Micro-electromechanical system (MEMS) gyroscopes intended for high-grade inertial applications must demonstrate exceptional bias stability and attain impressive resolution. Most MEMS gyroscopes utilize capacitive measurements of angular rates, which arise from the Coriolis force on a moving suspended mass along a defined sensing direction. Sometimes, dual-proof mass gyroscopes (DMG) have vibration-induced errors because of the asymmetricity between proof masses, damping, or stiffness imperfections grown by fabrication scarification. We have developed a closed-loop quadrature error feedback control system to address these challenges. This paper introduces a novel approach to mitigating quadrature error in a DMG system by integrating a quadrature error control loop employing a phase-locked loop and automatic gain control mechanisms within a drive and sense comb architectures. The proposed model delivers a demodulated response without any phase drift in the system, which ensures the accuracy and reliability of DMG-based systems across various aerospace, defense, and industrial applications.