Roll stabilization is a critical aspect of ship motion control, particularly for vessels operating in low-speed or zero-speed conditions, where traditional hydrodynamic fins lose their effectiveness. In this paper, we consider a roll damping system, developed by Navis JSC, based on two actively controlled zero-speed fins. Unlike conventional fin stabilizers, zero-speed fins employ a drag-based mechanism and active oscillations to generate stabilizing forces even when the vessel is stationary. We propose a simple linear control architecture that, however, accounts for nonlinear drag forces and actuator limitations. Simulation results on a high-fidelity vessel model used for HIL testing demonstrate the effectiveness of the proposed approach.