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

Abstract

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.

Analysis of Nonlinear Dynamics of a Quadratic Boost Converter Used for Maximum Power Point Tracking in a Grid-Interlinked PV System

“…The gain margin is infinite because the total loop gain presents six stable poles (four from the power stage and two from the controller) and four stable zeros (three from the power stage and one from the controller), and the asymptotic behavior at high frequencies is similar to a minimum phase continuous-time second order system whose phase never crosses −180 degrees; therefore, the gain can be increased as much as possible without destabilizing the system. However, the values of the gain and the phase obtained from the small-signal average model are different from the actual phase of the switched system in the vicinity of the Nyquist frequency, as was recently reported in [37]. Indeed, it will be shown later using accurate discrete-time modeling that the system exhibits instability in the form of subharmonic oscillation for values of irradiance larger than approximately 820 W/m 2 with the fixed values of parameters shown in Tables 1-3.…”

“…Once the MPP voltage is obtained by maximizing the PV power, the steady-state duty cycle D is determined according to (16). The expression of v i (DT) that appears in (39) can be obtained from (37) in steady-state:…”

Microsecond nonlinear model predictive control for DC‐DC converters

“…Operation between subsystems 0 and 1 presents CCM of the boost converter. The equilibrium states of the boost converter in CCM for a fixed desired duty-ratio d are, according to (2), equal to…”

“…Because of the switching dynamics, the control of power converters is very demanding and complex. For that reason, there is a need for better control algorithms and estimation and reduction of the instabilities in the converter . In this work, we propose a nonlinear model predictive controller (NMPC) for a specific type of power converters, namely, DC‐DC converters.…”

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

“…Hence, accurate techniques to predict and avoid their occurrence in PV applications is essential in order to maximize the efficiency of the overall system. A variety of different control algorithms for DC‐DC converters have been proposed in the literature to avoid such undesirable behavior 12‐15 …”