Stable control under frequency aliasing between rigid and flexible characteristics

This study can play an important role in addressing the issue of achieving stable control of launch vehicles when the first-order elastic frequency is near or overlaps with the rigid-body frequency, especially without prior frequency knowledge. Much of the research up to now, such as those based on notch-filter or signal-processing techniques, requires a gap of 3 to 5 times between the low-order elastic frequencies and the rigid-body cutoff frequency. Observer-based methods, on the other hand, require prior knowledge of the frequency data. In this paper, a method is proposed, which takes advantage of the fact that attitude measurements of the rigid-body, obtained by Inertial Measurement Units (IMUs) installed at different locations, are identical, whereas elastic-mode signals differ only in their modal slopes. By differentially processing these IMU measurements, we can extract only the elastic information, thus identifying the frequencies of the elastic modes, and design an observer to distinguish the first-order elastic signal using redundant measurements. Simulations demonstrate that this method can autonomously identify low-order elastic frequencies, even when they are identical to or less than the rigid-body frequency, thereby enhancing controller performance.