Analytical Port Inversion For A Flexible Model In The Two-Input Two-Output Port Approach

Abstract

In the context of multi-body modeling techniques, this paper introduces a new analytical approach to build a Two-Input-Two-Output Port (TITOP) model for a clamped-clamped flexible appendage. By expanding the previous work found in literature, which relied on numerical procedures, this model represents a fundamental block for the construction of parametric multi-body systems in a sub-structuring approach, such as closed-loop kinematic mechanisms. Specifically, this new procedure allows to assemble a linear state-space system by analytically inversing the input-output channels of the original clamped-free TITOP model. This analytical method presents the advantage of avoiding non-physical behaviors introduced by numerical inversions as well as removing the need to reduce the quasi-zero poles associated with the nonanalytical model. This paper presents the mathematical formulation of the system, as well as the formalism behind the method, and an illustrative case study to showcase the advantages of this approach.