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A robust controller design to obtain output voltage regulation in a quadratic boost converter with high dc gain is discussed in this paper. The proposed controller has an inner loop based on sliding-mode control whose sliding surface is defined for the input inductor current. The current reference value of the sliding surface is modified by a proportional-integral compensator in an outer loop that operates over the output voltage error. The stability of the two-loop controller is proved by using the Routh-Hurwitz criterion, which determines a region in the Kp-Kiplane, where the closed-loop system is always stable. The analysis of the sliding-mode-based control loop is performed by means of the equivalent control method, while the outer loop compensator is derived by means of the Nyquist-based Robust Loop Shaping approach with the M-constrained Integral Gain Maximization technique. Robustness is analyzed in depth taking into account the parameter variation related with the operation of the converter in different equilibrium points. Simulations and experimental results are presented to validate the approach for a 20-100-W quadratic boost converter stepping-up a low dc voltage (15-25-V dc) to a 400-V dc level.
López‐Santos et al. (2014) studied this question.