Voltage sag, unbalance, and harmonic distortion are major power quality (PQ) problems that reduce power system reliability and increase economic losses. This paper proposes a Dynamic Voltage Restorer (DVR) control scheme that integrates synchronverter dynamics with proportional-resonant controllers for unified mitigation of these PQ disturbances. The proposed strategy emulates synchronous generator swing dynamics to generate a grid-forming voltage reference for series injection, restoring load voltages within acceptable limits. Multi-resonant control loops are incorporated to selectively suppress dominant harmonic components and negative-sequence voltages, enabling simultaneous mitigation of sag, unbalance, and harmonic distortion within a single coordinated framework. The control scheme is evaluated through small-signal stability analysis and MATLAB/Simulink simulations under individual and combined disturbance scenarios, demonstrating fast disturbance rejection and robust performance. For the combined disturbance case, results show restoration of phase voltages to 1.0 pu., reduction of total harmonic distortion by 98.9%, from 12.7% to 0.14%, and suppression of voltage unbalance factor by 95.8%, from 10.4% to 0.44%. Real-time implementation is assessed using a hardware-in-the-loop (HIL) setup based on an OPAL-RT real-time simulator and a DSP-based controller. HIL results show restoration of load voltages during a sag event and reduction of voltage unbalance factor from 4.84% to 0.94% under voltage unbalance conditions. The comparative results confirm the effectiveness of the coordinated control structure for unified PQ compensation.