Effects Of The Nonlinearity Of PWM Modulator On DC-DC Converters And Cascaded Systems And The Solutions

The pulse-width modulator(PWM)has the nonlinear charateristics such as natural sampling,sideband effect and aliasing effect,which have great effect on the stability of dc-dc converters.The power conversion system,composed of multiple dc-dc converters,also faces the stability issue due to the interaction among the constituent converters.The averaged model is the most widely used mathematical model.However,it is a linear model and can not analyze the effect of the nonlinearity of PWM modulator on the converters.This dissertation aims to establish more accurate mathematical models of dc-dc converters,with which,the effect of the nonlinearity of PWM modulator on the stability of dc-dc converters and the cascade systems is studied,and the methods for improving the stability are proposed.According to the form of triangular carrier,the implementation of PWM can be leading-edge modulation and trailing-edge modulation.Since PWM modulation is a natural sampling process,and the sampling instants occurs at the intersections of the modulation signal and the carrier wave,the discrete-time model of the dc-dc converters is derived with the sampling instants fixed at the intersection instants to distinguish the impact of different modulations.Furthermore,the discrete-time model is converted from z-domain to s-domain,and then is approximated based on the low-pass filtering characteristics of dc-dc converters.Thus,an approixmate discrete-time model that can be accurate up to half of the switching frequency is obtained.Using this proposed model,it is shown that the buck converter is unaffected by the type of PWM used,but for the boost and buck–boost converters,the phase margin of the loop gain is wider when the leading-edge PWM is used.Since the trailing-edge modulation is commonly available in PWM controller integrated circuits,the modulation signal zeroorder holding(ZOH)method is proposed for use in the trailing-edge modulated boost and buck–boost converters to equivalently achieve the same effect of the leading-edge modulated converters.Experimental buck,boost and buck-boost converter are constructed for verification of the accuracy of the approximate discrete-time model and the validity of the proposed control scheme.Application of PWM is known to produce sideband effects.The accuracy of the models of dc-dc converters can be improved if essential information of the sideband effects of PWM can be incorporated.In this dissertation,the aliasing effect of the sideband components on the closed-loop control is analyzed,and an effective representation of the transfer function of the pulse-width modulator is derived.Applying this transfer function to the dc-dc converter,an extended-frequency-range small-signal model is obtained,which can be conveniently used for deriving the loop gain of a PWM-controlled dc-dc converter.Furthermore,for wideband control applications,the large switching ripple in the modulation signal necessitates adjustment of the representation of the gain of the pulsewidth modulator,which is dependent on the controller.Despite being highly accurate for stability assessment,the extended-frequency-range model is relatively complex after incorporating the effects of the sideband components and the large switching ripple.An approximate approach is introduced to simplify the loop gain expression and to provide physical insights into the effects of the sideband components and large modulation ripple amplitude.The relationship between the discrete-time model and the extended-frequency-range small-signal model is analyzed,and it is shown that they are equivalent in stability assessment.Three prototypes,including buck,boost and buck-boost converters are built in the lab,and the effectiveness of the extended-frequency-range small-signal model is verified by measuring the loop gain with a network analyzer.Impedance-based criteria are often used for assessing the stability of cascaded converter systems.In this dissertation,it is pointed out that the switching ripple interaction(SRI)between the source converter and the load converter in a cascaded system would change the gain of the pulse width modulator of the source converter,causing the cut-off frequency and the phase margin of the source converter to change accordingly.Thus,even if a cascaded system is shown to be stable under an impedance-based criterion,it can in fact be unstable due to the SRI.This paper proposes an adaptive modulation sample-and-hold method,where the samplig instant of the zero-order holder is adaptively adjusted with the duty-cycle,for eliminating the effect of SRI.A cascaded system composed of two buck converters are built in the lab,and the experimental results are provided to verify the correctness of the analysis of SRI on the stability of cascaded system and the effectiveness of the adaptive modulation signal zero-order holding method.