On the zeros of three-DoF damped flexible systems

Abstract

This paper presents an investigation of the non-minimum phase (NMP) zeros in the single input single output (SISO) transfer function of three-DoF (degrees of freedom) damped flexible linear time-invariant (LTI) systems under the assumption of classical damping. It is well-known that when all the modal residue signs of any multi-DoF damped flexible LTI system are the same, NMP zeros never occur in the system dynamics for any value of system parameters including modal residue, modal frequency and modal damping ratio. However, when all the modal residue signs are not the same, then additional conditions in terms of the system parameters are required to guarantee the elimination of NMP zeros. In this paper, the zero loci of a three-DoF damped flexible LTI system are developed to derive the sufficient and necessary conditions for the elimination of all NMP zeros. These conditions can be employed in the robust physical design of flexible systems, i.e., as long as these conditions are satisfied, the elimination of NMP zeros is guaranteed even when the system parameters undergo variations.