Inherent stability analysis for multibody systems with semi-active inerters

Abstract

Inherent stability reflects the reliability performance of a semi-active control system, where for “active” semi-active inerter-based systems, the inherent stability problem has not been studied. The motivation of this paper is to present sufficient conditions that ensure inherent stability for such systems. The absolute stability theory is adopted, and the general multibody system with semi-active inerters is formulated in a Lurè form. Sufficient conditions are derived based on the circle criterion for three different cases including the case with only one semi-active inerter, the case with several semi-active inerters without common connection points, and the case with several semi-active inerters where the ground is the common connection point. Extensive numerical examples based on low-degree-of-freedom systems are provided to show the effectiveness of the derived conditions.