  The plant (system to be controlled) produces a periodic signal containing a
broad spectrum of the Fourier harmonics. The first Fourier harmonic (sine-type
signal) is assumed to be undesirable and should be removed by an external
force, while other harmonics should be preserved. Because the measured plant
data has an unknown amount of time delay and the sensitivity of the plant to
external force is unknown, thus the amplitude and the phase of an anti-sine
control force are unknown as well. We developed an adaptive controller
described as a linear time-invariant system that can remove the first harmonic
from the plant's output by constantly adjusting its parameters of control
force. That type of controller was requested to further extend the capabilities
of a newly developed high-speed large-area rotational scanning atomic force
microscopy technique where the sample is rotated and a tilt angle between the
normal of the sample surface and the axis of rotation produces the parasitic
first Fourier harmonic which significantly limits the scanning area.
