An Improved Approach for Spatial Discretization of Transfer Matrix Models of Flexible Structures

Abstract

The transfer matrix method (TMM) is a powerful modeling approach with unique strengths for modeling flexible structures under feedback control. The TMM can model distributed parameter systems without spatial discretization, ensuring that the models are protected against model spillover. Feedback and actuator dynamics can be directly included in the structural model, leading to accurate models of ac-tuator/structure interaction. The TMM can produce closed-form symbolic expressions for the infinite-dimensional closed-loop transfer functions of distributed parameter systems under feedback control. These infinite-dimensional transfer functions can be used directly for compensator design via Bode plots. However, if modern state-space control design tools are to be applied to a flexible structure model with the TMM, the TMM model must first be discretized. The infinite-dimensional nature of TMM models and the fact that they involve transcendental expressions in the Laplace variable $s$ make it difficult to apply most of the model reduction procedures in the literature. This paper presents a technique for discretizing TMM models that is an improvement upon one discretization technique from the literature that is specific to the TMM.