Change bonds graph

Changing the bond graph—reconstructive phase transitions... 

Reconstructive phase transitions occur when major changes are made in the topology, i.e. when the bond graph is reorganized. The transitions usually observed in structures with lattice-induced strain are displacive and often second order (no latent heat). Reconstructive transitions arise when two quite different structures with the same composition have similar free energies. Unlike the displacive transitions they involve the dissolution of one structure and the recrystallization of a quite different structure. These phase transitions possess a latent heat and often display hysteresis. 

In order to define the governing equations, the bond graph method identifies the cause (force) and effect (flow) relation for the energy exchange. This model can be modified easily to account for changes in the system or its environmental perturbations. Initial and boundary conditions can be related to one another within the formulations. 

The bond graph method of network thermodynamics is widely used in studying homogeneous and heterogeneous membrane transport. Electroosmosis and volume changes within the compartments are the critical properties in the mechanism of cell membrane transport, and these properties can be predicted by the bond graph method of network thermodynamics. In another study, a network thermodynamics model was developed to describe the role of epithelial ion transport. The model has four membranes with series and parallel pathways and three transported ions, and simulates the system at both steady-state and transient transepithelial electrical measurements. 

The bond graph structure can be extended for multiple coupled reactions. For example, the change of /th substance in the Mi chemical reaction is expressed by... 

The bond-graph network of liquid membrane process can be successfully exploited for modeling the separation and transport ability of complex reaction-diffusion phenomena. However, such models involving appropriate mathematical formulations are especially useful in predicting the system s response to the changes in operating conditions and specific characteristics of the liquid membrane components. In general, such models are not... 

In online model-based FDI, ARRs are evaluated using measurements from the real system being subject to disturbances. The time evolution of ARR residuals serve as fault indicators. For hybrid systems, ARRs are system mode dependent. Hence, an unobserved mode change invalidates the actual set of ARRs. As a result, computed values of fault indicators may exceed current thresholds indicating faults in some system components that have not happened. ARR residuals derived from a bond graph can not only serve as fault indicators but may also be used for model-based system mode identification. 

Clearly, for FDI it is necessary that a system is structurally observable. As switches temporarily disconnect and reconnect model parts they change the structure of a hybrid system model. Consequently, control properties, i.e. structural observability and structural controllability as well as characteristics of the mathematical model derived fl om the bond graph, i.e. the number of state variables, or the index of a DAE system become system mode dependent. Chapters briefly addresses these issues by confining to switched LTI systems and provides some small illustrating examples. 

A causality change at a switch port propagates at least locally into the bond graph and affects the causality at the ports of other elements as indicated in Fig. 2.6 for the example of the mechanical stop. 

Back in 1993, Asher proposed to assist an ideal switch by a resistor he called causality resistor that adapts its causality to causality changes at the switch port so that the rest of the bond graph remains causally unaffected [23]. As long as the simulated dynamic behaviour is not significantly affected, the parameter value of a causality resistor can be chosen within reasonable limits but may lead to stiff model equations and thus may give rise to an increase of computational costs. 

The causality resistor R / 2 clearly avoids the propagation of causality changes at the port of the ideal switch into the rest of the bond graph and captures the diode s high resistance Roft in reverse mode. The resistor R Ri represents the diode s small ON-resistance Ron-... 

As a result, if the dynamic behaviour of a system can be described by a switched LTI system, the DAE system derived from the bond graph is of index <1 as long as no structural changes occur. If a structural change modelled by a switched residual sink happens, the DAE index jumps to two. 

If the dynamic behaviour of a system can be described by a switched LTI system, a linear implicit DAE system can be derived from the bond graph. The entries of its matrices depend on the discrete switch states. As long as no structural changes occur, i.e. no residual sinks are switched on, the DAE system is of index <1. For system modes in which residuals sinks are switched on, the DAE system is of index 2. There are solvers available for its direct numerical computation that are based on the BDF-method. An alternative may be to perform a DEVS simulation that uses quantised based integration. 

If there are na storage elements with derivative causality in a bond graph with preferred integral causality and their causality cannot be changed by inverting the causality of some switches then they do not contribute a state variable and do not need to be considered in a test for structural observability. The number of state variables equals the number of storage elements in integral causality. 

For illustration, consider the example of a buck converter displayed in Fig.2.19. As can be seen, in this bond graph in preferred integral causality, the inductor I L is in derivative causality. The bond graph captures the physical feasible system mode in which the two switches are off (m2 = 0 a mi =0). However, derivative causality at the I-element indicates that the inductor current is not observable in this mode. If one of the two switches is closed, its causality can be changed into resistive causality. As... 

Simulation results in Fig.4.17 obtained by numerical evaluation of the coupled bond graph models in Fig. 4.16 confirm that residuals V2 and indicate this change in the behavioural model of the real circuit in accordance with the FSM in Table4.1. 

Switched LTI systems are just LTI systems for the time intervals betweens between discrete mode changes. Therefore, first, the incremental bond graph approach is recalled for LTI systems. In a second step, an incremental model for switches is... 

The book briefly recalls various bond graph representations of hybrid system models proposed in the literature. The development of hybrid models for the purpose of fault detection and isolation, in this book, makes use of conceptual nonideal switches representing devices for which it is justified to abstract their fast state transitions into instantaneous discrete state switches and accounts for stmctural model changes by special sources that are switched on or off at the advent of a discrete event. As other possible approaches, this approach has its pros and cons. For illustration, the presented method is applied in a number of elaborated case studies that consider fault scenarios for switched power electronic systems that are commonly used in a variety of applications. Power electronic systems have been chosen because they may be appropriately described by a hybrid model and are well suited for application of the presented bond graph model-based approach to fault detection and isolation. The approach, however, is not limited to this kind of systems. 

The bond-graph method of network thermodynamics is widely used in studying homogeneous and heterogeneous membrane transport. Electroosmosis and volume changes within the compartments are the... 

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