Robust Control of DC Converter in DC Microgrid Applications Using Linear Matrix Inequality (LMI)

The aim of this paper is development of a distributed robust controller for distributed generators (DGs) interfaced to a DC microgrid through a boost converter. The suggested controller is robust static state feedback local controller based on $\mathbf{H}_{\mathbf{2}}/\mathbf{H}_{\infty}/\mathbf{pole}$ -placement/polytope technique. The proposed technique considers the system robustness against uncertainty, the system speed, and the system damping simultaneously, through construction a set of linear matrix inequalities (LMI) and polytopic representation of the system. The control problem is solved using LMI optimization approach, Using MATLAB LMI toolbox, because of LMI ability to handle multi-objective design problems. To test the effectiveness of the proposed technique, different simulation cases are carried out under diverse disturbances such as generation outage and variation of constant power loads (CPL). Eventually, the results of the suggested technique are compared with three other tuning techniques known as $\mathbf{H2}/\mathbf{H}\infty, \mathbf{H}_{\mathbf{2}}/\mathbf{H}_{\infty}/\mathbf{pole}$-placement, and H2 techniques. The comparisons prove the superiority of the proposed technique.