Accounting for Input Limitation in the Control of Buck Power Converters

We are considering the problem of controlling a DC–DC switched power converter of the Buck type. The converter involves an inherent control limitation; accordingly the control signal (duty ratio) can only take values in the interval $(0, 1)$ . In the relevant literature, such a physical control limitation is generally not taken into account when designing the converter regulators. This is only dealt with in the control implementation stage, placing an isolated limiter between the (linear) controller and the controlled system. Furthermore, the presence of such a limiter is generally ignored when analyzing the closed-loop control system. In the present paper, the control signal limitation is dealt with using a nonlinear regulator that involves an internal limiter. The resulting closed-loop control system is shown to be equivalent to a nonlinear feedback involving a linear dynamics block in closed-loop with a nonlinear static element. Using absolute stability tools, sufficient conditions are established for the involved feedback to be $L_{2}$ -stable. If these conditions are respected when choosing the control design parameters then the regulator meets its objectives (closed-loop stability and output reference tracking). It is worth noting that, though the focus is made on a specific power converter, the paper includes an important theoretical dimension that may be of general interest.