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This paper proposes a novel approach to the generation of state equations from a bond graph (BG) of a mode switching linear time invariant model. Fast state transitions are modelled by ideal or non-ideal switches. Fixed causalities are assigned following the Standard Causality Assignment Procedure such that the number of storage elements in integral causality is maximised. A system of differential and algebraic equations (DAEs) is derived from the BG that holds for all system modes. It is distinguished between storage elements with mode independent causality and those that change causality due to switch state changes.
BGML - a novel XML format for the exchange and the reuse of bond graph models of engineering systems
(2006)
The paper proposes a bond graph approach to model based fault detection and isolation (FDI) that uses residual sinks. These elements couple a reference model of a process engineering system to a bond graph model of the system that is subject to disturbances caused by faults. In this paper it is assumed that two faults do not appear simultaneously. The underlying mathematical model is a Differential Algebraic Equations (DAE) system. The approach is illustrated by means of the often used hydraulic two tanks system.
Bond graph modelling
(2006)
In this paper, residual sinks are used in bond graph model-based quantitative fault detection for the coupling of a model of a faultless process engineering system to a bond graph model of the faulty system. By this way, integral causality can be used as the preferred computational causality in both models. There is no need for numerical differentiation. Furthermore, unknown variables do not need to be eliminated from power continuity equations in order to obtain analytical redundancy relations (ARRs) in symbolic form. Residuals indicating faults are computed numerically as components of a descriptor vector of a differential algebraic equation system derived from the coupled bond graphs. The presented bond graph approach especially aims at models with non-linearities that make it cumbersome or even impossible to derive ARRs from model equations by elimination of unknown variables. For illustration, the approach is applied to a non-controlled as well as to a controlled hydraulic two-tank system. Finally, it is shown that not only the numerical computation of residuals but also the simultaneous numerical computation of their sensitivities with respect to a parameter can be supported by bond graph modelling.