Optimal active absorber with internal state feedback for controlling resonant and transient vibration

An active, standalone vibration absorber utilizing the state feedback taken from the absorber mass is proposed. Expressions of the optimum absorber parameters are obtained both by optimizing the Η∞ norm of the frequency response function. For improved transient response featuring low peak response and fast attenuation, the design procedure utilizes the mode equalization followed by the maximization of the damping. An interesting feature of the proposed absorber is that the performance of the absorber does not require having its natural frequency close to the natural frequency of the primary system as is generally the case for tuned passive absorbers or other active and semi-active tuned vibration absorbers. In fact, the performance of the proposed system can be progressively enhanced by increasing the absorber frequency. Compared to the optimum passive absorber, the optimal active absorber can yield wider bandwidth of operation around the natural frequency of the primary system and lower frequency response within the suppression band. The active absorber also offers better transient response compared to the passive absorber both optimized for the best transient responses. The efficacy of the absorber is analyzed both for a single-degree-of-freedom and beam like primary structure.