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FMU ME: Bouncing Ball

This example demonstrates Model Exchange FMU integration with PathSim. Unlike co-simulation FMUs, Model Exchange FMUs provide only the differential equations. PathSim's solvers perform the numerical integration and event detection.

You can also find the FMU integration tests in the GitHub repository.

The bouncing ball combines continuous dynamics with discrete events:

MATHDISPLAY0ENDMATH MATHDISPLAY1ENDMATH

where MATHINLINE2ENDMATH is height, MATHINLINE3ENDMATH is velocity, and MATHINLINE4ENDMATH. At impact (MATHINLINE5ENDMATH), velocity reverses with energy loss: MATHINLINE6ENDMATH where MATHINLINE7ENDMATH is the restitution coefficient.

This example demonstrates the ModelExchangeFMU block, which provides PathSim with continuous states and derivatives from an FMU. PathSim's solvers handle integration, event detection, and error control.

Import and Setup

Note that FMPy must be installed to use FMU blocks:

pip install fmpy

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FMU Path

The FMU contains binaries for multiple platforms (Windows, Linux, macOS):

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System Definition

The ModelExchangeFMU block exposes continuous states $(h, v)$ and provides derivatives $(\dot{h}, \dot{v})$ to PathSim's solvers. Event indicators signal zero-crossings for accurate bounce detection.

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Display FMU metadata:

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Simulation Setup

PathSim integrates the FMU using an adaptive Runge-Kutta solver (RKBS32) with error control. The solver automatically adjusts timesteps for accurate event detection.

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Results

Plot the trajectory:

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Event Visualization

Mark the detected bounce events:

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