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.

Keywords

bond graph,state space,junction structure,algebraic loop,zero-order causal paths

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