pyBondGraph

pyBondGraph is a Python library for modeling and analyzing linear bond graph systems using symbolic computation.

The library allows users to construct bond graph models programmatically, automatically derive the governing equations, and analyze the resulting dynamic systems using tools from control theory.

Bond graphs provide a domain-independent modeling framework for physical systems. Using a unified representation of power exchange, the same modeling approach can be used for electrical, mechanical, hydraulic, and multi-domain systems.

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Features

• Programmatic construction of bond graph models
• Automatic symbolic equation derivation using SymPy
• Conversion of models to state-space systems
• Example models for electrical and mechanical systems

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Installation

Install from PyPI or Github

The easiest way to install the library is via your preferred package manager (e.g. pip) directly from PyPI:

pip install pyBondGraph

Alternatively one can install the latest development version directly from the GitHub repository:

pip install git+https://github.com/MrP123/pyBondGraph.git

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Development installation

To work with the source code:

git clone https://github.com/MrP123/pyBondGraph.git
cd pyBondGraph
pip install -e .

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Dependencies

The main dependencies are:

• sympy
• numpy
• networkx
• matplotlib
• control only needed for the examples

Optional dependencies are used for experimental visualization tools.

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Basic Usage

A bond graph model is constructed by creating elements and connecting them via bonds.

Simple RC-Filter circuit:

from pyBondGraph import BondGraph, SourceEffort, Resistor, Capacitor, OneJunction, Bond, Causality

bg = BondGraph()

# create elements
voltage_source = SourceEffort("U", "u_in")
resistor = Resistor("R", "R")
capacitor = Capacitor("C", "C")
series_junction = OneJunction("J1")

# connect elements
# causalities need to be assigned manually 
bg.add_bond(Bond(voltage_source, series_junction, Causality.EFFORT_OUT))
bg.add_bond(Bond(series_junction, resistor, Causality.EFFORT_OUT))
bg.add_bond(Bond(series_junction, capacitor, Causality.FLOW_OUT))

# plot the resulting BondGraph
bg.plot()

# derive system equations in linear state space form
A, B, C, D, x, n_states, n_inputs, n_outputs = bond_graph.get_state_space()

The library automatically derives the symbolic system equations describing the dynamics of the model.

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Core Concepts

Bond graphs represent power exchange between system components, where power is the product of effort and flow associated with the following components:

Elements

Element	Meaning
R	Dissipation
C	Energy storage (compliance, capacitance)
I	Energy storage (inertia, inductance)
Se	Effort source
Sf	Flow source

Junctions

Junction	Meaning
0	Common effort
1	Common flow

Sensors

Sensor	Meaning
IntegratedEffortSensor	Measures integral of the effort at its bond
IntegratedFlowSensor	Measures integral of the flow at its bond

In mechanical bond graph models:

• flow corresponds to velocity
• effort corresponds to force

An integrated flow sensor can therefore be used to compute position:

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Example Systems

The repository contains example models illustrating typical applications of bond graphs.

RLC Circuit

Demonstrates modeling of an electrical circuit using bond graph elements.

DC Motor

A multi-domain electromechanical system coupling electrical and mechanical dynamics.

Transformer

Example of energy transformation between two ports.

Two DOF Mass–Spring–Damper System

Classical mass-spring-damper system with two degrees of freedom.

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Typical Applications

Bond graph modeling is particularly useful for:

• electromechanical systems
• robotics and mechatronics
• multi-domain energy systems
• control system modeling
• teaching system dynamics