With a causal bond graph model, equivalent dynamic equations can easily be derived. To create the dynamic equations, the following steps have to be performed.
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As an example in the figure below a causal bond graph model is shown. We will derive the set of dynamic equations out of this model.
1. | Denote all efforts and flows. This is shown below: |
2. | Write the dynamic equations of the elements and junctions: |
elements |
equations |
uin = constant , iin = free |
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ur = Re ir |
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il = (1/L) int(ul) |
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iin = ir = il = im uin - ur - ul - um = 0 |
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um = km ωm Tm = km im |
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Tj = (1/J) int(ωj) |
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Tr = d ωr |
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ωm = ωj = ωr Tm - Tl - Tr = 0 |
3. | Reduce the amount of equations. We replace the equalities of the 1 junctions: iin = ir = il = im= i and ωm = ωj = ωr= ω . |
elements |
equations |
uin = constant |
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ur = Re i |
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i = (1/L) int(ul) |
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uin - ur - ul - um = 0 |
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um = km ω Tm = km i |
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Tj = (1/J) int(ω) |
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Tr = d ω |
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Tm - Tl - Tr = 0 |
The resulting dynamic equations can be used for simulation. 20-sim can automatically extract the dynamic equations out of a bond graph model. The equations can be shown using the Show Equations command or used in the Simulator for simulation.