Accurate Sliding-Mode Control System Modeling for Buck Converters

This paper shows that classical sliding mode theory fails to correctly predict the output impedance of the highly useful sliding mode PID compensated buck converter. The reason for this is identified as the assumption of the sliding variable being held at zero during sliding mode, effectively modeling the hysteretic comparator as an infinite gain. Correct prediction of output impedance is shown to be enabled by the use of a more elaborate, finite-gain model of the hysteretic comparator, which takes the effects of time delay and finite switching frequency into account. The demonstrated modeling approach also predicts the self-oscillating switching action of the sliding-mode control system correctly. Analytical findings are verified by simulation as well as experimentally in a 10-30V/3A buck converter.