Robust LQR Control for PWM Converters: An LMI Approach

A consistent framework for robust linear quadratic regulators (LQRs) control of power converters is presented. Systems with conventional LQR controllers present good stability properties and are optimal with respect to a certain performance index. However, LQR control does not assure robust stability when the system is highly uncertain. In this paper, a convex model of converter dynamics is obtained taking into account uncertainty of parameters. In addition, the LQR control for switching converters is reviewed. In order to apply the LQR control in the uncertain converter case, we propose to optimize the performance index by using linear matrix inequalities (LMIs). As a consequence, a new robust control method for dc-dc converters is derived. This LMI-LQR control is compared with classical LQR control when designing a boost regulator. Performance of both cases is discussed for load and line perturbations, working at nominal and nonnominal conditions. Finally, the correctness of the proposed approach is verified with experimental prototypes.