Virtual Vibration Absorbers with Inherent Damping

A physically motivated control algorithm is proposed to suppress nondecaying harmonic disturbances in mechanical structures and rotary machinery. The control scheme mimics a passive vibration absorber constructed of a symmetric pair of virtual mass-spring subsystems interconnected by a dashpot, which provides inherent damping to the controlled plant. When implemented as a feedback algorithm, this virtual absorber does not require velocity measurement to stabilize the system, and multisets of absorbers can be combined in parallel to suppress mixed-frequency vibrations. This virtual passive control technique not only ensures stability independent of detailed system structure and parameters, but also facilitates the design of a high-performance controller: It is shown that redundant sets of virtual absorbers containing different damping ratios can significantly reduce settling time. This paper starts with a single-degree-of-freedom plant and then extends to more complicated systems including multiple-degrees-of-freedom structures and a couple of nonlinear systems.