In this article, the adhesion modeling and control case of a Vortex Climbing Robot (VCR) is investigated against a surface of variable orientations. The critical adhesion force exerted from the implemented Vortex Actuator (VA) and the VCR's achievable payload are analyzed under 3-DOF rotations of the test surface, while extracted from both geometrical analysis and dynamically-simulated numerical results. A model-based control scheme is later proposed, with the goal of achieving adhesion while the VCR remains immobilized, limiting the power consumption and compensating for disturbances (e.g. moving cables) leading to Center-of-Mass (CoM) changes. Finally, the model-based control scheme is experimentally evaluated, with the VCR prototype on a rotating and moving flat surface. The presented results support the use of the proposed methodology in climbing robots targeting inspection and maintenance of stationary surfaces (flat, curved etc.), as well as future robotic solutions operating on moving structures (e.g. ships, cranes, folding bridges).