Structural vibration control

Undesirable time-variable motions of dynamical structures (e.g. scales, balances, vibratory platforms, bridges and buildings) are mainly caused by unknown or uncertain excitations. In a variety of applications it is desirable or even necessary to attenuate these disturbances in an effective way and with moderate effort. Hence, several passive as well as active methods and techniques have been developed in order to treat these problems. However, employment of active techniques often fails because of their considerable financial costs. We propose an affordable control scheme which accounts for the above-mentioned deficiencies. In addition, we allow constraints on control actions. Furthermore, the number of control inputs (actuators) may be arbitrary, i.e., the system may be mismatched. The scheme is based on Lyapunov stability theory and, provided that the bounds of the uncertainties are a priori known, a stable attractor (ball of ultimate boundedness) of the structure can be computed. In case measurement errors or uncertainties, respectively, are significant, it is shown how the Lyapunov-based control scheme may be combined with a fuzzy control concept. The effectiveness and behavior of the control scheme is demonstrated on two simplified models of elastic structures such as a two story building and a bridge subjected to a moving truck.