Search results for: Nonlinear polarization rotation

Authors: M. G. M. Khan, V. D. Prasad, D. K. Rao

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In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique.

Keywords: Auxiliary variable, Dynamic programming technique, Nonlinear programming problem, Optimum stratification, Uniform distribution.

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Authors: D.Elleuch, T.Damak

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In this paper, the performance of two adaptive observers applied to interconnected systems is studied. The nonlinearity of systems can be written in a fractional form. The first adaptive observer is an adaptive sliding mode observer for a Lipchitz nonlinear system and the second one is an adaptive sliding mode observer having a filtered error as a sliding surface. After comparing their performances throughout the inverted pendulum mounted on a car system, it was shown that the second one is more robust to estimate the state.

Keywords: Adaptive observer, Lipchitz system, Interconnected fractional nonlinear system, sliding mode.

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Authors: Yanling Zhu

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In this paper, a higher order nonlinear neutral functional differential equation with distributed delay is studied by using the continuation theorem of coincidence degree theory. Some new results on the existence of periodic solutions are obtained.

Keywords: Neutral functional differential equation, higher order, periodic solution, coincidence degree theory.

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Authors: Roozbeh Keshmiri, Alireza Mohamad Shahri

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Fuzzy controllers are potential candidates for the control of nonlinear, time variant and also complicated systems. Anti lock brake system (ABS) which is a nonlinear system, may not be easily controlled by classical control methods. An intelligent Fuzzy control method is very useful for this kind of nonlinear system. A typical antilock brake system (ABS) by sensing the wheel lockup, releases the brakes for a short period of time, and then reapplies again the brakes when the wheel spins up. In this paper, an intelligent fuzzy ABS controller is designed to adjust slipping performance for variety of roads. There are tow major sections in the proposing control system. First section consists of tow Fuzzy-Logic Controllers (FLC) providing optimal brake torque for both front and rear wheels. Second section which is also a FLC provides required amount of slip and torque references properties for different kind of roads. Simulation results of our proposed intelligent ABS for three different kinds of road show more reliable and better performance in compare with two other break systems.

Keywords: Fuzzy Logic Control, ABS, Anti lock BrakingSystem.

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Authors: B. S. Raghavendra, D. Narayana Dutt

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Many recent electrophysiological studies have revealed the importance of investigating meditation state in order to achieve an increased understanding of autonomous control of cardiovascular functions. In this paper, we characterize heart rate variability (HRV) time series acquired during meditation using nonlinear dynamical parameters. We have computed minimum embedding dimension (MED), correlation dimension (CD), largest Lyapunov exponent (LLE), and nonlinearity scores (NLS) from HRV time series of eight Chi and four Kundalini meditation practitioners. The pre-meditation state has been used as a baseline (control) state to compare the estimated parameters. The chaotic nature of HRV during both pre-meditation and meditation is confirmed by MED. The meditation state showed a significant decrease in the value of CD and increase in the value of LLE of HRV, in comparison with premeditation state, indicating a less complex and less predictable nature of HRV. In addition, it was shown that the HRV of meditation state is having highest NLS than pre-meditation state. The study indicated highly nonlinear dynamic nature of cardiac states as revealed by HRV during meditation state, rather considering it as a quiescent state.

Keywords: Correlation dimension, Embedding dimension, Heartrate variability, Largest Lyapunov exponent, Meditation, Nonlinearity score.

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Authors: Karuppsamy K., Eswara Prasad C. R.

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In this paper analysis of an infinite beam resting on tensionless extensible geosynthetic reinforced granular bed overlying soft soil strata under moving load with constant velocity is presented. The beam is subjected to a concentrated load moving with constant velocity. The upper reinforced granular bed is modeled by a rough elastic membrane embedded in Pasternak shear layer overlying a series of compressible nonlinear Winkler springs representing the under-lied very poor soil. The tensionless extensible geosynthetic layer has been assumed to deform such that at interface the geosynthetic and the soil have some deformation. Nonlinear behavior of granular fill and the very poor soil has been considered in the analysis by means of hyperbolic constitutive relationships. Detailed parametric study has been conducted to study the influence of various parameters on the response of soil foundation system under consideration by means of deflection and bending moment in the beam and tension mobilized in the geosynthetic layer. This study clearly observed that the comparisons of tension and tensionless foundation and magnitude of applied load, relative compressibility of granular fill and ultimate resistance of poor soil has significant influence on the response of soil foundation system.

Keywords: Infinite Beams, Tensionless Extensible Geosynthetic, Granular layer, Moving Load and Nonlinear behavior of poor soil

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Authors: Vishwesh Kulkarni, Nikhil Bellarykar

Abstract:

Cellular complexity stems from the interactions among thousands of different molecular species. Thanks to the emerging fields of systems and synthetic biology, scientists are beginning to unravel these regulatory, signaling, and metabolic interactions and to understand their coordinated action. Reverse engineering of biological networks has has several benefits but a poor quality of data combined with the difficulty in reproducing it limits the applicability of these methods. A few years back, many of the commonly used predictive algorithms were tested on a network constructed in the yeast Saccharomyces cerevisiae (S. cerevisiae) to resolve this issue. The network was a synthetic network of five genes regulating each other for the so-called in vivo reverse-engineering and modeling assessment (IRMA). The network was constructed in S. cereviase since it is a simple and well characterized organism. The synthetic network included a variety of regulatory interactions, thus capturing the behaviour of larger eukaryotic gene networks on a smaller scale. We derive a new set of algorithms by solving a nonlinear optimization problem and show how these algorithms outperform other algorithms on these datasets.

Keywords: Synthetic gene network, network identification, nonlinear modeling, optimization.

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Authors: Swarniv Chandra, Parthasona Maji, Basudev Ghosh

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The nonlinear self-interaction of an electrostatic surface wave on a semibounded quantum plasma with relativistic degeneracy is investigated by using quantum hydrodynamic (QHD) model and the Poisson’s equation with appropriate boundary conditions. It is shown that a part of the second harmonic generated through self-interaction does not have a true surface wave character but propagates obliquely away from the plasma-vacuum interface into the bulk of plasma.

Keywords: Harmonic Generation, Quantum Plasma, Quantum Hydrodynamic Model, Relativistic Degeneracy, Surface waves.

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Authors: J. Kala, P. Hradil, V. Salajka

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Reinforced concrete crash barriers used in road traffic must meet a number of criteria. Crash barriers are laid lengthwise, one behind another, and joined using specially designed steel locks. While developing BSV reinforced concrete crash barriers (type ŽPSV), experiments and calculations aimed to optimize the shape of a newly designed lock and the reinforcement quantity and distribution in a crash barrier were carried out. The tension carrying capacity of two parallelly joined locks was solved experimentally. Based on the performed experiments, adjustments of nonlinear properties of steel were performed in the calculations. The obtained results served as a basis to optimize the lock design using a computational model that takes into account the plastic behaviour of steel and the influence of the surrounding concrete [6]. The response to the vehicle impact has been analyzed using a specially elaborated complex computational model, comprising both the nonlinear model of the damping wall or crash barrier and the detailed model of the vehicle [7].

Keywords: Crash Barrier, impact, static analysis, concrete nonlinear model.

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Authors: Babesse Saad, Ameddah Djameleddine

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In this paper, a learning algorithm using neuronal networks to improve the roll stability and prevent the rollover in a single unit heavy vehicle is proposed. First, LQR control to keep balanced normalized rollovers, between front and rear axles, below the unity, then a data collected from this controller is used as a training basis of a neuronal regulator. The ANN controller is thereafter applied for the nonlinear side force model, and gives satisfactory results than the LQR one.

Keywords: Rollover, single unit heavy vehicle, neural networks, nonlinear side force.

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Authors: R.K. Behera, S.Behera

Abstract:

In a wind power generator using doubly fed induction generator (DFIG), the three-phase pulse width modulation (PWM) voltage source converter (VSC) is used as grid side converter (GSC) and rotor side converter (RSC). The standard linear control laws proposed for GSC provides not only instablity against comparatively large-signal disturbances, but also the problem of stability due to uncertainty of load and variations in parameters. In this paper, a nonlinear controller is designed for grid side converter (GSC) of a DFIG for wind power application. The nonlinear controller is designed based on the input-output feedback linearization control method. The resulting closed-loop system ensures a sufficient stability region, make robust to variations in circuit parameters and also exhibits good transient response. Computer simulations and experimental results are presented to confirm the effectiveness of the proposed control strategy.

Keywords: Doubly fed Induction Generator, grid side converter, machine side converter, dc link, feedback linearization.

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Authors: Vivekanandan C., Prabhakar .R., Prema D.

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This paper presents the application of discrete-time variable structure control with sliding mode based on the 'reaching law' method for robust control of a 'simple inverted pendulum on moving cart' - a standard nonlinear benchmark system. The controllers designed using the above techniques are completely insensitive to parametric uncertainty and external disturbance. The controller design is carried out using pole placement technique to find state feedback gain matrix , which decides the dynamic behavior of the system during sliding mode. This is followed by feedback gain realization using the control law which is synthesized from 'Gao-s reaching law'. The model of a single inverted pendulum and the discrete variable structure control controller are developed, simulated in MATLAB-SIMULINK and results are presented. The response of this simulation is compared with that of the discrete linear quadratic regulator (DLQR) and the advantages of sliding mode controller over DLQR are also presented

Keywords: Inverted pendulum, Variable Structure, Sliding mode control, Discrete-time systems, Nonlinear systems.

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Authors: N. Fusun Oyman Serteller

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In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: Finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations.

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Authors: Joseph V. M. Halim, Hesham El-Badawy, Hadia M. El-Hennawy

Abstract:

In this paper, an adaptive polarized Multiple-Input Multiple-Output (MIMO) Multicarrier Spread Spectrum Code Division Multiple Access (MC-SS-CDMA) system is designed for downlink mobile communications. The proposed system will be examined in Frequency Division Duplex (FDD) mode for both macro urban and suburban environments. For the same transmission bandwidth, a performance comparison between both nonoverlapped and orthogonal Frequency Division Multiplexing (FDM) schemes will be presented. Also, the proposed system will be compared with both the closed loop vertical MIMO MC-SS-CDMA system and the synchronous vertical STBC-MIMO MC-SS-CDMA system. As will be shown, the proposed system introduces a significant performance gain as well as reducing the spatial dimensions of the MIMO system and simplifying the receiver implementation. The effect of the polarization diversity characteristics on the BER performance will be discussed. Also, the impact of excluding the cross-polarization MCSS- CDMA blocks in the base station will be investigated. In addition, the system performance will be evaluated under different Feedback Information (FBI) rates for slowly-varying channels. Finally, a performance comparison for vehicular and pedestrian environments will be presented

Keywords: Closed loop technique, MC-SS-CDMA, Polarized MIMO systems, Transmit diversity.

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Authors: N. Khon, A. Kim, T. Mukhitdinova

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The aim of this research was to reveal the link between mental variables, such as spatial abilities, memory, intellect and professional experience of drivers. Participants were allocated to four groups: no experience, inexperienced, skilled and professionals (total 85 participants). The level of ability for spatial navigation and indicator of nonverbal memory grow along the process of accumulation of driving experience. At high levels of driving experience, this tendency is especially noticeable. The professionals having personal achievements in driving (racing) differ from skilled drivers in better feeling of direction, which is specific for them not just in a short-term situation of an experimental task, but also in life-size perspective. The level of ability of mental rotation does not grow with the growth of driving experience, which confirms the multiple intelligence theory according to which spatial abilities represent specific, other than logical intelligence type of intellect. The link between spatial abilities, memory, intellect and professional experience of drivers seems to be different relating spatial navigation or mental rotation as different kinds of spatial abilities.

Keywords: Memory, spatial abilities, intellect, drivers.

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Authors: Gulgassyl Nugmanova, Zhanat Zhunussova, Kuralay Yesmakhanova, Galya Mamyrbekova, Ratbay Myrzakulov

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In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr¨odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields.

Keywords: Spin systems, equivalent counterparts, integrable reductions, self-consistent potentials.

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Authors: Ashok Kumar, Narottam Chand, Vinod Kumar

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Due to the limited energy resources, energy efficient operation of sensor node is a key issue in wireless sensor networks. Clustering is an effective method to prolong the lifetime of energy constrained wireless sensor network. However, clustering in wireless sensor network faces several challenges such as selection of an optimal group of sensor nodes as cluster, optimum selection of cluster head, energy balanced optimal strategy for rotating the role of cluster head in a cluster, maintaining intra and inter cluster connectivity and optimal data routing in the network. In this paper, we propose a protocol supporting an energy efficient clustering, cluster head selection/rotation and data routing method to prolong the lifetime of sensor network. Simulation results demonstrate that the proposed protocol prolongs network lifetime due to the use of efficient clustering, cluster head selection/rotation and data routing.

Keywords: Wireless sensor networks, clustering, energy efficient, localization.

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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).

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Authors: N. Boshkova, K. Kamburova, N. Tabakova, N. Boshkov, Ts. Radeva

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Coatings based on polyaniline (PANI) can improve the resistance of steel against corrosion. In this work, the preparation of stable suspensions of colloidal PANI-SiO₂ particles, suitable for obtaining of composite anticorrosive coating on steel, is described. Electrokinetic data as a function of pH are presented, showing that the zeta potentials of the PANI-SiO₂ particles are governed primarily by the charged groups at the silica oxide surface. Electrosteric stabilization of the PANI-SiO₂ particles’ suspension against aggregation is realized at pH>5.5 (EB form of PANI) by adsorption of positively charged polyelectrolyte molecules onto negatively charged PANI-SiO₂ particles. The PANI-SiO₂ particles are incorporated by electrodeposition into the metal matrix of zinc in order to obtain composite (hybrid) coatings. The latter are aimed to ensure sacrificial protection of steel mainly in aggressive media leading to local corrosion damages. The surface morphology of the composite zinc coatings is investigated with SEM. The influence of PANI-SiO₂ particles on the cathodic and anodic processes occurring in the starting electrolyte for obtaining of the coatings is followed with cyclic voltammetry. The electrochemical and corrosion behavior is evaluated with potentiodynamic polarization curves and polarization resistance measurements. The beneficial effect of the stabilized PANI-SiO₂ particles for the increased protective ability of the composites is commented and discussed.

Keywords: Corrosion, polyaniline particles, zinc, protective ability.

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Authors: Iman Mousavinejad, Reza Kazemi, , Mohsen Bayani Khaknejad

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Active Front Steering system (AFS) provides an electronically controlled superposition of an angle to the steering wheel angle. This additional degree of freedom enables a continuous and driving-situation dependent on adaptation of the steering characteristics. In an active steering system, there needs be no fixed relationship between the steering wheel and the angle of the road wheels. Not only can the effective steering ratio be varied with speed, for example, but also the road wheel angles can be controlled by a combination of driver and computer inputs. Features like steering comfort, effort and steering dynamics are optimized and stabilizing steering interventions can be performed. In contrast to the conventional stability control, the yaw rate was fed back to AFS controller and the stability performance was optimized with Sliding Mode control (SMC) method. In addition, tire uncertainties have been taken into account in SM controller to provide the control robustness. In this paper, 3-DOF nonlinear model is used to design the AFS controller and 8-DOF nonlinear model is used to model the controlled vehicle.

Keywords: Active Front Steering (AFS), Sliding Mode Control method (SMC), Yaw rate, Vehicle Stability, Robustness

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Authors: Ho Young Son, Bu Seog Ju, Woo Young Jung

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This study presents the seismic safety evaluation of weir structure subjected to strong earthquake ground motions, as a flood defense structure in civil engineering structures. The seismic safety analysis procedure was illustrated through development of Finite Element (FE) and InFinite Element (IFE) method in ABAQUS platform. The IFE model was generated by CINPS4, 4-node linear one-way infinite model as a sold continuum infinite element in foundation areas of the weir structure and then nonlinear FE model using friction model for soil-structure interactions was applied in this study. In order to understand the complex behavior of weir structures, nonlinear time history analysis was carried out. Consequently, it was interesting to note that the compressive stress gave more vulnerability to the weir structure, in comparison to the tensile stress, during an earthquake. The stress concentration of the weir structure was shown at the connection area between the weir body and stilling basin area. The stress both tension and compression was reduced in IFE model rather than FE model of weir structures.

Keywords: Weir, Finite Element, Infinite Element, Nonlinear, Earthquake.

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Authors: Swarniv Chandra, Basudev Ghosh

Abstract:

Using the quantum hydrodynamic (QHD) model for quantum plasma at finite temperature the modulational instability of electron plasma waves is investigated by deriving a nonlinear Schrodinger equation. It was found that the electron degeneracy parameter significantly affects the linear and nonlinear properties of electron plasma waves in quantum plasma.

Keywords: Amplitude Modulation, Electron Plasma Waves, Finite Temperature Model, Modulational Instability, Quantum Plasma.

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Authors: Fotis N. Koumboulis, Michael G. Skarpetis, Maria P. Tzamtzi

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The problem of robust disturbance rejection (RDR) using a proportional state feedback controller is studied for the case of Left Invertible MIMO generalized state space linear systems with nonlinear uncertain structure. Sufficient conditions for the problem to have a solution are established. The set of all proportional feedback controllers solving the problem subject to these conditions is analytically determined.

Keywords: System theory, uncertain systems, robust control, singular systems.

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Authors: M. A. Ghorbani, M. Pasbani Khiavi

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The seismic response of steel shear wall system considering nonlinearity effects using finite element method is investigated in this paper. The non-linear finite element analysis has potential as usable and reliable means for analyzing of civil structures with the availability of computer technology. In this research the large displacements and materially nonlinear behavior of shear wall is presented with developing of finite element code. A numerical model based on the finite element method for the seismic analysis of shear wall is presented with developing of finite element code in this research. To develop the finite element code, the standard Galerkin weighted residual formulation is used. Two-dimensional plane stress model and total Lagrangian formulation was carried out to present the shear wall response and the Newton-Raphson method is applied for the solution of nonlinear transient equations. The presented model in this paper can be developed for analysis of civil engineering structures with different material behavior and complicated geometry.

Keywords: Finite element, steel shear wall, nonlinear, earthquake

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Authors: Fengxia Zheng

Abstract:

By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

Keywords: Fractional differential equation, boundary value problem, positive solution, existence and uniqueness, fixed point theorem, mixed monotone operator.

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Authors: Pankaj K. Gupta, Krishnan V. Pagalthivarthi

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The present work compares the performance of three turbulence modeling approach (based on the two-equation k -ε model) in predicting erosive wear in multi-size dense slurry flow through rotating channel. All three turbulence models include rotation modification to the production term in the turbulent kineticenergy equation. The two-phase flow field obtained numerically using Galerkin finite element methodology relates the local flow velocity and concentration to the wear rate via a suitable wear model. The wear models for both sliding wear and impact wear mechanisms account for the particle size dependence. Results of predicted wear rates using the three turbulence models are compared for a large number of cases spanning such operating parameters as rotation rate, solids concentration, flow rate, particle size distribution and so forth. The root-mean-square error between FE-generated data and the correlation between maximum wear rate and the operating parameters is found less than 2.5% for all the three models.

Keywords: Rotating channel, maximum wear rate, multi-sizeparticulate flow, k −ε turbulence models.

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Authors: S. A. Banani, M. A. Masnadi-Shirazi

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This paper presents a new algorithm which yields a nonlinear state estimator called iterated unscented Kalman filter. This state estimator makes use of both statistical and analytical linearization techniques in different parts of the filtering process. It outperforms the other three nonlinear state estimators: unscented Kalman filter (UKF), extended Kalman filter (EKF) and iterated extended Kalman filter (IEKF) when there is severe nonlinearity in system equation and less nonlinearity in measurement equation. The algorithm performance has been verified by illustrating some simulation results.

Keywords: Extended Kalman Filter, Iterated EKF, Nonlinearstate estimator, Unscented Kalman Filter.

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Authors: A. A. Vasin, N. V. Klassen, A. M. Likhter

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Water suspensions of in-organic (metals and oxides) and organic nano-objects (chitozan and collagen) were subjected to the treatment of direct and alternative electrical fields. In addition to quasi-periodical spatial patterning resonance-like performance of spatial distributions of these suspensions has been found at low frequencies of alternating electrical field. These resonances are explained as the result of creation of equilibrium states of groups of charged nano-objects with opposite signs of charges at the interparticle distances where the forces of Coulomb attraction are compensated by the repulsion forces induced by relatively negative polarization of hydrated regions surrounding the nanoparticles with respect to pure water. The low frequencies of these resonances are explained by comparatively big distances between the particles and their big masses with t\respect to masses of atoms constituting molecules with high resonance frequencies. These new resonances open a new approach to detailed modeling and understanding of mechanisms of the influence of electrical fields on the functioning of internal organs of living organisms at the level of cells and neurons.

Keywords: Bio-polymers, chitosan, collagen, nanoparticles, coulomb attraction, polarization repulsion, periodical patterning, electrical low frequency resonances, transformations.

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Authors: M. Mohebbi, K. Shakeri

Abstract:

The effect of different combinations of response feedback on the performance of active control system on nonlinear frames has been studied in this paper. To this end different feedback combinations including displacement, velocity, acceleration and full response feedback have been utilized in controlling the response of an eight story bilinear hysteretic frame which has been subjected to a white noise excitation and controlled by eight actuators which could fully control the frame. For active control of nonlinear frame Newmark nonlinear instantaneous optimal control algorithm has been used which a diagonal matrix has been selected for weighting matrices in performance index. For optimal design of active control system while the objective has been to reduce the maximum drift to below the yielding level, Distributed Genetic Algorithm (DGA) has been used to determine the proper set of weighting matrices. The criteria to assess the effect of each combination of response feedback have been the minimum required control force to reduce the maximum drift to below the yielding drift. The results of numerical simulation show that the performance of active control system is dependent on the type of response feedback where the velocity feedback is more effective in designing optimal control system in comparison with displacement and acceleration feedback. Also using full feedback of response in controller design leads to minimum control force amongst other combinations. Also the distributed genetic algorithm shows acceptable convergence speed in solving the optimization problem of designing active control systems.

Keywords: Active control, Distributed genetic algorithms, Response feedback, Weighting matrices.

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Authors: Gilberto Gonzalez-A, Dunia Nuñez-P

Abstract:

Bond graph models of an electrical transformer including the nonlinear saturation are presented. The transformer using electrical and magnetic circuits are modelled. These models determine the relation between self and mutual inductances, and the leakage and magnetizing inductances of power transformers with two windings using the properties of a bond graph. The equivalence between electrical and magnetic variables is given. The modelling and analysis using this methodology to three phase power transformers can be extended.

Keywords: Bond graph, electrical transformer, magnetic circuits, nonlinear saturation.

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