Bifurcation and Lyapunov's exponents characteristics of electrical scalar drive systems

Sangrody, Reza; Nazarzadeh, Jalal; Nikravesh, K.Y.

doi:10.1049/iet-pel.2011.0024

Cited by 10 publications

(12 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Among these different approaches, three models are commonly found in the literature: a switching model [18,19]; a continuous-time averaging, or averaged, model [10,20,21]; and a discrete-time iterative mapping model, or discrete-time model [7,[22][23][24][25]. Using circuit simulations and an iterative map, bifurcation diagrams can be obtained [3,26]; however, the diagram of the latter model might have a small shift to the right due to the truncated term of the Taylor series, which is used in the derivation of the iterative map [1]. The stability of the system can be studied by evaluating its eigenvalues at the equilibrium point using the averaged or discrete-time models [10].…”

Section: Introductionmentioning

confidence: 99%

Generalisation of an averaged model approach to estimate the period‐doubling bifurcation onset in power converters

Gavagsaz-Ghoachani

Phattanasak

Martin

et al. 2016

IET Power Electronics

View full text Add to dashboard Cite

The usual method of estimating the onset of bifurcation and studying non-linear phenomena in power electronic devices consists of defining the discrete-time model. This model provides more precise results than an averaged model. However, the discrete-time model cannot be developed easily for some particular systems. In this study, a continuoustime averaging model is developed for a boost converter in the continuous-conduction mode (CCM). This proposed model is used to obtain the eigenvalues of the system to predict the stable operation of the period-1 orbit. It is observed that the loss of the asymptotic stability of the proposed model corresponds to the onset of period-doubling bifurcation in the discrete-time model. The generalisation of this method is investigated by applying the proposed method to a DC active filter converter connected in parallel with a CCM boost converter. Using this model, it is possible to obtain the eigenvalues of the system to investigate robustness properties with regards to system parameter variations. To confirm the validity of the proposed method, simulation and experimental results are presented.

show abstract

Section: Introductionmentioning

confidence: 99%

Generalisation of an averaged model approach to estimate the period‐doubling bifurcation onset in power converters

Gavagsaz-Ghoachani

Phattanasak

Martin

et al. 2016

IET Power Electronics

View full text Add to dashboard Cite

show abstract

“…Equations (2), (4) and (7) indicate that the LED current is smaller than its value when valley switching is activated. Fig.…”

Section: Valley Switching Effect In Buck Led Driver In Current Contromentioning

confidence: 99%

“…An incorrect switching pattern causes some problems like fluctuations in input/output voltage and current, chaotic phenomena in their responses etc. [7, 8]. However, a proper switching method can decrease the switching losses and enhance efficiency.…”

Section: Introductionmentioning

confidence: 99%

Semi‐valley switching method for buck LED driver to increase its efficiency and performance

Sangrody

Marzband

et al. 2020

IET Power Electronics

View full text Add to dashboard Cite

Valley switching is one of the most efficient methods to decrease the switching losses in DC/DC converters. It uses a resonance between the converter's inductor and parasitic output capacitance of a metal-oxide-semiconductor field-effect transistor. In this study, the drawbacks of the valley switching in buck light-emitting-diode (LED) drivers are investigated. It shows that in spite of decreasing the switching losses, the valley switching method reduces its efficiency in some conditions. Also, it is clarified that the valley switching method not only causes current fluctuation in boost power factor correction converters but also malfunctions the buck LED drivers' performance. In this study, a semi-valley switching and its implementation are introduced to solve these problems. In general, it is shown that the proposed method improves both the efficiency and the performance of the buck LED driver, simultaneously. The methodologies are implemented in an experimental prototype to verify the proposed method.

show abstract

“…These studies can be divided into two parts: analysis and control of chaotic behavior in these systems. In the field of chaos behavior analysis of various types of electric drive systems, most of the work has been carried out in References 8‐17 The open‐loop IM drive system is modeled using eight differential equations in a nonlinear form, taking into account the motor, mechanical load, voltage inverter, and rectifier 8 . In Reference 9, this open‐loop system uses a voltage‐to‐frequency scalar control to adjust the speed, in the presence of constant and periodic load.…”

Section: Introductionmentioning

confidence: 99%

“…In completing the work, 10 modified Poincaré map, largest Lyapunov's exponent and bifurcation diagram have been used in order to analyze the effect of switching of the PWM inverter. 11 Therefore, numerical analysis is used to prove the simulation result. In the switched reluctance motor (SRM) drive system, considering the system in light load and low speed and also regardless of the effect of mutual inductance, the linear model of the flux linkage is used to obtain the mapping.…”

mentioning

confidence: 99%

Study of bifurcation and chaos in scalar drive systems of permanent magnet synchronous machines

Babaei

Feyzi

Marashi

2021

Int Trans Electr Energ Syst

View full text Add to dashboard Cite

In this paper, a nonlinear dynamic of permanent magnet synchronous machine scalar drive systems (PMSMSDS) is investigated thoroughly. At first, the mathematical dynamic model of the PMSMSDS is developed and formulated for open-and close-loop cases. Then, constant and periodic load torque are considered for the analysis of the system. The Jacobian matrix and the Poincaré mapping of the system are calculated analytically to study the feasibility of nonlinear phenomena at each point of equilibrium for constant and periodic loads, respectively. Computer simulation is used to obtain bifurcation diagram, time response, and phase plane of the state variables to investigate the complex behavior of the system by changing some parameters. It is shown that by changing the parameters of reference speed command, supply voltage range, and speed controller gain, the response of PMSMSDS state variables will be routed to limit cycle, bifurcated, and chaotic. Numerical analysis is provided to confirm the simulation results.

show abstract

Bifurcation and Lyapunov's exponents characteristics of electrical scalar drive systems

Cited by 10 publications

References 21 publications

Generalisation of an averaged model approach to estimate the period‐doubling bifurcation onset in power converters

Generalisation of an averaged model approach to estimate the period‐doubling bifurcation onset in power converters

Semi‐valley switching method for buck LED driver to increase its efficiency and performance

Study of bifurcation and chaos in scalar drive systems of permanent magnet synchronous machines

Contact Info

Product

Resources

About