Bicausality-based Procedures for Transfer and Transmission Matrix Determination of Single Source Single Load Linear Systems

摘要

In linear SISO systems the energy flows from the source to the load through each actuating power line. Bond graph representation is well suited for studying the energy transfer in these systems because, in most of the systems, we can consider that energy flows through a power line embedded in two-port subsystems. Moreover, with bond graph language, we benefit from the ease of analytical exploitation introduced by the calculus causality and bicausality concepts. In the bond graph representation of a system the power in some port is associated to a power bond to which two power variables are attached. The determination of the transmission matrix linking two power variables is an efficient tool for studying the energy transfer. Furthermore it is often useful to study the bi-directional energy transfer i.e. from the source to the load and vice versa. The latter case (namely from the load to the source) is quite useful for the energy sizing of a system from its dynamic specifications on an output variable. This paper proposes different procedures for determining direct and inverse transmission matrices and the transfer matrix between an internal bond and an environmental one for Single Source Single Load Linear systems represented by bond graphs. The procedures are based on the bicausality concept and the loop rule.