H<sub>2</sub>/H∞ Robust Observed-State Feedback Control Based on Slack LMI-LQR for LCL-Filtered Inverters
Thuy Vi Tran, Kyeong‐Hwa Kim, Jih‐Sheng Lai
Abstract
A robust controller for an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -filtered grid-connected inverter (GCI) is presented in this article in the context of the system model uncertainties and nonideal grid environment. Under the occurrence of exogenous inputs from parameter drifts affecting the controller and observer, the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H∞ approach of the linear quadratic regulator control is developed to obtain the state-feedback gain and observer gain with the system stability guarantee by means of Lyapunov stability theory. Furthermore, the use of slack-linear matrix inequalities to handle parameter-dependent Lyapunov functions in synthesizing the robust controller can achieve a less conservative condition than the conventional quadratic stability. System robustness and stability are assessed through the closed-loop pole map and the discrete-time frequency analysis approaches. Hardware experiments are conducted for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> -filtered GCI to validate the feasibility and effectiveness of the proposed control method. Fair comparisons with the conventional schemes are also performed to highlight the superior performance of the proposed scheme.