Removing the algebraic loops of a bond graph model

Abstract

A general straightforward procedure solving the problem of algebraic loops in a bond graph model of a linear time invariant (LTI) multi-input multi-output (MIMO) system is presented. This procedure is based on a proposed junction structure and an R-field. This junction structure allows interactions only between the state variables and the dissipation field and inputs, and between the dissipation field and the co-energy variables. This junction structure decouples the elements of the dissipation field, thereby removing the algebraic loops. The outputs are only functions of the co-energy variables and the inputs. In order to obtain a physical meaning for the proposed bond graph model, the initial R-field of this bond graph is transformed to a dissipative field of 1-port resistors, transformers, and gyrators. The proposed bond graph does not have algebraic loops and allows predefined integral (BGI) or derivative (BGD) causality assignments to be realized.