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

Abstract

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.

Digital Control of a Buck Converter Based on Input-Output Linearization. An Interpretation Using Discrete-Time Sliding Control Theory

“…which is coincident with the reported in [22] using an equivalent discrete-time sliding approach to obtain the recurrence for the output capacitor voltage. In fact, both approaches are completely equivalent if w = 0.…”

“…In fact, both approaches are completely equivalent if w = 0. It is possible to provide a sliding mode interpretation of our approach Equation (17) considering that it proposes a more general switching surface s e than the one in [22], which was the current error with negative sign. The new surface Equation (31) includes a dynamical term of the current error with the same decreasing geometric progression of the input-output linearization and becomes Equation (30) for w = 0.…”

“…It should be noted that the transfer function in Equation (37) presents a zero depending on the operating point associated with the delay inherent to the digitally PWM controlled converter [22].…”

“…A sensible design of the control parameters will usually consider the ranges 0 < β < 1 and 0 < k n . Let us consider the converter coefficients and operation point described in [22]. It can be shown that z D = −1 for D = 0.5 (V C = V g /2) and the pole z P in the plant Equation (37) corresponds to the converter coefficient h 22 .…”

“…A second exception is found in [21], where a time-domain design method is used to fit a digital PID template to the desired response. In [22], after a review of previous contributions, a methodology to design non-linear digital controllers based on discrete-time sliding mode control is presented where a dead-beat response is achieved [23]. Also, in [24] this methodology is applied to regulate the output voltage of a boost converter with constant power load, providing a comparison with one of the most referenced works in digital control of power converters [25].…”