Parameter Uncertainty Thresholds for ARR Residuals

As explained in Sect. 5.3.2, variations of ARR residuals due to parameter variations are obtained by summing increments of power variables at junctions of an incremental bond graph to which a virtual detector has been attached. Replacement of the switch model as well as the other bond graph elements in the DBG of the boost converter in Fig. 8.2 by their incremental model gives the incremental DBG depicted in Fig. 8.14. 

In this incBG, the capacitor C Ca has been added to resolve the causal conflict at junction Oi. During formulation of equations for variations of ARR residuals capacitance Ca is set to zero. Again, virtual detectors have been distinguished from detectors representing real sensors by an asterisk. 

Summation of incremental power variables at junctions 11 and O2 yields the part of the two ARR residuals that is due to parameter uncertainties. 

Equations (8.35)-(8.36) can be verified by either deducing them from the simplified incBG in Eig.8.15 or by taking the total differential of the simplified state Eq.(8.11). 

Upper bounds for the absolute values of the variations Ari and Arz may be found by application of the triangle inequality. 

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