Relations between two bond graph approaches to sensitivity analysis and study of robustness

Abstract

Recently Borutzky and Granda proposed to construct a so-called incremental bond graph from an initial bond graph with nominal parameters in order to determine unnormalized first order frequency domain sensitivities in symbolic form. At the same time Dauphin-Tanguy and Kam presented a bond graph approach that allowed them to set up a specific form of state equations in symbolic form commonly used for a robustness study of models with uncertain parameters. Both approaches designed for different purposes have been developed independently. Nevertheless, this paper shows that they can be used to obtain each other's results under some reasonable assumptions. For illustration both approaches are applied to an example, which has been kept fairly small for didactic reasons.