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Equation-based modeling

Modelon Impact is based on the idea of modeling reuse and acausal modeling. Acausal modeling is also known as equation-based or physics-based modeling.

The idea behind is that you never have to write a piece of code more than once. This means that you define the behavior of the model via equations but leave out the order of the calculations to the tool.

The same model can then be used in various types of systems and analysis, as the order of execution is automatically adjusted by the tool for each use case.


The automatic process of sorting the equations is done by the tool during the compilation process.

Physical modeling versus block-oriented modeling🔗

To illustrate the advantages with the physics-based modeling approach, we look at a model of an electric drive. The model consists of a rotational speed controller, electric circuit and a mechanical drive train.

Figure 1. Physical model of an electric drive-train.

Here the modeler defines how the components interact with each other using physical connections. The calculation order is taking care by the simulation tool during the compilation process.

Figure 2. Block-oriented model of an electric drive-train.

Comparing the models, it is obvious that the block-oriented approach is more difficult and time-consuming to set-up. It’s also more difficult to analyze as physical structure and interactions between the components have been replaced by signal-flow.

The main message is that modeling is greatly simplified by the concept of physical modeling. Here you only have one component implementation independent of how it will be connected and used in a system.

Changing the model structure🔗

A key advantage with the physics-based approach is the ability to reuse a model. Extending the physical-based model with a new component is straight-forward as seen in figure 3, where a flexible shaft has been added to the drive train.

Adding the flexible shaft change the calculation order of the model. For the block-oriented approach this means that a large part of the model needs to be re-modeled. This is not the case for the physics-based model as this step is done automatically by the tool.

Figure 3. Comparison of a physical drive train model with flexible shaft to it's equivalent block-oriented model

To conclude, block-oriented models are not suitable for large-scale modeling or when the modeling requirements or usage change.