scholarly journals Nonlinear Dynamics and Stability Analysis of a Three-Cell Flying Capacitor DC-DC Converter

2021 ◽  
Vol 11 (4) ◽  
pp. 1395
Author(s):  
Abdelali El Aroudi ◽  
Natalia Cañas-Estrada ◽  
Mohamed Debbat ◽  
Mohamed Al-Numay
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Monodromy Matrix ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Simple Expression ◽  
Buck Converter ◽  
State Variables ◽  
Bifurcation Phenomena ◽  
The Stability

This paper presents a study of the nonlinear dynamic behavior a flying capacitor four-level three-cell DC-DC buck converter. Its stability analysis is performed and its stability boundaries is determined in the multi-dimensional paramertic space. First, the switched model of the converter is presented. Then, a discrete-time controller for the converter is proposed. The controller is is responsible for both balancing the flying capacitor voltages from one hand and for output current regulation. Simulation results from the switched model of the converter under the proposed controller are presented. The results show that the system may undergo bifurcation phenomena and period doubling route to chaos when some system parameters are varied. One-dimensional bifurcation diagrams are computed and used to explore the possible dynamical behavior of the system. By using Floquet theory and Filippov method to derive the monodromy matrix, the bifurcation behavior observed in the converter is accurately predicted. Based on justified and realistic approximations of the system state variables waveforms, simple and accurate expressions for these steady-state values and the monodromy matrix are derived and validated. The simple expression of the steady-state operation and the monodromy matrix allow to analytically predict the onset of instability in the system and the stability region in the parametric space is determined. Numerical simulations from the exact switched model validate the theoretical predictions.

scholarly journals Stability Analysis in Positive Output and Negative Output DC to DC Converters Used in Renewable Energy Applications

2019 ◽  
Author(s):  
Maheswari Ellappan ◽  
Kavitha Anbukumar
Keyword(s):  
Renewable Energy ◽  
Stability Analysis ◽  
Output Voltage ◽  
Monodromy Matrix ◽  
Period Doubling ◽  
Current Mode ◽  
Power Converter ◽  
Control Technique ◽  
Step Down ◽  
The Stability

The renewable energy source plays a major role in the grid side power production. The stability analysis is very essential in the renewable energy converters. In this paper the bifurcation is analyzed in ZETA converter and Continuous input and output(CIO) power Buck Boost converter. The ZETA converter gives positive step down and step up output voltage and the CIO power converter gives the negative step up and step down output voltage. These converters are used in the DC micro grid with renewable energy as the source. The current mode control technique is applied to analyze the bifurcation behavior and the reference current is taken as the bifurcation parameter. When the reference current is varied, both the converters loses its stability and it enters into chaotic region through period doubling bifurcation. The simulation results are presented to study the performance behavior of both the converters. The stability region of both the converters are determined by deriving the Monodromy matrix approach.

Experimental Verification of Critical Speed Ranges for Elastic Closed Loop Linkage Systems

1992 ◽  
Vol 114 (1) ◽  
pp. 126-130 ◽  
Author(s):  
S. Nagarajan ◽  
D. A. Turcic
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Critical Speed ◽  
Closed Loop ◽  
Local Maximum ◽  
Experimental Methods ◽  
Strain Response ◽  
Maximum Value ◽  
Speed Range ◽  
The Stability

In this work critical speed ranges are determined and verified for an elastic four bar crank rocker mechanism where all links are modeled as elastic members. The procedure used for the dynamic stability analysis is described in Nagarajan and Turcic (1991). The speed range of interest where the stability analysis is performed is 195–390 rpm. The values of the critical speeds obtained in the above speed range are then verified using independent theoretical and experimental methods of analysis. The steady state strain response is obtained both theoretically and experimentally for a number of speeds in the speed range of 195–390 rpm. From these responses plots different strain characteristics versus operating speeds are obtained. These plots exhibit peaks in the response at certain speeds indicating that the dynamic response at these speeds reaches a local maximum value. The critical speed ranges determined are found to correspond quite closely to the speeds where the peaks occur. This indicates that the critical speed ranges are indeed speeds where the response of the system is larger when compared to neighboring speeds and that the methods of determining them are accurate for the application considered.

scholarly journals Stability Analysis of a Gear Pair System Supported by Squeeze-Film Dampers

2001 ◽  
Vol 7 (2) ◽  
pp. 143-151 ◽  
Author(s):  
T. N. Shiau ◽  
J. R. Chang ◽  
S. T. Choi
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Harmonic Balance Method ◽  
Squeeze Film ◽  
Hybrid Technique ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Squeeze Film Dampers ◽  
The Stability

This paper examines the stability of the steady-state periodic response of a gear pair system supported by squeeze-film dampers. The steady-state response of the system is obtained by using the hybrid technique of Harmonic Balance Method and Time Collocation. The Fioquet-Liapunov theory is used to perform the stability analysis of the first variation equations with periodic coefficients, which is generated by the perturbation technique. The stability charts on gear mesh stiffness, spin ratio, disk unbalance, gravity, and squeeze-film damper are used to perform parameter studies. The numerical results show that the unstable region always occurs when the spin ratio is near the second coupled mode of the gear pair system. Furthermore, the mesh stiffness has a significant influence on the coupled critical speeds. Therefore, it plays an important role in determining the spin ratio stability range.

scholarly journals Stability of the homogeneous steady state for a model of a confined quasi-two-dimensional granular fluid

2021 ◽  
Vol 249 ◽  
pp. 04005
Author(s):  
Vicente Garzó ◽  
Ricardo Brito ◽  
Rodrigo Soto
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Transport Coefficients ◽  
Nonlinear Dependence ◽  
Granular Gases ◽  
Two Dimensional ◽  
Hydrodynamic Equations ◽  
Homogeneous Steady State ◽  
Granular Fluid ◽  
The Stability

A linear stability analysis of the hydrodynamic equations of a model for confined quasi-two-dimensional granular gases is carried out. The stability analysis is performed around the homogeneous steady state (HSS) reached eventually by the system after a transient regime. In contrast to previous studies (which considered dilute or quasielastic systems), our analysis is based on the results obtained from the inelastic Enskog kinetic equation, which takes into account the (nonlinear) dependence of the transport coefficients and the cooling rate on dissipation and applies to moderate densities. As in earlier studies, the analysis shows that the HSS is linearly stable with respect to long enough wavelength excitations.

Symmetry Properties in the Symmetry-Breaking of Nonsmooth Dynamical Systems

2009 ◽  
Vol 5 (1) ◽  
Author(s):  
Alessio Ageno ◽  
Anna Sinopoli
Keyword(s):  
Group Theory ◽  
Stability Analysis ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Simply Supported ◽  
Symmetry Properties ◽  
Existence Conditions ◽  
Asymmetric Responses ◽  
The Stability ◽  
Nonsmooth Dynamical Systems

In this paper, the block simply supported on a harmonically moving ground is assumed as a system well representing a typical nonsmooth dynamical behavior. The aim of the work is to carry out the existence conditions of asymmetric responses; an analysis that comes first in any stability investigation. By using simple definitions belonging to the symmetry group theory, it is possible to completely clarify the relationships between the various initial conditions that allow simple asymmetric responses, and to develop tools, which will be very useful in the stability analysis of more complex asymmetric responses.

Bifurcation Analysis of a Belousov–Zhabotinsky Reaction Model

2015 ◽  
Vol 25 (06) ◽  
pp. 1550093 ◽  
Author(s):  
Xiaoli Wang ◽  
Yu Chang ◽  
Dashun Xu
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Period Doubling ◽  
Reaction Model ◽  
Bifurcation Phenomena ◽  
Route To Chaos ◽  
The Stability ◽  
Belousov Zhabotinsky Reaction

We investigate the bifurcation phenomena in a Belousov–Zhabotinsky reaction model by applying Hopf bifurcation theory in frequency domain and harmonic balance method. The high accurate predictions, i.e. fourth-order harmonic balance approximation, on frequencies, amplitudes, and approximation expressions for periodic solutions emerging from Hopf bifurcation are provided. We also detect the stability and location of these periodic solutions. Numerical simulations not only confirm the theoretical analysis results but also illustrate some complex oscillations such as a cascade of period-doubling bifurcation, quasi-periodic solution, and period-doubling route to chaos. All these results improve the understanding of the dynamics of the model.

scholarly journals V/C Digital Controlled DC-DC Converter

2020 ◽  
Vol 9 (3) ◽  
pp. 167-175
Keyword(s):  
Stability Analysis ◽  
Transient Analysis ◽  
Stability Boundary ◽  
Buck Converter ◽  
Sampled Data ◽  
Signal Model ◽  
Stability Range ◽  
Z Domain ◽  
Average Current ◽  
The Stability

In this paper, the switching of dc-dc converter using voltage/current digital control is proposed. It is the combination of existed digital average voltage and digital average current controls. The stability analysis of V/C digital controlled dc-dc converter is derived by using sampled data model. The transient analysis of V/C digital controlled dc-dc converter is also derived by using z-domain small signal model. The proposed V/C digital controlled dc-dc converter has over current protection, fast load transient response, no sub-harmonic oscillations at any value of duty cycle, and wider stability range. The proposed system is analysed with a simple buck converter. The output voltage and inductor current weighting factors influence the stability boundary and transient performances of V/C digital controlled dc-dc converter. The stability analysis and transient analysis is investigated and verified by circuit simulations

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