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This paper is focused on a comparison between Model-Free Control and Active Disturbance Rejection Control methods. These two techniques do not require a detailed mathematical description of the system, since they base on the on-line estimation and rejection of the unmodeled elements of the dynamics. Robustness of the closed-loop control system (against external perturbation) and its relation to energy consumption is discussed here. A model of a planar manipulator is used in the conducted case study as an exemplary plant. Conclusions are supported with results obtained with numerical simulations.