Time-varying notch filters for control of flexible structures and vehicles

Vibration due to flexible modes can be attenuated using a notch filter tuned at the known resonant frequencies of a flexible structure or vehicle. However, there are applications in which those particular resonant frequencies are not known a priori. Further complication arises when those frequencies are not constant in time. The next generation reusable launch vehicle poses such as problem. the X33 concept vehicle, for example, burns up to 90% of its fuel during the first few minutes of flight. The significantly alters the mass distribution and therefore the natural modes of the vehicle. The current work investigates the use of time-varying (TV) notch filters based on the PD-eigenvalue theory Both the notch frequency and the bandwidth of the filter can be adjusted in real time to attenuate the time-varying flexmodes whenever they are excited, and to reduce the undesirable phase lag caused by the filter when the flexmodes are quiescent. Real-time identification of resonant frequencies is performed by a bank of linear, time-invariant (LTI) ban pass filters spanning the entire operating spectrum and a flex-mode detection logic unit. The design principle, as well as some promising simulation results, is given in the paper.