Inversion of Linear Time-invariant SISO Systems Modelled by Bond Graph

Two different algorithms for deriving the inverse system state equations from a bond graph model are presented. The first method is based on the causal path analysis and it leads to the full-order inverse system. The second method which is procedural relies on the concept of bicausality and the state equations obtained from the resulting algorithm are those of a reduced inverse system. In both cases, some illustrative examples are given. The advantages of these methods are that they can easily be implemented in software using an algorithm of causality assignment and a procedure of causal paths analysis in a bond graph. Formal calculations of matrices are then avoided in the first case and also formal state transformations are not necessary to obtain the reduced inverse system in the second case.