Regulator/Kalman filter design for realizing wave-based controllers

In this paper, we put forth the idea that a wave—based controller can be realized by using a noisy modal model. This idea is based on the fact that a wave-based input—output relation may be interpreted as that of a usual modal model contaminated with colored measurement noise. Specifically, an identical controller can be derived from models based on either a traveling wave or standing one on a flexible structure. In general, we can design a controller in terms of a regulator and a Kalman filter in a linear stochastic system. Since the Kalman filter contains unknown dynamics of the colored noise in the present system, this dynamics can be selected to realize the wave-based controllers. Furthermore, we design a controller for vibration suppression of a flexible beam to investigate the validity of this idea numerically. The results show that a modal compensator agrees with the wave-based one well, and yields a new interpretation of a wave-based controller.