Transmission Matrices for Physical-System Modeling [Lecture Notes]

Power transmission matrices (PTMs) for structures are 2 X 2 matrices that relate force and velocity at one terminal to force and velocity at another terminal. This technique provides an elegant approach to deriving transfer functions for structures consisting of masses, springs, and dashpots, that is, dampers. PTMs were developed during the 1970s and 1980s, but they are rarely mentioned today except briefly in textbooks. The first goal of this tutorial is to highlight the utility of this modeling technique. A related aim is to bring inerters into this framework. The article revisits the classical topic of analogies by deriving PTMs for twoport networks. The across-through analogy is used to construct circuits whose transfer functions match those of the analogous structure. This article is intended for all students and practitioners of control systems who may benefit from awareness of this modeling technique.