In this paper, a compound control which combines a spatial internal model with a linear extended state observer (LESO) is proposed for continuously rotating machines. It is implemented digitally based on a uniform time sampling. An angular position-based internal model is synthesized in the spatial domain to suppress the spatially periodic disturbances existing in rotary machines, which is actuated with a fixed sampling period by introducing the angular position to the internal model in real-time. Further, an LESO is designed to estimate non-periodic disturbances and uncertain dynamics acting on the system so as to reduce the steady state error of the position output with respect to ramp angular position reference input. Comparisons and experimental results are presented to illustrate the feasibility and effectiveness of the compound control method. (C) 2016 Elsevier Ltd. All rights reserved.