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

Abstract: The plant (system to be controlled) is disturbed by an external periodic signal containing 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, while other harmonics should be preserved without distortion. Because the measured plant data has an unknown amount of time delay (dead time) and the sensitivity of the plant to external force is unknown, thus the amplitude and the phase of an anti-sine control force are also unknown. Based on an 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 parameters of control force. That type of controller was requested to extend further 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.