To successfully control the welding process and make it appropriate for the welding-based deposition (WBD) process, it is necessary to fully understand the influence of the welding process parameters and the geometry of the welding scenery on the resulting weld-bead dimensions. A new parameter, referred to as the geometrical factor, was defined in order to reflect on the geometrical configuration in the molten pool vicinity. An accurate dynamic model and an expression for the heat conduction rate that included the net heat input, the filler metal flow rate, the workpiece velocity and geometrical factor, were developed by balancing mass and energy flow through the control volume set around the molten pool. An open-loop controller for the gas tungsten arc welding (GTAW) process, based on the developed model, was designed and experimentally tested by controlling the metal layer deposition process on top of a workpiece with complex geometrical features, such as conformal channels, edges, and corners. The controller performed well and demonstrated the capability to adjust the welding process parameters according to demanding welding conditions.