A new general mathematical technique for stability and bifurcation analysis of DC-DC converters applied to one-cycle controlled buck converters with non-ideal reset

Gurbină, Mircea; Draghici, Daniel; Ciresan, Aurel; Lascu, Dan

doi:10.1109/optim.2014.6850891

Cited by 5 publications

(4 citation statements)

References 17 publications

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“…The exact mathematical method proposed to determine the point at which instability occurs in a converter with CCM operation, usually by bifurcation, uses the method of characteristic multipliers and a generalized discrete model. The technique has been successfully used by the authors in several applications and experiments [1][2][3][4] on converters with different controls including multiphase converters [5][6]. All these studies have been confirmed on clasical converters [7][8][9][10], or new converters [11][12][13][14][15][16], or quadratic converters [17][18][19].…”

Section: The General and Exact Mathematical Methods For Determining T...mentioning

confidence: 97%

Exact Mathematical Analysis of DC-DC Converters Employing Type 3 Controllers

Gurbină

Lascu

Lica

et al. 2023

Preprint

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A new method for analysing the stability of dc-dc converters in closed-loop operation is developed. A generalized discrete model is proposed consisting of two nonlinear vector equations: the state equation and the nondynamic constraint. After model linearization, the classical technique of using characteristic multipliers can be applied. Several problems were solved regarding: the nondynamic constraint derivation; the steady-state operation point calculation; verifying that the parameters defining the steady-state operation point are located in the linear region and are not in the proximity of a saturated vicinity; partial derivatives determination and Jacobian calculation. The above concepts have been easily implemented in Matlab, allowing: determination of the parameter value for which instability occurs; to demonstrate that instability is installed with a Neimark-Sacker bifurcation; to prove that the proposed exact method predicts a much larger stable region, 327% higher compared to that predicted by the traditional approach. The theoretical considerations were accurately validated by computer simulation.

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Section: The General and Exact Mathematical Methods For Determining T...mentioning

confidence: 97%

Exact Mathematical Analysis of DC-DC Converters Employing Type 3 Controllers

Gurbină

Lascu

Lica

et al. 2023

Preprint

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“…This can be achieved using (6) and taking into account that in steady state the discrete model becomes a dc one, that is x n + 1 = x n = X, d n = D, h n = H and the steady-state transition matrices are those given by (5)…”

Section: Partial Derivatives Of Functions G F 1 F 2 and Exact Steamentioning

confidence: 99%

“…A unified analysis of CCM converters employing different control techniques (e.g., one cycle control, charge control, etc.) is performed in [5][6][7][8] from a bifurcation point of view. The asynchronous switching map on studying the stability effects of circuit parameters in CCM fixed off-time controlled buck converter is performed in [9].…”

Section: Introductionmentioning

confidence: 99%

A New Exact Mathematical Approach for Studying Bifurcation in DCM Operated dc-dc Switching Converters

et al. 2018

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Abstract:A bifurcation study for dc-dc converters operated in DCM is performed using an accurate method. When applying classical techniques significant difficulties are encountered in the calculations. For example, using the averaging method the validity of the result is limited to half the switching frequency and higher order effects are neglected Another approach is to perform a Taylor expansion of the state transition matrices. However, this is somehow also an averaging but the fact that the Taylor series is truncated leads to unacceptable inaccuracy. A new mathematical technique for discontinuous conduction mode (DCM) analysis of dc-dc switching converters is proposed in order to predict bifurcation and chaos. The proposed technique is based on exact calculation of the state transition matrices and of the Jacobian thus providing higher accuracy of the results compared to other previously reported approaches. Beside the fact the new technique allows for exact diagnosis of instability, it is also highly general, in the sense that it can be applied to any dc-dc DCM operated converter employing any type of control. The good agreement between theoretical, simulation and experimental results, with an error lower than 0.94%, confirms the validity of the proposed method.

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“…But the traditional one‐cycle controlled QBC (TOCCQBC) suffers from infirmness with the occurrence of load disturbance, mainly because of the lack of output feedback. A kind of improved one‐cycle controlled QBC (IOCCQBC) has been presented in Gurbină et al This strategy is just used in buck converter, which cannot be applied to QBC. At the same time, to improve the response speed, it is necessary to add a current feedback loop into the circuit.…”

Section: Introductionmentioning

confidence: 99%

One‐cycle controlled quadratic buck converter

Wang

2018

Circuit Theory & Apps

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Summary The quadratic DC‐DC converter can broaden the voltage conversion ratio, which meets the requirements of wide input voltage. However, large‐scale variation of input voltage puts forward harsh requirements on ability to resist input disturbance of control strategy. Quadratic buck converter (QBC) is pulsed nonlinear dynamic systems, so the one‐cycle control strategy based on robustness principle may provide better rejection of power source than the linear feedback control. But the traditional one‐cycle controlled QBC (TOCCQBC) suffers from poor ability against load disturbance and steady‐state error. To overcome aforementioned shortages, an improved OCCQBC is proposed by adding inductor current to diode voltage as integral variable and introducing feedback of output voltage. The paper first introduces the working principle of the QBC, and second, the OCCQBC is presented. Then, a mathematical model using small signal analysis of the OCCQBC is established, and an experimental prototype with a power of 6 W is set up. Simulation and experimental results verify the correctness of the theoretical analysis and the feasibility of the strategy.

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A new general mathematical technique for stability and bifurcation analysis of DC-DC converters applied to one-cycle controlled buck converters with non-ideal reset

Cited by 5 publications

References 17 publications

Exact Mathematical Analysis of DC-DC Converters Employing Type 3 Controllers

Exact Mathematical Analysis of DC-DC Converters Employing Type 3 Controllers

A New Exact Mathematical Approach for Studying Bifurcation in DCM Operated dc-dc Switching Converters

One‐cycle controlled quadratic buck converter

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