  Repetitive operations are widely conducted by automatic machines in industry.
Periodic disturbances induced by the repetitive operations must be compensated
to achieve precise functioning. In this paper, a periodic-disturbance observer
(PDOB) based on the disturbance observer (DOB) structure is proposed. The PDOB
compensates a periodic disturbance including the fundamental wave and harmonics
by using a time delay element. Furthermore, an adaptive PDOB is proposed for
the compensation of frequency-varying periodic disturbances. An adaptive notch
filter (ANF) is used in the adaptive PDOB to estimate the fundamental frequency
of the periodic disturbance. Simulations compare the proposed methods with a
repetitive controller (RC) and the DOB. Practical performances are validated in
experiments using a multi-axis manipulator. The proposal provides a new
framework based on the DOB structure to design controllers using a time delay
element.
