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An algorithm for regulation of the vertical penetration rate in rotary drilling systems is developed under the assumption that parameters of the rock-bit interaction as well as those of the translational dynamics are unknown. The control design utilizes a multi-step approach, where the vertical penetration velocity is regulated through an appropriate assignment of a reference rotational velocity signal, while the tracking of the latter is achieved using tracking with disturbance rejection scheme. In contrast with the existing results, the algorithm does not require real-time measurement and communication to the ground level of the downhole variables, such as angular position, rotational velocity, and torque-on-bit. This is achieved through the use of high-order sliding mode observers which estimate the required downhole variables based on measurements performed at the ground level. Simulation results are presented which …