Controller for rejection of the first harmonic in a periodic signal with uncertain delay

The plant (the system to be controlled) is disturbed by a periodic external force with a broad spectrum of Fourier harmonics. The first Fourier harmonic (sine-type signal) is assumed to be undesirable and should be removed by a control force, whereas the other harmonics should be preserved without distortion. Because the measured plant data have an unknown amount of time delay (dead time) and the sensitivity of the plant to external force is unknown, therefore the amplitude and phase of a sine-type control force are also unknown. Based on the internal model principle, we developed a feedback controller described as a linear time-invariant system that can remove the first harmonic from the plant's output by constantly adjusting its control force parameters. Using this controller, we aimed to further extend the capabilities of a newly developed high-speed, large-area rotational scanning atomic force microscopy. In such a scanning technique, the sample is rotated, and the tilt angle between the normal of the sample surface and the axis of rotation produces a parasitic first Fourier harmonic, which significantly limits the scanning area.