Analysis Of Nonlinear Phenomena Research Articles

Modeling and Analysis of Non-Linear Phenomena of Satellite Power System in Space Environment and Hazard-Risk Evaluations

With the aim to solve the problem of the non-linear phenomenon of the satellite power system under the influence of the space environment factors, which threatens the stability of the power system, in this paper, the abnormal charging and discharging of solar arrays and solar array drive assembly (SADA) induced by the space plasma environment and accidental events, such as debris impact, and the non-linear behaviors of the solar array and load during the Earth eclipse are modeled and analyzed. On this basis, the hazard risk evaluations of the above non-linear phenomena are carried out, and the weak links of the satellite power system in the space environment are identified. The results show that the unexpected energy of the solar array will increase the current stress and power loss of the power device, resulting in S3R over-regulation. An SADA arc fault will reduce the power supply capacity of the solar array, damage the shunt regulator, and affect the quality of the bus. The non-linear behavior of the solar array and load during the Earth eclipse may damage the battery charge and discharge regulator, seriously affecting the stability of the power system.

Control of Bifurcation Behaviour of the Buck Converter via a Resonant Parametric Perturbation Circuit

Nonlinear circuits and systems research has been growing very quickl y over the past two decades. Activel y pursued in almost every branch of science and engineering, nonlinear systems theory luis found wide applications in a variety of practical engineering problems. Engineers, scientists and mathematicians have similarly advanced from the passive role of simpl y anal yzing, or identifying chaos to their present, active involvement in controlling chaos — control directed not onl y at suppression, but also at exploiting its enormous potential. We now stand at the threshold ofmajor advances in the control and synchronization of cluios for new applications across the range of engineering disciplines. All feedback controlled power converters exhibit certain non-linear phenomena over a specific breadth of parameter values. Despite being commonly encountered hy power electronics engineers, these non-linear phenomena are by and large not thoroughl y understood by engineers. Such phenomena remaining somewhat mysterious and hardl y ever been examined in a formal way. As the discipline of power electronics becomes more matured, demand for better functionality, dependability and performance of power electronics circuits will inevitably force researchers to engage themselves in more detailed stud y and analysis of non-linear phenomena and complex behaviour of power electronics converters. The bifurcation behaviour of the back converter occurs when the input voltage is varied. In this study, the computer simulation scheme, PSPICE is employed to model the behaviour of the ideal back converter. For certain values of the input voltage Vin instability occurs. The resonant parametric perturbation method is then applied to control the bifurcation behaviour of the voltage-mode controlled back converter. Analysis and simulations are presented to provide theoretical and practical evidence for the proposed control method. As the back converter has wide industrial application, it would be deemed necessary for designers to know about its bifurcation behaviour and how to control such behaviour.

Effects of Non-smooth Phenomena on the Dynamics of DC-DC Converters

Effects of Non-smooth Phenomena on the Dynamics of DC-DC ConvertersThis paper provides the analysis of nonlinear phenomena in switch-mode power converters. In distinction to majority of known researches this paper presents novelty approach, allowing the complete bifurcation analysis, considering stable and various types of unstable behavior of nonlinear systems. Main results are illustrated on one of the most widely used switching converters - current controlled boost converter, for which the complete one-parametric bifurcation diagrams are constructed. The results include the detection of various types of rare attractors, smooth bifurcations and non-smooth phenomena, specific to piecewise linear dynamical systems.

Analysis of Nonlinear Phenomena in High Speed Ball Bearings due to Radial Clearance and Unbalanced Rotor Effects

The dynamic behavior of a high speed unbalanced rotor supported on roller bearings with damping has been studied, focusing particular attention on its nonlinear aspects. The non-linearity in the rotor bearing system has been considered mainly due to Hertzian contact, unbalanced rotor effect and radial internal clearance. This is modeled as an oscillating spring-mass-damper system. Various techniques like Time Response curves, Poincaré maps, Orbits plots, fast Fourier transformation, Hopf bifurcation and Phase Trajectory are used to study the nature of response. The motion of an unbalanced rotor is categorized with respect to the ratio of the Forcing/Natural frequency of the system as Harmonic, Sub-harmonic, Quasi periodic and Chaotic. The results show the appearance of instability and chaos in the dynamic response as the speed of the rotor-bearing system is changed. Period doubling and mechanism of intermittency have been observed that lead to chaos. The outcomes illustrate the appearance of instability and chaos in the dynamic response as the speed of the rotor-bearing system is changed. This work differs from the previous studies in the way that the complex model simulates nonlinear vibrations, considering that both the lubricated nonlinear contact stiffness and damping correspond to the conservative and dissipative energies, respectively. The comprehensive model developed in this investigation is a useful tool to predict the system behavior and for performance evaluation of a rotor bearing system.

The Origin of Nonlinear Phenomena in TCR-SVC Associated With Parametric Excitation of Intrinsic Oscillation and External Excitation

This paper focuses on anomalous nonlinear phenomena in a thyristor controlled reactor-static var compensator (TCR-SVC) system, called switching time bifurcation, and clarifies the relationship between the occurrence of nonlinear phenomenon and the intrinsic characteristics of the circuit equation with switching function. The occurrence of nonlinear phenomenon in a TCR-SVC system cannot be predicted when the dynamics of the circuit related to the switching action is neglected. Therefore, this paper considers the dynamics related to the switching operations in the analysis of nonlinear phenomena. The parametric excitation of circuit is discussed in relation to the homogeneous expression of the circuit equation. This paper indicates that the homogeneous equation of the TCR-SVC system results in Hill's equation, and it can be approximated as Mathieu's equation. The occurrence of nonlinear phenomena in the system is evaluated using the characteristics of Mathieu's equation. The anomalous nonlinear phenomena occur when the natural frequency of Mathieu's equation coincides with the frequency of the ac voltage in a TCR-SVC system. The parametric excitation is also confirmed through the characteristics of Hill's equation. This study clarified the interaction between the switching dynamics of the circuit and its external excitation, and clued the occurrence of nonlinear phenomena in the circuit. The proposed procedure can also be applied to the analysis for other switching converter circuits with periodic excitation source.

Strongly Nonlinear Phenomena in Ship Hydrodynamics

This paper was presented as the 2003–2004 Georg Weinblum Memorial Lecture by Dr. Maurizio Landrini of Istituto Nazionale per Studied Esperienze di Architettura Navale (INSEAN, the Italian Ship Model Basin). Tragically, Maurizio was killed in an accident on June 26, 2003, before he could give the lecture. The lecture was presented in memoriam by Dr. Emilio F. Campana, a friend and colleague at INSEAN. The paper was finished by coresearchers and friends at INSEAN. The present paper is focused on the analysis of nonlinear phenomena in the naval context. The work is split into two parts. In the former, state-of-the-art numerical techniques handling nonlinear free-surface flows are analyzed. Related advantages and shortcomings are discussed through mutual verifications and comparisons with experiments for prototype cases. In the latter, practical problems relevant for ship hydrodynamics, where nonlinear phenomena play a major role, are studied. More in detail, water-on-deck, sloshing, and bow and stern ship breaking wave phenomena are attacked by means of both numerical and experimental techniques, and the main features connected with nonlinear mechanisms are identified.

Investigation of subharmonic ferroresonant oscillations in power systems

Steady state bifurcation diagram based on continuation technique is a versatile tool for analyzing the behaviour of ferroresonance circuit, since it gives the visualization of multiple solutions. Stability analysis of the solutions obtained by steady state bifurcation diagram [K. Al-Anbarri, R. Ramanujam, T. Keerthiga, K. Kuppusamy, Analysis of non-linear phenomenon in MOV connected transformer, IEE Proc. Generation Transmission Distrib.148 (6) (2001) 562–566; K. Al-Anbarri, R. Ramanujam, R. Saravanaselvan, K. Kuppusamy, Effect of iron core loss nonlinearity on the chaotic ferroresonance in power transformers, Electric Power Syst. Res. 65 (2003) 1–12; K. Al-Anbarri, R. Ramanujam, Ch. Subba Rao, K. Kuppusamy, Effect of circuit configuration on chaotic ferroresonance in a power transformer, Electric Power Components Syst. 30 (2002) 1015–1031] demarcates stable fundamental ferroresonant solution, unstable fold and flip segments. Flip segment in steady state bifurcation diagram [K. Al-Anbarri, R. Ramanujam, T. Keerthiga, K. Kuppusamy, Analysis of nonlinear phenomenon in MOV connected transformer, IEE Proc. Generation Transmission Distrib.148 (6) (2001) 562–566; K. Al-Anbarri, R. Ramanujam, R. Saravanaselvan, K. Kuppusamy, Effect of iron core loss nonlinearity on the chaotic ferroresonance in power transformers, Electric Power Syst. Res. 65 (2003) 1–12; K. Al-Anbarri, R. Ramanujam, Ch. Subba Rao, K. Kuppusamy, Effect of circuit configuration on chaotic ferroresonance in a power transformer, Electric Power Components Syst. 30 (2002) 1015–1031] implies unstable fundamental solution, but does not reveal the range, order and stability of subharmonics. This paper proposes an approach to explore the unstable flip segment further and unearth the hidden subharmonics. As a consequence of this approach, continuum of stable solutions of well-defined domains can be identified. It is found that the existence of subharmonic solutions is sensitive to various factors such as transformer saturation index, non-linearity in the core loss and presence of an arrester. Exhaustive studies reveal that in the presence of an arrester, subharmonic mode exists for wider range of bifurcation parameter value at a high value of core saturation index, there by reducing the range of chaotic attractors.

Analysis of nonlinear phenomena and design aspects of three-phase space-vector-modulated converters

The analysis, design aspects, and numerical results of a current-controlled three-phase space-vector-modulated (SVM) voltage-source converter (VSC) are presented. The aim of the current controller of the VSC is to track the sinusoidal reference currents in each phase. The current controller includes a complex saturation function in order to avoid overmodulation in the SVM. Due to this strong nonlinearity, the study leads to system states not treated so far. An approximate Poincare map is derived. The paper reports saddles in the state space as a consequence of fold bifurcation and other phenomena in conjunction with saddles. Design conditions are derived to avoid undesired operation.

Research on the dynamic property of piezoelectric micro displacement actuator for boring error compensation

The dynamic property of piezoelectric micro displacement actuator (PMDA) is analyzed, especially the mechanical characteristic, lag phase property and hysteresis phenomenon. The influence factors of static and dynamic mechanical characteristics and the lag phase property are analyzed systematically. Three main influence factors of lag phase property are discovered. With comparison to mechanical Coulomb friction, a generalized model of nonlinear hysteresis of PMDA is advanced, based on the essential analysis of nonlinear phenomenon. Finally the application of PMDA in error compensation control system of boring is introduced. A good compensation result is achieved.

Analysis of nonlinear phenomena in MOV connected transformer

This paper investigates the effect of a metal oxide arrester on the ferroresonance behaviour of a transformer connected in parallel. It is known that the arresters may in some cases cause ferroresonance ‘dropout’. This aspect is examined in detail here by proper modelling of the nonlinear characteristics such as arrester characteristics and transformer saturation. Time-domain simulation has been carried out using a fourth-order Runge–Kutta method and the results were corroborated using EMTP. The results reveal that the presence of the arrester has a mitigating effect on ferroresonant overvoltages. Extensive simulations have been carried out to analyse the sensitivity with respect to arrester parameters, transformer saturation characteristics and the amplitude of the voltage source occurring in the Thevenin equivalent of the circuit. The presence of the arrester has a significant effect on the onset of chaos, the range of parameter values for which chaos persists and the magnitude of ferroresonant over voltages.

Stability with Respect to Pseudodifferential Perturbations of Some Nonlinear Diffusive Equations

Let $g^\ve(k)$ be an even function of $k\in\Zed$ which satisfies the inequality \forall k \in \Zed, \quad g^\ve(k)\le \rho -\nu \abs{k}^2. Assume, moreover, that $\forall k$, $g^\ve(k)$ tend to a limit g0 (k) as $\ve$ tends to 0. Define a linear operator $\lv$ on periodic functions of period $2\pi$ by \bigl(\lv u\bigr)\,\,\hat{}\; (k) = g^\ve(k)\hat u(k). Joulin has asked whether the solution of \uv_t =\lv \uv -\bigl(\uv_x\bigr)^2 /2 converges to the solution of the analogous problem for $\ve=0$. It is proved here that the answer is positive. Such a positive answer is a means of validating a number of theoretical procedures in the analysis of nonlinear phenomena and particularly of combustion phenomena.

Method of lines for the analysis of nonlinear phenomena due to cascaded second-order nonlinearity

This letter reports the results of the analysis of all-optical switching caused by nonlinear refraction due to cascaded second-order nonlinearity performed by means of the method of lines (MoL). Comparison with the results obtained by a home-made fast Fourier transform beam propagation method with one-step procedure, shows that the MoL optimized procedure allows the assumption of a larger step /spl Delta/z with shorter CPU times.

Analysis of Nonlinear Phenomena in Piezoelectric Ceramics under High-Power Vibration

Generation of higher harmonic voltages in piezoelectric ceramics driven at high-power resonance frequency levels was investigated. Rectangular bar samples with a high mechanical quality factor were prepared for this study. The samples were driven at a fundamental resonance frequency of the length extensional vibration mode by a constant current method, and their current, voltage and displacement were simultaneously measured. When the samples were driven at a constant current higher than the threshold level, distinct distortion in voltage waveform was observed while current waveform and displacement were exactly sinusoidal. By analyzing the distorted voltage waves with a spectrum analyzer, the distortion of the voltage wave was found to be due to the generation of higher harmonic voltages. The 2nd and 3rd harmonic voltages were measured as a function of current, and their magnitudes satisfied the power laws of square and cubic of the current, respectively. These experimental results can be explained by nonlinear piezoelectric equations derived from the ferroelectric theory.

95/06139 Customer level analysis of dynamic pricing experiments using consumption-pattern models

Steady state bifurcation diagram based on continuation technique is a versatile tool for analyzing the behaviour of ferroresonance circuit, since it gives the visualization of multiple solutions. Stability analysis of the solutions obtained by steady state bifurcation diagram [K. Al-Anbarri, R. Ramanujam, T. Keerthiga, K. Kuppusamy, Analysis of non-linear phenomenon in MOV connected transformer, IEE Proc. Generation Transmission Distrib.148 (6) (2001) 562–566; K. Al-Anbarri, R. Ramanujam, R. Saravanaselvan, K. Kuppusamy, Effect of iron core loss nonlinearity on the chaotic ferroresonance in power transformers, Electric Power Syst. Res. 65 (2003) 1–12; K. Al-Anbarri, R. Ramanujam, Ch. Subba Rao, K. Kuppusamy, Effect of circuit configuration on chaotic ferroresonance in a power transformer, Electric Power Components Syst. 30 (2002) 1015–1031] demarcates stable fundamental ferroresonant solution, unstable fold and flip segments. Flip segment in steady state bifurcation diagram [K. Al-Anbarri, R. Ramanujam, T. Keerthiga, K. Kuppusamy, Analysis of nonlinear phenomenon in MOV connected transformer, IEE Proc. Generation Transmission Distrib.148 (6) (2001) 562–566; K. Al-Anbarri, R. Ramanujam, R. Saravanaselvan, K. Kuppusamy, Effect of iron core loss nonlinearity on the chaotic ferroresonance in power transformers, Electric Power Syst. Res. 65 (2003) 1–12; K. Al-Anbarri, R. Ramanujam, Ch. Subba Rao, K. Kuppusamy, Effect of circuit configuration on chaotic ferroresonance in a power transformer, Electric Power Components Syst. 30 (2002) 1015–1031] implies unstable fundamental solution, but does not reveal the range, order and stability of subharmonics. This paper proposes an approach to explore the unstable flip segment further and unearth the hidden subharmonics. As a consequence of this approach, continuum of stable solutions of well-defined domains can be identified. It is found that the existence of subharmonic solutions is sensitive to various factors such as transformer saturation index, non-linearity in the core loss and presence of an arrester. Exhaustive studies reveal that in the presence of an arrester, subharmonic mode exists for wider range of bifurcation parameter value at a high value of core saturation index, there by reducing the range of chaotic attractors.

Nonlinear vibrations of offshore structures under random wave excitation

An account is given of some mathematical methods which have been used to analyse the response of offshore structures to random wave excitation. The analysis of nonlinear phenomena and the assessment of related nongaussian probability distributions are emphasized. The following problems are analysed in some depth: probability distributions for Morison-type wave loading; response near resonance of nonlinearly damped systems to random excitation; parametric resonance and instability of nonlinearly damped systems with randomly fluctuating restoring force coefficient. Solutions to each of these problem areas are illustrated by practical examples.