Sampled-Data Analysis and Control of DC-DC Switching Converters

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Fang, Chung-Chieh
Abed, Dr. Eyad H.
A unified sampled-data method is proposed for the analysis and control of DC-DC switching converters. Two types of DC-DC converters are considered in this dissertation: PWM converters and load-resonant converters. Numerous examples are given to illustrate the results. In the study of PWM converters, general nonlinear sampled-data models are developed. Conditions are obtained for existence and local orbital stability of periodic solutions. The stability of the bifurcated solutions of a reduced model is also investigated. The input filter instability problem is studied using the Neimark-Sacker bifurcation. Audio- susceptibility and output impedance are also analyzed using the developed models. Several schemes are proposed for stabilizing unstable periodic solutions in PWM converters. Among these, washout filter-based designs are introduced to provide robust stability without reliance on knowledge of the nominal operating condition. In addition, gain-scheduling is used to enlarge the operating range. The power stage of the PWM converter is analyzed to facilitate control design. New results are obtained on the open-loop zeros of the power stage. New control designs are proposed to achieve line and load regulations as well as a faster transient response. These designs include state feedback with or without feedforward terms, state feedback through washout filters, dynamic state feedback and dynamic output feedback. These control laws can be applied to both voltage and current regulations. Moreover, a state observer for the PWM buck converter is derived. These results are extended to the study of load-resonant converters. The developed methods are more concise and unified than traditional methods used to analyze load- resonant converters. Analytical conditions are obtained for the existence and local orbital stability of periodic solutions is derived. Analytical formulae are derived for audio- susceptibility, output impedance, and half-cycle dynamics. Integral control is applied to this type of converter to achieve line and load regulation.