Sampled-Data Modeling and Analysis of the Power Stage of PWM DC-DC Converters

Fang, Chung-Chieh; Abed, Eyad H.

doi:10.21236/ada438683

Cited by 7 publications

(21 citation statements)

References 27 publications

(48 reference statements)

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“…Some discrete‐time models reported in the literature are obtained by discretizing the average model and mapping the s plane to the z ‐domain using well‐known approximations such as Euler, bilinear, zero‐order hold, and pole zero matching transformations() and, although they are control‐oriented models, they suffer from the the same inaccuracies inherited from the averaging process and those from the s ‐to‐ z transformation. The discrete‐time models obtained by directly sampling the switched model are obtained using an exact discretization of this model() are enough accurate but except for digitally controlled converters with uniformly sampled PWM,() they are of high level of abstraction to be appropriately used for design purposes. Hence, obtaining an optimal compromise between the accuracy and the control‐oriented formulation is a real challenge.…”

Section: Introductionmentioning

confidence: 99%

Nonaveraged control‐oriented modeling and relative stability analysis of DC‐DC switching converters

Al‐Turki

Aroudi

Mandal

et al. 2017

Circuit Theory & Apps

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Summary This paper presents a unified and exact nonaveraged approach to derive a frequency‐domain control‐oriented model for accurate prediction of the fast timescale dynamics and performances of switching converters with fixed frequency naturally sampled pulse width modulation and integrating feedback loop. Because the approach avoids averaging and approximations related to this process, a very good accuracy of the derived model is obtained. The main difference between the presented approach and the existing methodology for accurately predicting the behavior of switching converters is that, here, we break the feedback loop and we focus on analyzing the open‐loop gain and the effect of the system parameters on relative stability. This results in an approach much similar to control systems techniques rather than nonlinear dynamical system approaches. Consequently, the relative stability is tackled easily in the frequency domain. In particular, by treating the modulator as a gain depending on the operating point, the new model is formulated in such a way that standard control‐oriented tools such as Bode diagrams and root‐loci can be easily used. Therefore, the proposed approach gives some important issues like gain and phase margins that are highly useful in controller design. It is noticed that the crossover frequency, gain, and phase margins predicted by using the averaged model may deviate significantly from the actual values given by the proposed approach. The paper points out the sources of discrepancies and the theoretical results are validated by simulations using a circuit‐level switched model.

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Section: Introductionmentioning

confidence: 99%

Nonaveraged control‐oriented modeling and relative stability analysis of DC‐DC switching converters

Al‐Turki

Aroudi

Mandal

et al. 2017

Circuit Theory & Apps

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“…Let the durations of the first and the second stages be DT and D 2 T , respectively. The inductor current i L is zero in the third stage, and one discrete-time pole is zero [22]. The discrete-time dynamics is thus one-dimensional.…”

Section: Nonlinear Discrete-time Modelmentioning

confidence: 99%

Discrete-Time Poles and Dynamics of Discontinuous Mode Boost and Buck Converters Under Various Control Schemes

Fang

2012

Preprint

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Nonlinear systems, such as switching DC-DC boost or buck converters, have rich dynamics. A simple one-dimensional discrete-time model is used to analyze the boost or buck converter in discontinuous conduction mode. Seven different control schemes (open-loop power stage, voltage mode control, current mode control, constant power load, constant current load, constanton-time control, and boundary conduction mode) are analyzed systematically. The linearized dynamics is obtained simply by taking partial derivatives with respect to dynamic variables. In the discrete-time model, there is only a single pole and no zero. The single closed-loop pole is a linear combination of three terms: the open-loop pole, a term due to the control scheme, and a term due to the non-resistive load. Even with a single pole, the phase response of the discrete-time model can go beyond -90 degrees as in the two-pole average models. In the boost converter with a resistive load under current mode control, adding the compensating ramp has no effect on the pole location. Increasing the ramp slope decreases the DC gain of control-tooutput transfer function and increases the audio-susceptibility. Similar analysis is applied to the buck converter with a non-resistive load or variable switching frequency. The derived dynamics agrees closely with the exact switching model and the past research results.

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“…Sampled-data modeling [15][16][17][18][19][20][21][22][23] is another approach to analyze switching converters and is able to predict various converter instabilities [21]. Different from the improved continuous-time models, the system dimension of the sampled-data model is not increased.…”

Section: Introductionmentioning

confidence: 99%

“…Different from the improved continuous-time models, the system dimension of the sampled-data model is not increased. Many design guidelines based on the sampled-data models are proposed separately in [15][16][17][18][19][20][21][22][23]. A single summary is needed and is useful for design purpose.…”

Section: Introductionmentioning

confidence: 99%

Sampled‐data poles, zeros, and modeling for current‐mode control

Fang¹

2011

Circuit Theory & Apps

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SUMMARYExact and approximate sampled-data models in closed forms are derived for switching DC-DC converters under peak/valley current-mode control. The corresponding sampled-data poles and zeros in closed forms are also derived. The location and stability conditions of the poles and zeros, boundary conditions of subharmonic instability, and nulling of the audio-susceptibility are also derived. It is proved that the stable operating range of the source voltage is linearly proportional to the ramp slope. The sampled-data models agree with previous experiment results and accurately predict the subharmonic instability. The different view from the sampled-data model about the number and stability (minimum phase) of pole and zero does not necessarily invalidate the traditional continuous-time averaged model. However, this different view gives better prediction about converter dynamics and is useful for the analog or digital controller design for DC-DC converters.

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Sampled-Data Modeling and Analysis of the Power Stage of PWM DC-DC Converters

Cited by 7 publications

References 27 publications

Nonaveraged control‐oriented modeling and relative stability analysis of DC‐DC switching converters

Nonaveraged control‐oriented modeling and relative stability analysis of DC‐DC switching converters

Discrete-Time Poles and Dynamics of Discontinuous Mode Boost and Buck Converters Under Various Control Schemes

Sampled‐data poles, zeros, and modeling for current‐mode control

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