Stability and performance of supercritical inerter-based active vibration isolation systems

This paper presents an analytical study on stability and performance of supercritical linear active vibration isolation systems. The systems analyzed are consisted of source and receiving bodies. Receiving body is to be protected from vibrations. Supercritical scheme means that the uncoupled natural frequency of the receiving body is smaller than the uncoupled natural frequency of the source body. Broadband random kinematic/base excitation of the source body is imposed. Passive and active supercritical systems are studied. The isolation system is made active via direct velocity feedback, i.e. skyhook damping assumption. Serial and parallel arrangements of the inerter and dashpot in the isolator are considered. It is demonstrated that including an optimized inerter in the isolator introduces instabilities in otherwise unconditionally stable active system and consequently deteriorates isolator performance. However, by serial dashpot/inerter arrangement and simultaneous optimization of passive and active damping in this inerter-based isolator, improved performance may be achieved compared to the parallel systems without inerter. Optimization is based on the Script capital H2 displacement criterion where broadband vibrations of the receiving body are minimized. Proposed "optimum stable path" method is introduced via blending Script capital H2 optimization and Routh-Hurwitz stability criteria. Obtained expressions are given in closed-form.