Friction extrusion (FE) is a solid-state manufacturing process for producing high-strength wires, rods, tubes, and other extruded profiles. Force-controlled FE offers significant advantages by improving process stability and enabling straightforward adaptation to a wide range of alloys. However, numerical simulation of force-controlled FE remains particularly challenging due to computational costs that prohibit systematic parameter studies and make iterative tuning of closed-loop controllers impractical. Current numerical models rely on experimentally measured die plunging velocity profiles as prescribed simulation inputs, which fundamentally limit their predictive capabilities and require prior experimental data before simulations can be conducted. To date, no numerical framework has been developed to directly simulate the force-controlled friction extrusion process. This study presents a framework that integrates a proportional–integral–derivative (PID) controller with a GPU-accelerated smoothed particle hydrodynamics (SPH) method to enable direct simulation of the force-controlled friction extrusion process. GPU acceleration reduces computation times from hundreds of hours to less than five hours on a single modern graphics card, making systematic tuning of the integrated PID controller feasible. The proposed PID–SPH framework is validated against experimental measurements of extrusion force, die displacement, and die and billet temperatures. The simulations provide physical insight into the dominant sources of heat generation, material flow behavior, grain refinement mechanisms, and the influence of active cooling. By enabling closed-loop force control within the numerical model, the proposed framework eliminates dependence on experimentally prescribed die velocity profiles and significantly enhances the predictive capability of friction extrusion simulations. This approach paves the way for designing and optimizing closed-loop controlled friction-based manufacturing processes using fully predictive numerical tools.