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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.
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 and Simulation of Mechatronic Systems: An Introduction into the Methodology
(2006)
This paper introduces into a graphical, computer aided modelling methodology that is particularly suited for the concurrent design of mechatronic systems, viz. of engineering systems with mechanical, electrical, hydraulic or pneumatic components including interactions of physical effects from various energy domains. Beyond the introduction, bond graph modelling of multibody systems, as an example of an advanced topic, is briefly addressed in order to demonstrate the potential of this powerful approach to modelling mechatronic systems. It is outlined how models of multibody systems including flexible bodies can be build in a systematic manner.
Switched power electronic subsystems are widely used in various applications. A fault in one of their components may have a significant effect on the system’s load or may even cause a damage. Therefore, it is important to detect and isolate faults and to report true faults to a supervisory system in order to avoid malfunction of or damage to a load. If, in a model-based approach to fault detection and isolation of hybrid systems, switching devices are considered as ideal switches then some equations must be reformulated whenever some devices have switched. In this paper, a fixed causality bond graph representation of hybrid system models is used, i.e., computational causalities assigned according to the Standard Causality Assignment Procedure (SCAP) are independent of system modes of operation. The latter are taken into account by transformer moduli mi(t) ∈ {0, 1} ∀t ≥ 0 in a unique set of equations of motion. In a case study, this approach is used for fault diagnosis in a three-phase full-wave rectifier. Residuals of Analytical Redundancy Relations (ARRs) holding for all modes of operations and serving as fault indicators are computed in an offline simulation as part of a DAE system by using a bond graph model of the faulty system instead of the real one and by coupling it to a bond graph of the healthy system by means of residual sinks.
This paper picks up on one of the ways reported in the literature to represent hybrid models of engineering systems by bond graphs with static causalities. The representation of a switching device by means of a modulated transformer (MTF) controlled by a Boolean variable in conjunction with a resistor has been used so far to build a model for simulation. In this paper, it is shown that it can also constitute an approach to bond graph based quantitative fault detection and isolation in hybrid system models. Advantages are that Analytical Redundancy Relations (ARRs) do not need to be derived again after a switch state has changed. ARRs obtained from the bond graph are valid for all system modes. Furthermore, no adaption of the standard sequential causality assignment procedure (SCAP) with respect to fault detection and isolation (FDI) is needed.