Robust constrained stabilization of boost DC–DC converters through bifurcation analysis

Yfoulis, Christos; Giaouris, Damian; Stergiopoulos, Fotis; Ziogou, Chrysovalantou; Papadopoulou, Simira

doi:10.1016/j.conengprac.2014.11.004

Cited by 24 publications

(29 citation statements)

References 21 publications

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“…This establishes the following relationship between the steady‐state duty cycle D and

y_{avg} false[\infty false]

y_{avg} false[\infty false] = - boldC {false(A_{1} D + A_{0} \overset{D}{true} false)}^{- 1} false(B_{1} D + B_{0} \overset{D}{true} false) boldw .

As commented in El Aroudi and El Aroudi et al,() the steady‐state value D can be obtained from the previous equation once all the matrices and the parameters of the system are specified and there is no need to obtain it using numerical root‐finding algorithms such as in previous studies. () Once D is obtained, the steady‐state state vector x (0) and x ( D T ) are straightforward from and , respectively.…”

Section: Review Of Discrete‐time Modeling Of Switching Converters Undmentioning

confidence: 99%

“…system stability requirements while maximizing the bandwidth of the system thus and optimizing the fast controllers design. Unlike many existing models in the literature dealing with accurate prediction of switching converters based on nonaveraging procedures, 4,19,[36][37][38][39] 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. As a consequence, the integral loop widely used in the output feedback to get zero static error is separated from the rest of dynamics hence avoiding many singularity problems appearing in the expressions of the system trajectories and their steady-state values.…”

mentioning

confidence: 99%

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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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“…This establishes the following relationship between the steady‐state duty cycle D and

y_{avg} false[\infty false]

y_{avg} false[\infty false] = - boldC {false(A_{1} D + A_{0} \overset{D}{true} false)}^{- 1} false(B_{1} D + B_{0} \overset{D}{true} false) boldw .

Section: Review Of Discrete‐time Modeling Of Switching Converters Undmentioning

confidence: 99%

mentioning

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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“…We consider the boost DC–DC converter used in with nominal parameter values L = 1.5 mH , C = 10 μF , R = 40Ω, V in = 5 V , V ref = 10 V and a wide range of operating conditions, i.e. V ref ∈ [8, 10] V, V in ∈ [3.5, 6.5] V, R ∈ [20, 80]Ω, which result in d ss ∈ [0.1875, 0.65].…”

Section: Simulation Resultsmentioning

confidence: 99%

“…We consider the boost DC-DC converter used in [21,25] The problem of designing robust wide-range Lyapunov-based control laws for this converter has been studied recently in [21,26]. In [21] a design methodology for selecting λ has been introduced.…”

Section: Example 2-optimal Switching Gains For Wide Range Operationmentioning

confidence: 99%

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Optimal switching Lyapunov‐based control of power electronic converters

Yfoulis

Giaouris

Ziogou

et al. 2016

Circuit Theory & Apps

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Summary This paper presents new ideas and insights towards a novel optimal control approach for power electronic converters. The so‐called stabilizing or Lyapunov‐based control paradigm is adopted, which is well known in the area of energy‐based control of power electronic converters, in which the control law takes a nonlinear state‐feedback form parameterized by a positive scalar λ. The first contribution is the extension to an optimal Lyapunov‐based control paradigm involving the specification of the optimal value for the parameter λ in a typical optimal control setting. The second contribution is the extension to more flexible optimal switching‐gain control laws, where the optimal switching surfaces are parameterized by a number of positive scalars λj. Systematic derivation of gradient information to apply gradient‐descent algorithms is provided. The proposed techniques are numerically evaluated using the exact switched model of a DC–DC boost converter. Copyright © 2016 John Wiley & Sons, Ltd.

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Application of the Filippov Method to PV‐fed DC‐DC converters modeled as hybrid‐DAEs

Hayes

Condon

Giaouris

2020

Engineering Reports

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In this article, a method to study the nonlinear dynamics of a PV-fed boost converter is developed. The model for the solar panel introduces an algebraic constraint into the system and the resulting mathematical model is a set of hybrid differential algebraic equations (DAEs). The behavior of the system is observed to exhibit undesired operation as parameter values vary. Conventional mathematical tools developed to analyze DC-DC converters are not directly applicable to systems modeled as a set of hybrid DAEs. In order to find the monodromy matrix to assess the eigenvalues of the system, we modify the Filippov method to calculate the saltation matrix. The derived formula is general and versatile such that it can be applied to any PV-fed DC-DC converter irrespective of the topology or control algorithm employed. Two case studies are investigated: current mode control and maximum power point tracking. Each case study serves to demonstrate different considerations that must be taken into account when conducting stability analysis of hybrid-DAEs. K E Y W O R D S DC-DC converters, hybrid differential algebraic equations, maximum power point tracking, nonlinear dynamics, photovoltaic, saltation matrix This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Robust constrained stabilization of boost DC–DC converters through bifurcation analysis

Cited by 24 publications

References 21 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

Optimal switching Lyapunov‐based control of power electronic converters

Application of the Filippov Method to PV‐fed DC‐DC converters modeled as hybrid‐DAEs

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