Multiport node

From the fact that one of the variables on a port is an independent variable of the constitutive relation and the other one a dependent variable, it follows that the computational direction of the two conjugate variables at a bond is always bi-directional and can in principle be expanded into two opposite signals, in other words, a bond can be considered a bilateral signal flow. The effort is the input of the multiport node at the one side and the output of the node at the other side. Only after a particular choice is made about the two possibilities of these directions, this can be represented by causally augmenting the (multi)bond with a so-called causal stroke, a little line drawn orthogonal to the bond at the end of the bond where the effort serves as an output of the bond from a computational point of view. This implicates that it serves as an input for the port that is connected to that side of the bond. Similarly the conjugate flow at that side of the bond is an output of this port and an input to... 

The following categories of multiport node types can be distinguished in a bond... 

Stored, transformed from one form into another, especially irreversibly into heat, or power may be distributed to other nodes. In bond graphs, the latter ones have got so-called power ports where energy may enter or leave a node. Of course, nodes may have more than one power port. They are called multiports. The edges of a bond graph are connections between the power ports of different nodes. They are called power bonds, or just bonds. They represent the transfer of power between ports and may be associated with physical links between real systems such as a shaft between a motor and a mechanical load, or a hydraulic line between hydraulic components if it is assumed that energy is neither stored nor dissipated into heat in a physical link. Otherwise, a physical model is to be developed for the physical link. 

Source nodes All dependent port variables of a source node are independent of its independent port variables. This means that the dependent variables are either constant (linear case with one parameter) or the function of an input (modulated source). This means that a multiport source node can always be split into a set of (modulated) one-port sources. When the dependent port variable is an effort the source is called an effort source (node label Se). When the dependent port variable is a flow the source is called a flow source (node label Sf). A modulated source has node label MSe or MSf. 

It can be proven by means of a linear transformation of the conjugate variables into so-called scattering variables [9, 10] that all power continuous nodes have constitutive relations with a multiplicative form. This means that the vector of dependent port variables can be written as a product of some operator on the vector of independent port variables. When this operator only relates efforts to efforts and flows to flows, a property called non-mixing [11], the multiport is called a transformer (node label TF). If the operator is a function of one or more additional node inputs, it is called a modulated transformer (node label MTF). When this operator only relates efforts to flows and flows to efforts, a property called mixing [11], the multiport is called a gyrator (node label GY). If the operator is a function of node inputs it is called a modulated gyrator (node label MGY). 

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