Numerical Stability Analysis for Independent Modal Vibration Suppression of a Fluid-Conveying Pipe Using a Piezoelectric Inertia Actuator

Abstract

This study deals with numerical stability analysis for independent modal vibration suppression of a fluid-conveying pipe using a piezoelectric inertia actuator (PIA). The stability issue of the approach as proposed by the pioneer developers is addressed. The approach utilizes an infinite control weight for one component of the modal control input and results in a severe control spillover problem for the complex mode controlled, easily leading to closed loop instability even for open loop stable systems. The stability of the system depends on how the left eigenvector is normalized for transforming the original coupled equations to the decoupled ones in the modal space. A novel approach by rotating the left eigenvector on the complex plane is systematically examined to define the region of stability in this work. A feasible modal control design for systems possessing complex modes can thus be accomplished using the proposed approach.