PI-Type Controllers and Σ- Modulation for Saturated DC-DC Buck Power Converters

Departing from analyzing a general input-saturated second-order system, a Lyapunov-based constructive procedure for the output-feedback stabilization of the constantly perturbed DC-DC buck power converter is presented. The proposed scheme also incorporates a $\Sigma $ – $\Delta $ modulator. The obtained control scheme is developed in two parts: a proportional-integral-type family of algorithms devoted to regulating the uncertain system by using measurements of the output voltage and a $\Sigma $ – $\Delta $ modulator dedicated to transforming the control action into a {0,1} discrete-valued signal. This modulator is a kind of a sliding controller, which can be seen as a subsystem with an on-off output. This combination, the PI–type family of controllers and the $\Sigma $ – $\Delta $ modulator, assures the global stability of the closed-loop system, even if parametric uncertainties are presented. The convergence analysis was carried out using Lyapunov’s method. The theoretical results are confirmed using real–time experimental tests, which demonstrate the anti-windup scheme and the $\Sigma $ – $\Delta $ modulator efficiency. The experiments consider the saturation of the control input and disturbances, having obtained convincing results.