Direct digital design of a sliding mode-based control of a PWM synchronous buck converter

A discrete-time sliding mode approach allowing direct digital design of a pulse width modulation (PWM) control of a synchronous buck converter is presented in this study. Without the need of a compensating ramp, a non-linear difference equation representing the output voltage dynamic behaviour is employed to demonstrate the global stability of the internal control loop of the inductor current. Discrete-time small-signal model is derived from the linearisation of the ideal sliding-mode equations, which facilitates the design of the output voltage controller. This model exhibits a zero whose value depends on the operating point coordinates and explains the duty cycle delay associated to digitally PWM controlled converters. The validity of the transfer function is demonstrated through simulation by comparing its frequency behaviour with that obtained from the more accurate switched model of the converter. Experimental results for start-up, load and line perturbations, current and voltage reference variations in a 25 W prototype switching at 100 kHz are in good agreement with the theoretical predictions.