The paper deals with the control strategies advancement for robots with double encoders for industrial applications and human-robot collaboration. It addresses both external force/torque detection, classification the nature of the force applied to the manipulator as well as selection of an appropriate reaction strategy for either human-robot collaboration and technological process execution. In contrast to previous works, the external force is estimated based on the stiffness model and double encoders technology. To estimate the validity of the implemented compliance error estimation and compensation techniques based on the reduces stiffness model additional analyses were done. It showed that a widely used reduced stiffness model for the compliance error compensation is able to compensate about 90% of the end-effector errors caused by the external loading. Proposed control algorithms and reaction strategies were validated by a simulation study and experimental study with a collaborative robot with torque sensors Kuka IIWA LBR 14.