An LMI Approach for Robust LQR Control of PWM Buck Converter with Parasitics

In this paper, a polytopic model of an uncertain buck converter with parasitic resistances is obtained in continuous conduction mode. Although linear quadratic regulators (LQRs) provide good stability and are optimal but they do not ensure robustness for the highly uncertain system. Therefore, A robust LQR designing method for power converters is presented using linear matrix inequalities (LMIs) to ensure robust stability of highly uncertain systems and the output is analyzed in the presence of line and load perturbations. In addition, an input voltage feedforward gain is included in this closed loop converter system to achieve a good line regulation. It is shown that with feedforward, there is no transient due to the line voltage perturbations. The results of the proposed approach are verified through simulation.