Bond Graph-based Analysis of Structural Observability

2 Bond Graph-based Analysis of Structural Observability 

If integral causality is applied to the energy storage elements as the preferred causality then every storage element in integral causality must have at least one causal path to either an effort sensor De or to a flow sensor (Df). This reachability requirement is a necessary condition. 

If derivative causality is the preferred causality, then all storage elements in integral causality must be able to take derivative causality. If integral causality cannot be turned into derivative causality for some storage elements, then this must be possible after some sensors in appropriate locations have been dualised, i.e. a flow sensor (Df) has been replaced by an effort sensor (De) or vice versa. This requirement is a sufficient condition. 

It both conditions are met, then the model is structurally completely observable with the given set of sensors and the rank of the observability matrix O equals the number of states n. If rank(A) = n then one single sensor is sufficient to assure complete state observability. Its type and position is to be chosen so that both conditions are fulfilled. 

If the second condition cannot be satisfied so that k = n —q storage elements remain in integral causality in the bond graph with preferred derivative causality (BGD), then k additional sensors are needed to assure complete observability. Their type and their position is to be chosen so that both conditions are satisfied.  

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