Bond graph realizations of state space linear time-invariant multivariable descriptions

Abstract

Given a state space description of a linear time-invariant multivariable system, a similarity transformation is applied to get a controllability canonical form. This transformation assures a Bond Graph (BG) realization and avoids the use of active bonds. Active or signal bonds do not preserve the continuity of power flows and consequently, energy conservation properties are lost. The state matrix of the system in transformed coordinates contains an antisymmetric matrix associated with the storage field and the rest is associated with the dissipative field. Thus, in general, the dissipative field is implemented with a multiport element, and in order to give physical meaning, the storage field is implemented with one-port elements. The resulting BG model does not have zero-order causal paths, that is, algebraic loops between the dissipative elements. The results are applied to the BG realization of a linear robust multivariable controller that is designed for a two mass system modelled in BG.