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

• Published in: International journal of circuit theory and applications Vol. 46; no. 3; pp. 565 - 580
• Main Authors: Al‐Turki, Y., El Aroudi, A., Mandal, K., Giaouris, D., Abusorrah, A., Al Hindawi, M., Banerjee, S.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.03.2018
• Subjects: Computer simulation; Control stability; Control systems design; Control theory; control‐oriented modeling; Converters; Dynamic stability; Feedback loops; Mathematical models; Model accuracy; nonaveraged modeling; Nonlinear systems; Predictions; Pulse duration; Pulse duration modulation; PWM control; Stability analysis; Switching; switching converters
• ISSN: 0098-9886; 1097-007X
• DOI: 10.1002/cta.2387

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. This paper presents a non‐averaged approach for studying the relative stability of switching converters. By treating the modulator as a gain, the model is formulated in a way that standard control‐oriented tools such as Bode diagrams and root‐loci can be used hence giving gain and phase margins that are highly useful in controller design. The paper points out the sources of discrepancies between the new approach and the averaged model. The theoretical results are validated by simulations using the switched model.