Active Controllers for Reducing Vibration Amplitude

Linear quadratic regulators (LQR) have been used extensively in many feedback control applications. In the area of control and structure interaction, LQR have been applied to large space structures to suppress the vibration due to flexibility. To prevent structural damages, LQR can be used to reduce the vibration due to large external excitations. Although, both applications are concerned about the suppression of vibration, in the space application it seems more important to reduce the vibration to zero in a short period of time. This is usually related to the case where the vibration deteriorates control performance. On the other hand, to prevent structure damages it is more important to reduce the vibration amplitude. As long as the amplitude of vibration is small the vibration is not required to be suppressed to exact zero, and the vibration is allowed to last a long period of time. One should note that the instantaneous amplitude of vibration is not minimized in an LQR formulation; instead, the total sum of the square of the vibration amplitude during the whole operation period is minimized. Therefore, an LQR may have an unacceptable amplitude at some time instants but still have an acceptable performance. In this paper, we investigate an LQR in terms of its ability in reducing the vibration amplitude. We have obtained an LQR with adjustable gains to control the vibration amplitude.