Friction-damping devices are robust, low-cost solutions for structural control. Semi-active friction dampers in particular are able to dissipate sizable amounts of energy with comparatively little input power. However, modeling friction is a difficult problem, and the development of control algorithms for a semi-active friction damper proves challenging. Previously introduced by the authors is a novel semi-active friction damper termed the Banded Rotary Friction Device (BRFD). During operation, the BRFD develops friction between an internal steel drum and friction bands; this is achieved by transducing input displacement into rotation of the drum. Given its unique geometry, the BRFD is capable of providing sizable damping force, especially compared to that afforded using a traditional, planar friction surface. In this preliminary work, a semi-active model for the BRFD is introduced whereby damping is controlled via displacements to electric actuators. The model is validated using devised semi-active displacement profiles, and results show that the BRFD is capable of achieving large levels of force amplification, lending itself to applications in structural control and multihazard mitigation.