DC-DC Converters - Dynamic Model Design and Experimental Verification
Abstract: To obtain high performance control of a dc-dc converter, a good model of the converter is needed. The load usually affects the dynamics and one way to take this into consideration is to regard the load as a part of the converter. The load is often the most variable part of this system. If the load current and the output voltage are measured there are good possibilities to obtain a good model of the load on-line. Adaptive control can then be applied to improve the control.
In peak current-mode control, the output voltage and the inductor current are measured and utilized for control. In the author's licentiate thesis, analytic models were derived for the case where the load current is also measured and utilized for control. The control-to-output transfer function, the output impedance, and the audio susceptibility were derived for the buck, boost, and buck-boost converters operated in continuous conduction mode in the case of resistive load. The use of load current can be seen as gain scheduling in the case where the load is a resistor. Gain scheduling can be considered a special case of adaptive control. The majority of the results in the licentiate thesis were validated by comparing the frequency responses predicted by the analytic models and switched large-signal simulation models.
In this thesis, additional results are presented for the buck converter. Experimental results obtained by means of a network analyzer verify the derived control-to-output transfer function and the audio susceptibility but not the output impedance at low frequencies. In the experimental buck converter there are stray resistances in the inductor, transistor, and diode but these stray resistances were not considered in the licentiate thesis. A new transfer function for the output impedance is derived where these stray resistances are considered and it is in good agreement with the experimental result also at low frequencies.
If the current to the output capacitor is measured in addition to the output voltage and the inductor current, the load current can be calculated as the difference between the inductor and capacitor currents in the case of the buck converter. Hence, the measurement of the load current can be replaced by measurement of the capacitor current. If this possibility is utilized and the capacitor current is measured by means of a current transformer, a low-frequency resonance is introduced in the frequency responses according to experimental results. The reason for this resonance is due to the high-pass-filter characteristics of the current transformer. A new analytic model is derived which predicts the resonance.
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