In this work, a new robust control algorithm is introduced for uncertain systems with harmonic disturbances of unknown frequencies. The proposed solution works under the active disturbance rejection control (ADRC) framework and utilizes a specialized observer for sinusoidal uncertainties, aided with an on-line harmonic disturbance frequency estimator. The entire governing structure is derived in a convenient error-based domain, easily deployable in various industrial control software. The idea behind the introduced approach is general, but is conveyed here using solely a three degrees-of-freedom torsional system, which is considered a benchmark for vibration phenomenon in many mechanical systems. The efficacy of the proposed control scheme is validated with a set of experiments on a laboratory testbed and a theoretical analysis based on theory of singular perturbation.