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Copy file name to clipboardExpand all lines: docs/src/API/linear_analysis.md
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The interface described here is currently experimental and at any time subject to breaking changes not respecting semantic versioning.
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Linear analysis refers to the process of linearizing a nonlinear model and analysing the resulting linear dynamical system. To facilitate linear analysis, ModelingToolkitStandardLibrary provides the concept of an [`AnalysisPoint`](@ref), which can be inserted in-between two causal blocks (such as those from the `Blocks` sub module). Once a model containing analysis points is built, several operations are available:
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Linear analysis refers to the process of linearizing a nonlinear model and analysing the resulting linear dynamical system. To facilitate linear analysis, ModelingToolkitStandardLibrary provides the concept of an `AnalysisPoint`, which can be inserted in-between two causal blocks (such as those from the `Blocks` sub module). Once a model containing analysis points is built, several operations are available:
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-[`get_sensitivity`](@ref) get the [sensitivity function (wiki)](https://en.wikipedia.org/wiki/Sensitivity_(control_systems)), $S(s)$, as defined in the field of control theory.
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-[`get_comp_sensitivity`](@ref) get the complementary sensitivity function $T(s) : S(s)+T(s)=1$.
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-[`get_looptransfer`](@ref) get the (open) loop-transfer function where the loop starts and ends in the analysis point. For a typical simple feedback connection with a plant $P(s)$ and a controller $C(s)$, the loop-transfer function at the plant output is $P(s)C(s)$.
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-[`linearize`](@ref) can be called with two analysis points denoting the input and output of the linearized system.
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-[`open_loop`](@ref) return a new (nonlinear) system where the loop has been broken in the analysis point, i.e., the connection the analysis point usually implies has been removed.
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-`get_sensitivity` gets the [sensitivity function (wiki)](https://en.wikipedia.org/wiki/Sensitivity_(control_systems)), $S(s)$, as defined in the field of control theory.
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-`get_comp_sensitivity` gets the complementary sensitivity function $T(s) : S(s)+T(s)=1$.
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-`get_looptransfer` gets the (open) loop-transfer function where the loop starts and ends in the analysis point. For a typical simple feedback connection with a plant $P$ and a controller $C$, the loop-transfer function at the plant output is $P(s)C(s)$.
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-`linearize` can be called with two analysis points denoting the input and output of the linearized system.
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-`open_loop` returns a new nonlinear system where the loop has been broken at the analysis point.
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An analysis point can be created explicitly using the constructor [`AnalysisPoint`](@ref), or automatically when connecting two causal components using `connect`:
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An analysis point can be created explicitly using the `AnalysisPoint` constructor, or automatically when connecting two causal components using `connect`:
Copy file name to clipboardExpand all lines: docs/src/connectors/connections.md
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In Physical Network Acausal modeling, each physical domain must define a **connector** to combine model components. Each physical domain **connector** defines a minimum of 2 variables, one which is called a *Through* variable, and one which is called an *Across* variable. Both Modelica and SimScape define these variables in the same way:
However, the standard libraries differ on the selection of the Across variable for the Mechanical Translation and Rotation libraries, Modelica choosing position and angle and SimScape choosing velocity and angular velocity, respectively for Translation and Rotation. Modelica describes their decision [here](https://mbe.modelica.university/components/connectors/simple_domains/). In summary, they would like to provide less integration in the model to avoid lossy numerical behavior, but this decision assumes the lowest order derivative is needed by the model. Numerically it is possible to define the connector either way, but there are some consequences of this decision, and therefore we will study them in detail here as they relate to ModelingToolkit.
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