Discrete Control by Pole Allocation with Minimum Time Response and Relaxations Applied to DC-DC Converters

Abstract

This paper proposes a control for the output voltage of DC-DC buck converters using an optimized state feedback that takes into account the delay in the implementation of the discrete-time control signal and an integral action over the error. First, it is shown a minimum time response, with zero steady-state error, obtained without considering limitation on the duty cycle of the converter (ideal deadbeat response). In the sequence, the limitation on the duty cycle of the converter is taken into account and then a relaxation in the closed-loop poles location is carried out, to allow a sufficiently fast transient response for the application, without violating the limits of the control signal, and in a scenario with parametric uncertainties. The control gains in this last case are obtained with the help of a particle swarm optimization algorithm, considering in the design the minimization of the module of the closed-loop poles and, simultaneously, respecting the limits of the control signal and taking into account parametric uncertainties in the converter, referred in this word as a quasi-deadbeat robust controller. Simulations indicate the viability of the quasi-deadbeat robust controller for this application.