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1

Chaos Elimination for a Buck Converter Using the Multi-Objective Grey Wolf Optimiser

Bakria Derradji, Gozim Djamal, Korich Belkacem

Power Electronics and Drives

|

2023

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Vol. 8 (43)

165-173

EN

A wide variety of nonlinear phenomena, such as bifurcation and chaos, have been observed in power electronics converters. Much research has been conducted on these behaviours in different converter topologies. The buck converter is known to exhibit chaotic behaviour in a wide parameter range, giving rise to unstable behaviours depending on the circuit parameters values. This paper investigates this bifurcation behaviour by varying the parameters of a voltage PI (Proportional Integral) controlled buck converter operating in continuous conduction mode, using a continuous-time model and constant frequency control signal. Furthermore, a novel and improved version of the PI compensation technique, designed using the multi-objective grey wolf optimiser (MOGWO), is proposed to stabilise the buck converter from chaotic state to periodic orbit.

2

A fully-coupled three-dimensional fluid-structure interaction study on the externally-pressurized collapsible tube and the internal flow

Zhang Sen, Liu HaoFei

Journal of Theoretical and Applied Mechanics

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2023

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Vol. 61 nr 2

395--406

EN

We study the behavior of a collapsible tube conveying a fluid subject to external pressure that could occur in many physiological applications. The method of rotating spines is developed to enable an automatic mesh adaptation when the tube is deformed largely. We examine bifurcation diagrams when the tube is collapsed under a pressure driven condition and reveal that multiple solutions exist for a range of the Reynolds number. The stability characteristic of the system is discovered by determining stability of these solutions by the eigenvalue method for the first time, which is validated by solving a time-dependent problem of the system.

3

A new modified WINDMI jerk system with exponential and sinusoidal nonlinearities, its bifurcation analysis, multistability, circuit simulation and synchronization design

Mohamed Mohamad Afendee, Vaidyanathan Sundarapandian, Hannachi Fareh, Sambas Aceng, Darwin P.

Archives of Control Sciences

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2023

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Vol. 33, No. 4

711--735

EN

In this work, a new 3-D modified WINDMI chaotic jerk system with exponential and sinusoidal nonlinearities is presented and its dynamical behaviours and properties are investigated. Firstly, some properties of the system are studied such as equilibrium points and their stability, Lyapunov exponents and Kaplan-Yorke dimension. Also, we study the new jerk system dynamics using numerical simulations and analyses, including phase portraits, Lyapunouv exponent spectrum, bifurcation diagram and Poincaré map, 0-1 test. Next, we exhibit that the new 3-D chaotic modified WINDMI jerk system has multistability with coexisting chaotic attractors. Moreover, we design an electronic circuit using MultiSim 14.1 for real implementation of the modified WINDMI chaotic jerk system. Finally, we design an active synchronization scheme for the complete synchronization of the modified WINDMI chaotic jerk systems via backstepping control.

4

Stability and bifurcation analysis for an airfoil model with a high-order nonlinear spring

Li Shuqun, Zhou Liangqiang

Journal of Theoretical and Applied Mechanics

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2022

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Vol. 60 nr 2

185--197

EN

In this paper, the stability and bifurcation of an airfoil model with a high-order nonlinear spring are investigated both analytically and numerically. Two possible types of bifurcation at the equilibrium point are studied. It is proved that the zero characteristic root can only be a single zero. With the help of the center manifold theory and the normal form theory, the expressions of critical bifurcation curves leading to initial bifurcation and secondary bifurcation are obtained. Numerical simulations confirm the theoretical results.

5

New Construction Methods and Performance Analysis of WINDMI Chaotic System

Salih Thair A.

International Journal of Electronics and Telecommunications

|

2022

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Vol. 68, No. 1

129--136

EN

Chaos is an active topic of study in the field of secure communication systems that have garnered much consideration in recent years because of excessive sensitivity to a simple change in its initial conditions. In this paper, the essential features of the suggested WINDMI chaotic system like the phase portraits of the attractors, bifurcation, PSD, correlation, and balance property of the windmi chaotic system have been depicted in detail through MATLAB tools simulations and circuital application. The bifurcation examination detects a wealthy and attractive characteristic of the proposed windmi chaotic oscillator such as periodical multiple bifurcations, has two stable states chaotic demeanor, periodical windows, and recapture bifurcations. In this paper, after exploring the dynamic features of the windmi chaos paradigm, a practical chaotic circuit is implemented on the fpaa chip. Eventually, the circuit practical results of the windmi chaotic attractors present similarities with numerical simulations. The importance of the work is reflected in the use of field programmable analog array in the implementation of the windmi oscillator, and the possibility of varying the initial condition during the operation of the system. An unlimited number of signals can be generated, which enables it to be used as an oscillator utilized in many transceiver systems, that utilized an unlimited number of signals.

6

Deficiency-surplus transition function (DeSuTra) in semi-empirical formulas for tumbling of freely falling card

Vorohobovs Vladimirs, Kleinhofs Martins

Composites Theory and Practice

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2022

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R. 22, nr 2

92--98

EN

A new phenomenological method for composing analytical formulae to describe dynamic systems using the DeSuTra function as a building block is introduced. Based on heuristic considerations, it is possible to write a correct formula with several unknown coefficients. Next, these coefficients are tuned such a way that the result coincides with the experimental data. To illustrate the viability of such a method, a simple but not trivial aerodynamic system was chosen: the autorotation of a rectangular piece of paper that falls in air. Three correction coefficients (diminishers) were introduced to calculate its rotation frequency Then a simple expression for the Magnus effect and drag force was used. All the obtained formulae were experimentally proved and the coefficients calculated. The conclusions drawn confirm the usefulness of the presented calculation procedure for the design of composites with chaotically distributed reinforcements.

7

A new multistable jerk chaotic system, its bifurcation analysis, backstepping control-based synchronization design and circuit simulation

Vaidyanathan Sundarapandian, Benkouider Khaled, Sambas Aceng

Archives of Control Sciences

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2022

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Vol. 32, No. 1

123--152

EN

In this work, we present results for a new dissipative jerk chaotic system with three quadratic terms in its dynamics.We describe the bifurcation analysis for the new jerk system and also show that the proposed system exhibits multi-stability. Next, we describe a backstepping control-based synchronization design for a pair of new jerk chaotic systems. MATLAB simulations are put forth to exhibit the various findings in this work. Furthermore, we exhibit a circuit simulation for the new jerk system using MultiSim.

8

Comparison of the Vibration Response of a Rotary Dobby with Cam-Link and Cam-Slider Modulators

Yu Hongbin, Yin Honghuan, Peng Junqiang, Wang Lei

Autex Research Journal

|

2021

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Vol. 21, no. 4

491--500

EN

This article presents the kinematic modeling and analysis of cam profiles of two different types of modulator: a cam-link and a cam-slider modulators. Kinematic and dynamic models of the two different modulators were established based on the motion curves of the main shaft of the rotary dobby. Simulations were carried out in Simulink to analyze the vibration responses under different rotary speeds, and vibration responses of the two mechanisms were compared. The results show that the cam-link modulator vibrates smoothly at speeds of <700 rpm, and theoretically, the speed should not exceed 1,400 rpm. The cam-slider modulator vibrates smoothly at speeds of <500 rpm, and theoretically, the speed should not exceed 1,000 rpm. The cam-slider modulator is more suitable for use at low speeds, whereas the cam-link modulator is more appropriate for high speeds. When both the cam-slider and cam-link modulators operate at high speeds, vibration distortion occurs, leading to bifurcation and chaotic vibration. Further knowledge of the complex behaviors associated with detachment of the follower from the cam can support the design of more sophisticated controllers aimed at avoiding follower detachment.

9

Stability and bifurcation analysis of an overhung rotor with electromagnetic actuators

Przybyłowicz Piotr M., Kurnik Włodzimierz

Journal of Theoretical and Applied Mechanics

|

2020

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Vol. 58 nr 2

525--539

EN

A rotating system consisting of a slender massless viscoelastic shaft simply supported in rolling bearings and a rigid massive disc mounted to the overhung end of the shaft is considered to study its stabilization against flutter. Instability and transverse vibration occurs due to the internal friction in the shaft. It is shown in the paper that the disc can be stabilized and its bifurcating self-excited vibration can be effectively reduced and modified by contactless radial magnetic actuators, using two alternative control strategies – semi-active utilizing constant or rotation-dependent actuator voltage or fully active with closed-loop state-dependent feedback. The near-critical transverse disc vibration is analyzed using the theory of Hopf bifurcation. Smooth, soft-type self-excitation is presented after activation of the dynamic vibration control which prevents the system from sudden jumps of vibration amplitude near the critical point.

10

Nonlinear coupled moving-load excited dynamics of beam-mass structures

Ghayesh M. H., Farokhi H., Zhang Y., Gholipour A.

Archives of Civil and Mechanical Engineering

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2020

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Vol. 20, no. 2

207--217

EN

Investigated in this paper is the first on the moving-load-caused nonlinear coupled dynamics of beam-mass systems. A constant value load excites the beam-mass system where its position on the beam-mass system changes periodically. The energy contribution of the moving load is included via a virtual work formulation. The kinetic energy of the mass together with the beam as well as energy stored in the beam after deflection is formulated. Hamilton’s principle gives nonlinear equations of the beam-mass system under a moving load in a coupled transverse/longitudinal form. A weighted-residual-based discretisation gives a 20 degree of freedom which is numerically integrated via continuation/time integration along with Floquet theory techniques. The resonance dynamics in time, frequency, and spatial domains is investigated. As we shall see, torus bifurcations are present for some beam-mass structure parameters as well as travelling waves. A finite element analysis is performed for a simpler linear version of the problem for to-some-extend verifications.

11

Parallel computing of two-parameter bifurcation diagrams of an electric arc model with chaotic dynamics using Nvidia CUDA and OpenMP technologies

Pala Artur, Machaczek Marek

Przegląd Elektrotechniczny

|

2019

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R. 95, nr 3

138--142

EN

This paper presents parallel and massively parallel calculations of two-parameter bifurcation diagrams of an electric arc model. A simple dynamical model of electric arc is used. Such a model can show complex two-parameter bifurcations with periodic and chaotic responses. Two different parallel computing technologies were used to implement the calculations. Parallel computations are implemented using the OpenMP library and CPU processors. Massively parallel computations are implemented using the Nvidia CUDA technology and GPU processors.

PL

W artykule przedstawiono równoległe i masowo równoległe obliczenia dwuparametrycznych diagramów bifurkacyjnych dla modelu łuku elektrycznego. Do analizy wykorzystano dynamiczny model łuku elektrycznego z okresowymi i chaotycznymi odpowiedziami. Do realizacji obliczeń wykorzystano dwie różne technologie. Obliczenia równoległe zaimplementowano przy użyciu biblioteki OpenMP i procesorów CPU. Obliczenia masowo równoległe zostały zaimplementowane przy użyciu technologii Nvidia CUDA i procesorów GPU.

12

Theoretical and experimental investigations of the bifurcation behavior of creep groan of automotive disk brakes

Zhao X., Gräbner N., Wagner U. von

Journal of Theoretical and Applied Mechanics

|

2018

|

Vol. 56 nr 2

351--364

EN

There are several low frequency vibration phenomena which can be observed in automotive disk brakes. Creep groan is one of them provoking noise and structural vibrations of the car. In contrast to other vibration phenomena like brake squeal, creep groan is caused by the stick-slip-effect. A fundamental investigation of creep groan is proposed in this paper theoretically and experimentally with respect to parameter regions of the occurrence. Creep groan limit cycles are observed while performing experiments in a test rig with an idealized brake. A nonlinear model using the bristle friction law is set up in order to simulate the limit cycle of creep groan. As a result, the system shows three regions of qualitatively different behavior depending on the brake pressure and driving speed, i.e. a region with a stable equilibrium solution and a stable limit cycle, a region with only a stable equilibrium solution, and a region with only a stable limit cycle. The limit cycle can be interpreted as creep groan while the equilibrium solution is the desired vibration-free case. These three regions and the bifurcation behavior are demonstrated by the corresponding map. The experimental results are analyzed and compared with the simulation results showing good agreement. The bifurcation behavior and the corresponding map with three different regions are also confirmed by the experimental results. At the end, a similar map with the three regions is also measured at a test rig with a complete real brake.

13

Bifurcation and chaos analysis of a gear-rotor-bearing system

Gou X., Zhu L., Qi C.

Journal of Theoretical and Applied Mechanics

|

2018

|

Vol. 56 nr 3

585--599

EN

To study chaos and bifurcation of a gear system, a five-degree-of-freedom nonlinear dynamic model of a gear-rotor-bearing system is established. It consists of a gear pair, supporting shafts, bearings and other auxiliary components. The effects of frequency, backlash, bearing clearance, comprehensive transmission error and stiffness on nonlinear dynamics of the system are investigated according to bifurcation diagrams, phase portraits and Poincar´e maps by a numerical method. Some nonlinear phenomena such as grazing bifurcation, Hopf bifurcation, inverse-Hopf bifurcation, chaos and coexistence of attractors are investigated. Different grazing bifurcations and their causes are discussed. The critical parameters are identified, too.

14

On the elimination of nonlinear phenomena in DC/DC converters using type-2 fuzzy logic controller

Gozim D., Guesmi K., Mahi D.

Diagnostyka

|

2018

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Vol. 19, No. 3

73--80

EN

DC/DC converters are wealthy of nonlinear phenomena that appear when the converter parameters are subject to perturbation or variation. The converter may exhibit bifurcation from behavior to another, quasi periodic and chaotic responses. In such cases, it is difficult and even impossible to analyze, to predict and to control the converter behavior. This paper gives a description of a DC/DC converter and shows their desirable and undesirable behaviors; then a solution, based on type-2 fuzzy logic controller, is proposed to eliminate the undesirable behaviors and to enhance the converter dynamics.

15

Chaotic Processes In PWM Converter

Zhuikov V., Matiiko A.

Present Problems of Power System Control

|

2016

|

Nr 7

43--51

EN

The possibility of chaotic oscillations in them is determined. The structure of the chaotic oscillations in the DC converter is considered. The system stability at various gain values of the feedback signal is investigated. The task is building a precision DC buck converter. The goal is achieved by means of providing high feedback signal gain converter operation mode. The work of the converter is commended in a case of: a) changing the input voltage; b) changing the value of the load resistance. It is shown that while ensuring the appropriate converter operation mode it is possible to improve stabilising properties and reduce the system operation frequency.

16

Stateczność rozwiązań i bezpieczeństwo ruchu po łuku modelu pojazdu szynowego

Dusza M.

Prace Naukowe Politechniki Warszawskiej. Transport

|

2016

|

z. 109

21--44

PL

Artykuł przedstawia wyniki badań mających na celu określenie wpływu stanu powierzchni tocznych kół i szyn na stateczność i bezpieczeństwo ruchu modelu pojazdu szynowego po łuku. Większość czynników środowiskowych ma wpływ na stan powierzchni szyn i tym samym na zjawiska kontaktowe koła - szyny. W badaniach modelowych stan współpracujących powierzchni kół i szyn reprezentowany jest przez współczynnik tarcia. Badany jest model 4-osiowego pojazdu szynowego utworzony z wykorzystaniem oprogramowania inżynierskiego VI-Rail. Dla kilku wybranych wartości współczynnika tarcia wykonano badania stateczności ruchu po łukach oparte na metodzie bifurkacyjnej. Wyniki badań odniesiono do powszechnie stosowanego kryterium bezpieczeństwa przeciw wykolejeniu.

EN

To evaluate the condition of wheel and rail surface influence on rail vehicle model stability and safety is main aim of presented research. Some environment and whether conditions may have significant influence on the rail vehicle dynamics in curve. Wheels and rails surface properties directly depend on the humidity, temperature and environment pollutions. The coefficient of friction between wheels and rails is the parameter, which characterize the changeable conditions. The investigations focus on determination of coefficient of friction influence on rail vehicle dynamics. The 4-axle rail vehicle model of passenger coach was prepared with use of the engineering software VI-Rail. The wheel-rail forces are calculated using the FASTSIM algorithm of Kalker. One value of coefficient of friction is applied for single simulation process. Twenty four series of simulations for coefficient of friction changed from 0.1 to 0.8 and curve radius R = 2000, 3000 and 4000 m were performed. The results are presented in form of bifurcation diagrams. The stability of motion results are compared to Nadal’s safety of motion criterion.

17

Experimental study on amplitude-frequency characteristic and basin stability of horizontally driven pendulum

Jia J., Wu Y., Liu W., Xiao J.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 3

839--846

EN

In this article, an inverted pendulum system is set up to explore the dynamics of a horizontally driven pendulum which exhibits a great variety of dynamical behavior and appears in a wide range of applications in the field of engineering. The facility is efficient to experimentally explore two kinds of coexisting movement patterns in the horizontally driven pendulum, i.e. in-phase and anti-phase patterns between the angular velocity of the pendulum rod and the direction of the driving forces. Theoretical analysis is applied to reveal the regimes of the coexistence of the two movement patterns, which is promising to control the system to a desired pattern.

18

Prediction of aircraft lost of control in the flight by continuation, bifurcation, and catastrophe theory methods

Sibilski K., Kowalski M.

Journal of KONES

|

2016

|

Vol. 23, No. 4

451--460

EN

Lost of Control in Flight (LOC-I) is ordinarily associated with flight outside of the normal flight envelope, with nonlinear behaviours, and with an inability of the pilot to control the aircraft. These results provide a means for analysing accident data to establish whether or not the accident should be classified as LOC-I. Moreover, they help identify when the initial upset occurred, and when control was lost. The analysis also suggests which variables were involved, thereby providing clues as to the underlying mechanism of upset. However, it does not provide direct links to the flight mechanics of the aircraft, so it cannot be used proactively to identify weaknesses or limitations in the aircraft or its control systems. Moreover, it does not explain how departures from controlled flight occur. The complexity of the disaster aetiology stems from both the scale and coupling of the systems (not only the physical aircraft systems but also the organizational systems that support the operation). This complexity creates a pattern of disaster that evolves or it is precipitated through a series of several small failures. The cusp catastrophe model facilitates the mapping of Reason’s latent failure model, providing a descriptive and predictive illustration of the emergence of latent conditions under the trigger of situational factors. The risk of an accident increases as the situational and systematic factors combine to create an inherent instability resulting in the catastrophic event.

19

Stability analysis and internal heating effect on oscillatory convection in a viscoelastic fluid saturated porous medium under gravity modulation

Bhadauria B. S., Singh M. K., Singh A., Singh B. K., Kiran P.

International Journal of Applied Mechanics and Engineering

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2016

|

Vol. 21, no. 4

785--803

EN

In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.

20

Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation

Reit M., Berens M., Mathis W.

Archives of Electrical Engineering

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2016

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Vol. 65, nr 2

337--347

EN

Since the so-called Hopf-type amplifier has become an established element in the modeling of the mammalian hearing organ, it also gets attention in the design of nonlinear amplifiers for technical applications. Due to its pure sinusoidal response to a sinusoidal input signal, the amplifier based on the normal form of the Andronov-Hopf bifurcation is a peculiar exception of nonlinear amplifiers. This feature allows an exact mathematical formulation of the input-output characteristic and thus deeper insights of the nonlinear behavior. Aside from the Hopf-type amplifier we investigate an extension of the Hopf system with focus on ambiguities, especially the separation of solution sets, and double hysteresis behavior in the input-output characteristic. Our results are validated by a DSP implementation.