been calculated.

Keywords: Mathematical Modelling, Radial Power System, Steady-State, Transients

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Authors: Arti Vaish, Harish Parthasarathy

Abstract:

In this paper, a novel wave equation for electromagnetic waves in a medium having anisotropic permittivity has been derived with the help of Maxwell-s curl equations. The x and y components of the Maxwell-s equations are written with the permittivity () being a 3 × 3 symmetric matrix. These equations are solved for Ex , Ey, Hx, Hy in terms of Ez, Hz, and the partial derivatives. The Z components of the Maxwell-s curl are then used to arrive to the generalized Helmholtz equations for Ez and Hz.

Keywords: Electromagnetism, Maxwell's Equations, Anisotropic permittivity, Wave equation, Matrix Equation, Permittivity tensor.

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Authors: Rafal Maciag

Abstract:

Due to the development of the current civilization, one must create suitable models of its pervasive massive phenomena. Such a phenomenon is the digital transformation, which has a substantial number of disciplined, methodical interpretations forming the diversified reflection. This reflection could be understood pragmatically as the current temporal, a local differential state of knowledge. The model of the discursive space is proposed as a model for the analysis and description of this knowledge. Discursive space is understood as an autonomous multidimensional space where separate discourses traverse specific trajectories of what can be presented in multidimensional parallel coordinate system. Discursive space built on the world of facts preserves the complex character of that world. Digital transformation as a discursive space has a relativistic character that means that at the same time, it is created by the dynamic discourses and these discourses are molded by the shape of this space.

Keywords: Knowledge, digital transformation, discourse, discursive space, complexity.

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Authors: Jinfeng Wang, Yang Liu, Hong Li

Abstract:

In this article, we propose a new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic equations. We introduce two transformations q = ut and σ = ux and formulate a first-order system of equations. We can obtain the approximation solution for the scalar unknown u, time derivative q = ut and space derivative σ = ux, simultaneously. Finally, some examples are provided to illustrate the effectiveness of our method.

Keywords: Hyperbolic wave equation, Nonlinear, He’s variational iteration method, Transformations

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Authors: Afaq Ahmad

Abstract:

Using state space technique and GF(2) theory, a simulation model for external exclusive NOR type LFSR structures is developed. Through this tool a systematic procedure is devised for computing pseudo-random binary sequences from such structures.

Keywords: LFSR, external exclusive NOR type, recursivebinary sequence, initial state - next state, state transition matrix.

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special non-empty closed convex set and utilizing M¨onch fixed point theory, we investigate the existence of solution for a class of fourth-order singular differential equation in Banach space, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

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Authors: G.Mehdiyeva, M.Imanova, V.Ibrahimov

Abstract:

Beginning from the creator of integro-differential equations Volterra, many scientists have investigated these equations. Classic method for solving integro-differential equations is the quadratures method that is successfully applied up today. Unlike these methods, Makroglou applied hybrid methods that are modified and generalized in this paper and applied to the numerical solution of Volterra integro-differential equations. The way for defining the coefficients of the suggested method is also given.

Keywords: Integro-differential equations, initial value problem, hybrid methods, predictor-corrector method

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Authors: M. T. Sichani, B. J. Pedersen, S. R. K. Nielsen

Abstract:

Turbulence of the incoming wind field is of paramount importance to the dynamic response of civil engineering structures. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper an empirical cross spectral density function for the along-wind turbulence component over the wind field area is taken as the starting point. The spectrum is spatially discretized in terms of a Hermitian cross-spectral density matrix for the turbulence state vector which turns out not to be positive definite. Since the succeeding state space and ARMA modelling of the turbulence rely on the positive definiteness of the cross-spectral density matrix, the problem with the non-positive definiteness of such matrices is at first addressed and suitable treatments regarding it are proposed. From the adjusted positive definite cross-spectral density matrix a frequency response matrix is constructed which determines the turbulence vector as a linear filtration of Gaussian white noise. Finally, an accurate state space modelling method is proposed which allows selection of an appropriate model order, and estimation of a state space model for the vector turbulence process incorporating its phase spectrum in one stage, and its results are compared with a conventional ARMA modelling method.

Keywords: Turbulence, wind turbine, complex coherence, state space modelling, ARMA modelling.

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Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

Abstract:

The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L₂. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: Arbitrary cross section waveguide, analytical regularization method, evolutionary equations of electromagnetic theory of time-domain, TM field.

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