Optimum vibration suppression of flexible structures using delayed feedback

Date of Completion

January 1998


Applied Mechanics|Engineering, Electronics and Electrical|Engineering, Mechanical




A recently introduced active vibration absorber, the Delayed Resonator (DR), forms the fundamental motivation for this study. The DR absorber uses a partial state feedback control with variable gain and time delay to reconfigure the dynamics of a mass-spring-damper trio such that it behaves like an ideal absorber with real-time tunable frequency. This device completely removes undesired oscillations from the primary structure at the tuning frequency. It introduces, however, some vulnerable side frequencies typically one below and the other one above the excitation frequency it suppresses. This scenario suggests a trade-off: improve the side frequency peaks at the cost of less perfection in suppressing oscillations at the tuning frequency. The DR feedback formation is revised so that primary system exhibits minimum Mpeak (maximum frequency response) within a given frequency band. For this, a min-max problem is solved. Stability of the controlled system needs to be assured which brings a crucial constraint on the optimization process. The final structure, which is named Delayed Feedback Vibration Absorber (DFVA), offers considerable frequency response improvement over the DR. ^ These optimum absorbers become de-tuned over time due to variations in the structural parameters, which yields sub optimal vibration suppression characteristics. For practical applications, DFVA performance under parametric variations is to be maintained at an acceptable level. A quasi real-time control strategy is proposed to achieve this. It consists of an on-line parameter identification process and an optimum absorber controller, which forms a nested quasi real-time system identification/control optimization structure. The main contribution of the thesis is on the theoretical fundamentals and the supporting simulations of this proposition. ^ The strengths of the new tunable, optimum delayed feedback vibration absorption scheme consist of: frequency response which is flat to the extent possible over a wide frequency range, comparably simple implementation of the control algorithm, full effectiveness of vibration suppression for structures with parametric variations and fault-tolerant performance in the case of control failure. ^