$H_{\infty}$ Robust Second-Order Generalized Integrator Phase-Locked Loop

This article proposes a second-order generalized inte-grator phase-locked loop (SOGI PLL) based on
$H_{\infty}$
control theory framework. The control problem is formulated in the context of the PLL's voltage-controlled oscillator while considering dynamics of the SOGI block. By specifying the weighting function as a function of PLL settling time in the
$H_{\infty}$
control problem, an optimal controller is obtained to achieve robustness in the PLL's tracking performances. Furthermore, reduction in the controller's implementation and computational cost without loss in performance are achieved by means of Hankel singular value approximation. Experimental results show that proposed SOGI PLL is able to robustly estimate the frequency and phase angle of a single-phase voltage compared to its standard SOGI PLL counterpart.