From 7d133167cf559c1ac9470fdb165f5dccb0f1bed9 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Wed, 23 Apr 2025 08:07:12 +0200 Subject: [PATCH 01/33] added paper/paper.md --- paper/paper.md | 63 ++++++++++++++++++++++++++++++++++ src/pathsim/blocks/function.py | 1 - 2 files changed, 63 insertions(+), 1 deletion(-) create mode 100644 paper/paper.md diff --git a/paper/paper.md b/paper/paper.md new file mode 100644 index 00000000..99daa129 --- /dev/null +++ b/paper/paper.md @@ -0,0 +1,63 @@ +--- +title: 'PathSim: A Decentralized Python Framework for Dynamical System Simulation' +tags: + - Python + - system simulation + - dynamical systems + - block diagram + - ODE solver + - automatic differentiation + - event handling + - hybrid systems + - scientific computing + - numerical integration +authors: + - name: Your Name Here # TODO: Add your name + orcid: 0000-0000-0000-0000 # TODO: Add your ORCID + affiliation: 1 # TODO: Add affiliation index +affiliations: + - name: "Your Affiliation Here (e.g., University, Institute, Company, or 'Independent Researcher')" # TODO: Define your affiliation + index: 1 +date: DD Month Iodide # TODO: Add submission date +bibliography: paper.bib # TODO: Create a paper.bib file for references +--- + +# Summary + +PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems using an object-oriented and **decentralized architecture**. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination via fixed-point iteration. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features like automatic differentiation for sensitivity analysis, discrete event handling for hybrid systems, automatic linearization, hierarchical subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries (`numpy`, `scipy`, `matplotlib`). + +# Statement of Need + +Simulating dynamical systems is vital across disciplines. PathSim meets the need for a Python-native framework combining a programmatic block-diagram approach with advanced features. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's **decentralized architecture** offers distinct advantages: enhanced **modularity** (blocks are self-contained units), easier **extensibility** (new blocks integrate naturally without core modification), and greater **flexibility** in model composition and analysis. PathSim specifically addresses: + +* **Accessible Hybrid System Simulation:** Integrates event detection (zero-crossing, scheduled) directly into the block-diagram paradigm, simplifying the modeling of systems with both continuous and discrete dynamics. +* **Gradient-Enabled Simulation:** Provides built-in automatic differentiation, facilitating sensitivity analysis and integration with gradient-based optimization or machine learning frameworks. +* **Unified Framework for Diverse Dynamics:** Offers a wide range of solvers, including implicit methods (ESDIRK, BDF/GEAR) for stiff systems, within a single environment. +* **Extensibility in Python:** Leverages the scientific Python ecosystem with minimal dependencies. Its architecture allows straightforward creation and integration of custom blocks. + +PathSim provides a powerful, flexible, and extensible open-source tool for simulating complex dynamical systems in Python. + +# Architecture and Design + +PathSim employs a decentralized, object-oriented design centered around three primary components: + +1. **Blocks (`Block`):** Represent individual system components or operations. They encapsulate their parameters and, if stateful (like `Integrator` or `ODE`), manage their own internal state via a dedicated numerical integration engine (`engine`) instance. This contrasts with centralized approaches where a single solver manages all system states. Blocks define `update` methods for algebraic computations within a timestep and `step`/`solve` methods for interacting with their `engine` for state evolution. +2. **Connections (`Connection`):** Define the explicit data flow pathways between block output ports and input ports, mirroring the connections in a block diagram. +3. **Simulation (`Simulation`):** Coordinates the overall simulation process. It maintains the list of blocks and connections. During each time step, it manages a fixed-point iteration loop. In this loop, `Connection.update()` propagates output values to inputs, and `Block.update()` computes algebraic outputs based on current inputs and states. This iterative process resolves algebraic loops and ensures consistency across interconnected blocks. The `Simulation` object then triggers the `step` (for explicit solvers) or `solve` (for implicit solvers) methods of the blocks' engines to advance their internal states. It also manages the event handling system. + +This decentralized design promotes modularity, as blocks are largely self-contained. It simplifies adding new block types without altering the core simulation loop and provides flexibility in configuring individual block behaviors. + +# Example Usage: Harmonic Oscillator + +The following example demonstrates simulating a damped harmonic oscillator ($\ddot{x} + \frac{c}{m} \dot{x} + \frac{k}{m} x = 0$) using PathSim's block-based approach. + +```python + + +``` + +This example illustrates how the system's differential equation is translated into interconnected blocks, forming feedback loops. The Simulation object manages the execution and data recording via the Scope. + + +# References + diff --git a/src/pathsim/blocks/function.py b/src/pathsim/blocks/function.py index fae76bcf..33db3bd9 100644 --- a/src/pathsim/blocks/function.py +++ b/src/pathsim/blocks/function.py @@ -18,7 +18,6 @@ dict_to_array ) - from ..optim.operator import Operator From e8a58bf0c5ef567377a55d470fde82e985e664ba Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Wed, 23 Apr 2025 08:28:57 +0200 Subject: [PATCH 02/33] added draft-pdf.yml to github workflows --- .github/workflows/draft-pdf.yml | 24 ++++++++++++++++++++++++ paper/paper.md | 16 ++++++++-------- 2 files changed, 32 insertions(+), 8 deletions(-) create mode 100644 .github/workflows/draft-pdf.yml diff --git a/.github/workflows/draft-pdf.yml b/.github/workflows/draft-pdf.yml new file mode 100644 index 00000000..86457b03 --- /dev/null +++ b/.github/workflows/draft-pdf.yml @@ -0,0 +1,24 @@ +name: Draft PDF +on: + push: + paths: + - paper/** + - .github/workflows/draft-pdf.yml + +jobs: + paper: + runs-on: ubuntu-latest + name: Paper Draft + steps: + - name: Checkout + uses: actions/checkout@v4 + - name: Build draft PDF + uses: openjournals/openjournals-draft-action@master + with: + journal: joss + paper-path: paper/paper.md + - name: Upload + uses: actions/upload-artifact@v4 + with: + name: paper + path: paper/paper.pdf \ No newline at end of file diff --git a/paper/paper.md b/paper/paper.md index 99daa129..8205b136 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -12,23 +12,23 @@ tags: - scientific computing - numerical integration authors: - - name: Your Name Here # TODO: Add your name - orcid: 0000-0000-0000-0000 # TODO: Add your ORCID - affiliation: 1 # TODO: Add affiliation index + - name: Milan Rother + orcid: 0009-0006-5964-6115 + affiliation: 1 affiliations: - - name: "Your Affiliation Here (e.g., University, Institute, Company, or 'Independent Researcher')" # TODO: Define your affiliation + - name: University of Technology Braunschweig index: 1 -date: DD Month Iodide # TODO: Add submission date -bibliography: paper.bib # TODO: Create a paper.bib file for references +date: 23 april 2025 +bibliography: paper.bib --- # Summary -PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems using an object-oriented and **decentralized architecture**. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination via fixed-point iteration. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features like automatic differentiation for sensitivity analysis, discrete event handling for hybrid systems, automatic linearization, hierarchical subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries (`numpy`, `scipy`, `matplotlib`). +PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems using an object-oriented and decentralized architecture. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features like automatic differentiation for sensitivity analysis or gradient based optimization, discrete event handling for hybrid systems, automatic linearization, hierarchical subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries (`numpy`, `scipy`, `matplotlib`). # Statement of Need -Simulating dynamical systems is vital across disciplines. PathSim meets the need for a Python-native framework combining a programmatic block-diagram approach with advanced features. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's **decentralized architecture** offers distinct advantages: enhanced **modularity** (blocks are self-contained units), easier **extensibility** (new blocks integrate naturally without core modification), and greater **flexibility** in model composition and analysis. PathSim specifically addresses: +Simulating dynamical systems is vital across many disciplines. PathSim meets the need for a Python-native framework combining a programmatic block-diagram approach with advanced features. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), easier extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis. PathSim specifically addresses: * **Accessible Hybrid System Simulation:** Integrates event detection (zero-crossing, scheduled) directly into the block-diagram paradigm, simplifying the modeling of systems with both continuous and discrete dynamics. * **Gradient-Enabled Simulation:** Provides built-in automatic differentiation, facilitating sensitivity analysis and integration with gradient-based optimization or machine learning frameworks. From 45b02d3362c9ee0749025322a58eefc8a9764a68 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Wed, 23 Apr 2025 09:19:27 +0200 Subject: [PATCH 03/33] updated paper.md --- paper/paper.md | 117 +++++++++++++++++++++++++++++++++++++++++++++++-- 1 file changed, 114 insertions(+), 3 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 8205b136..a83f85f8 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -47,16 +47,127 @@ PathSim employs a decentralized, object-oriented design centered around three pr This decentralized design promotes modularity, as blocks are largely self-contained. It simplifies adding new block types without altering the core simulation loop and provides flexibility in configuring individual block behaviors. -# Example Usage: Harmonic Oscillator +# Example Usage -The following example demonstrates simulating a damped harmonic oscillator ($\ddot{x} + \frac{c}{m} \dot{x} + \frac{k}{m} x = 0$) using PathSim's block-based approach. +The following examples demonstrate PathSims core functionalities and features. + + +## Continuous Nonlinear Dynamics - Pendulum ```python +import numpy as np + +from pathsim import Simulation, Connection +from pathsim.blocks import Integrator, Amplifier, Function, Adder, Scope +from pathsim.solvers import RKBS32 + +#initial angle and angular velocity +phi0, omega0 = 0.9*np.pi, 0 + +#parameters (gravity, length) +g, l = 9.81, 1 + +#blocks that define the system +in1 = Integrator(omega0) +in2 = Integrator(phi0) +amp = Amplifier(-g/l) +fnc = Function(np.sin) +sco = Scope(labels=[r"$\omega$", r"$\varphi$"]) + +#connections between the blocks +connections = [ + Connection(in1, in2, sco[0]), + Connection(in2, fnc, sco[1]), + Connection(fnc, amp), + Connection(amp, in1) + ] + +#simulation instance from the blocks and connections +sim = Simulation( + blocks, + connections, + dt=0.1, + Solver=RKBS32, + tolerance_lte_rel=1e-6, + tolerance_lte_abs=1e-8 + ) + +#run the simulation for 15 seconds +sim.run(duration=15) + +#read the results directly from the scope +time, [omega, phi] = sco.read() + +#plot the results for quick visualization +sco.plot(".-") +sco.plot2D() +``` +## Stiff Systems and Subsystems - Van der Pol + +```python +from pathsim import Simulation, Connection, Interface, Subsystem +from pathsim.blocks import Integrator, Scope, Function +from pathsim.solvers import ESDIRK43 + +#initial conditions +x1_0, x2_0 = 2, 0 + +#van der Pol parameter +mu = 1000 + +#blocks that define the system +sco = Scope() + +#subsystem with two separate integrators to emulate ODE block +ifx = Interface() +in1 = Integrator(x1_0) +in2 = Integrator(x2_0) +fnc = Function(lambda x1, x2: mu*(1 - x1**2)*x2 - x1) + +sub_blocks = [ifx, in1, in2, fnc] +sub_connections = [ + Connection(in2, in1, fnc[1], ifx[1]), + Connection(in1, fnc, ifx), + Connection(fnx, in2) + ] + +#the subsystem acts just like a normal block +vdp = Subsystem(sub_blocks, sub_connections) + +#blocks of the main system +blocks = [vdp, sco] + +#the connections between the blocks in the main system +connections = [ + Connection(vdp, sco) + ] + +#initialize simulation with the blocks and connections +sim = Simulation( + blocks, + connections, + Solver=ESDIRK43, + tolerance_lte_abs=1e-6, + tolerance_lte_rel=1e-3, + tolerance_fpi=1e-9 + ) + +#run the simulation +sim.run(3*mu) + +#quickly visualize the results +sco.plot(".-") ``` -This example illustrates how the system's differential equation is translated into interconnected blocks, forming feedback loops. The Simulation object manages the execution and data recording via the Scope. + +## Event Handling - Bouncing Ball + + +## Sensitivity Analysis - PID Controler + + # References From dacf6b9604896f4a94c55b602b6e4384451d64ea Mon Sep 17 00:00:00 2001 From: milanofthe Date: Wed, 23 Apr 2025 13:46:20 +0200 Subject: [PATCH 04/33] added paper.bib and updated paper.md --- paper/paper.bib | 144 ++++++++++++++++++++++++++++++++++++++++++++++++ paper/paper.md | 113 ++++++++----------------------------- 2 files changed, 166 insertions(+), 91 deletions(-) create mode 100644 paper/paper.bib diff --git a/paper/paper.bib b/paper/paper.bib new file mode 100644 index 00000000..a74ab34d --- /dev/null +++ b/paper/paper.bib @@ -0,0 +1,144 @@ +@misc{PathSimRepo, + author = {Milan Rother}, + title = {PathSim - A System Simulation Framework}, + howpublished = {\url{https://github.com/milanofthe/pathsim}}, + month = {September}, + year = {2024}, + note = {Source Code Repository} +} + +@misc{PathSimDocs, + author = {Milan Rother}, + title = {PathSim - A System Simulation Framework}, + howpublished = {\url{https://pathsim.readthedocs.io/en/latest/}}, + month = {February}, + year = {2024}, + note = {Package Documentation} +} + +@misc{pycollimator, + author = {Collimator.ai}, + title = {Collimator.ai core simulation engine and API client}, + howpublished = {\url{https://pypi.org/project/pycollimator/}}, + month = {August}, + year = {2022}, + note = {Package Distribution on PyPi} +} + +@software{PathSimZenodo, + author = {Milan Rother}, + title = {PathSim - A System Simulation Framework}, + month = {April}, + year = {2025}, + publisher = {Zenodo}, + version = {v0.6.6}, + doi = {10.5281/zenodo.14992799}, + url = {https://doi.org/10.5281/zenodo.14992799} +} + +@misc{bdsimRepo, + author = {Peter Corke}, + title = {bdsim: Simulate dynamic systems expressed in block diagram form using Python}, + howpublished = {\url{https://github.com/petercorke/bdsim}}, + month = {May}, + year = {2020}, + note = {Source Code Repository} +} + +@misc{SimuPyRepo, + author = {Benjamin W. l. Margolis}, + title = {SimuPy: A framework for modeling and simulating dynamical systems}, + howpublished = {\url{https://github.com/simupy/simupy}}, + month = {September}, + year = {2017}, + note = {Source Code Repository} +} + +@article{Margolis2017, + doi = {10.21105/joss.00396}, + url = {https://doi.org/10.21105/joss.00396}, + year = {2017}, + publisher = {The Open Journal}, + volume = {2}, + number = {17}, + pages = {396}, + author = {Benjamin W. l. Margolis}, + title = {SimuPy: A Python framework for modeling and simulating dynamical systems}, + journal = {Journal of Open Source Software} + } + +@software{Simulink, + author = {{The MathWorks, Inc.}}, + title = {Simulink - Simulation and model-based design}, + url = {https://www.mathworks.com/products/simulink.html} +} + +@software{Matlab, + author = {{The MathWorks, Inc.}}, + title = {Matlab - The language of technical computing}, + url = {https://www.mathworks.com/products/matlab.html} +} + +@ARTICLE{virtanen2020scipy, + author = {Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and + Haberland, Matt and Reddy, Tyler and Cournapeau, David and + Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and + Bright, Jonathan and {van der Walt}, St{\'e}fan J. and + Brett, Matthew and Wilson, Joshua and Millman, K. Jarrod and + Mayorov, Nikolay and Nelson, Andrew R. J. and Jones, Eric and + Kern, Robert and Larson, Eric and Carey, C J and + Polat, {\.I}lhan and Feng, Yu and Moore, Eric W. and + {VanderPlas}, Jake and Laxalde, Denis and Perktold, Josef and + Cimrman, Robert and Henriksen, Ian and Quintero, E. A. and + Harris, Charles R. and Archibald, Anne M. and + Ribeiro, Ant{\^o}nio H. and Pedregosa, Fabian and + {van Mulbregt}, Paul and {SciPy 1.0 Contributors}}, + title = {{{SciPy} 1.0: Fundamental Algorithms for Scientific + Computing in Python}}, + journal = {Nature Methods}, + year = {2020}, + volume = {17}, + pages = {261--272}, + adsurl = {https://rdcu.be/b08Wh}, + doi = {10.1038/s41592-019-0686-2}, +} + + +@Article{hunter2007matplotlib, + Author = {Hunter, J. D.}, + Title = {Matplotlib: A 2D graphics environment}, + Journal = {Computing in Science \& Engineering}, + Volume = {9}, + Number = {3}, + Pages = {90--95}, + abstract = {Matplotlib is a 2D graphics package used for Python for + application development, interactive scripting, and publication-quality + image generation across user interfaces and operating systems.}, + publisher = {IEEE COMPUTER SOC}, + doi = {10.1109/MCSE.2007.55}, + year = 2007 +} + + +@Article{harris2020array, + title = {Array programming with {NumPy}}, + author = {Charles R. Harris and K. Jarrod Millman and St{\'{e}}fan J. + van der Walt and Ralf Gommers and Pauli Virtanen and David + Cournapeau and Eric Wieser and Julian Taylor and Sebastian + Berg and Nathaniel J. Smith and Robert Kern and Matti Picus + and Stephan Hoyer and Marten H. van Kerkwijk and Matthew + Brett and Allan Haldane and Jaime Fern{\'{a}}ndez del + R{\'{i}}o and Mark Wiebe and Pearu Peterson and Pierre + G{\'{e}}rard-Marchant and Kevin Sheppard and Tyler Reddy and + Warren Weckesser and Hameer Abbasi and Christoph Gohlke and + Travis E. Oliphant}, + year = {2020}, + month = sep, + journal = {Nature}, + volume = {585}, + number = {7825}, + pages = {357--362}, + doi = {10.1038/s41586-020-2649-2}, + publisher = {Springer Science and Business Media {LLC}}, + url = {https://doi.org/10.1038/s41586-020-2649-2} +} diff --git a/paper/paper.md b/paper/paper.md index a83f85f8..55a1d296 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -24,18 +24,22 @@ bibliography: paper.bib # Summary -PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems using an object-oriented and decentralized architecture. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features like automatic differentiation for sensitivity analysis or gradient based optimization, discrete event handling for hybrid systems, automatic linearization, hierarchical subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries (`numpy`, `scipy`, `matplotlib`). +PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems using an object-oriented and decentralized architecture. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features like automatic differentiation for sensitivity analysis or gradient based optimization, discrete event handling for hybrid systems, automatic linearization, hierarchical subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries: NumPy [@harris2020array], SciPy [@virtanen2020scipy], and Matplotlib [@hunter2007matplotlib]. # Statement of Need -Simulating dynamical systems is vital across many disciplines. PathSim meets the need for a Python-native framework combining a programmatic block-diagram approach with advanced features. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), easier extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis. PathSim specifically addresses: +Simulating dynamical systems is vital across many disciplines. PathSim meets the need for a Python-native framework combining a programmatic block-diagram approach with advanced features. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), easier extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis, Cosimulation and Hardware in the Loop (HiL) testing. PathSim specifically addresses: -* **Accessible Hybrid System Simulation:** Integrates event detection (zero-crossing, scheduled) directly into the block-diagram paradigm, simplifying the modeling of systems with both continuous and discrete dynamics. -* **Gradient-Enabled Simulation:** Provides built-in automatic differentiation, facilitating sensitivity analysis and integration with gradient-based optimization or machine learning frameworks. -* **Unified Framework for Diverse Dynamics:** Offers a wide range of solvers, including implicit methods (ESDIRK, BDF/GEAR) for stiff systems, within a single environment. +* **Accessible Hybrid System Simulation:** Integrates event detection (zero-crossing, scheduled) directly into the block-diagram paradigm, simplifying the modeling of systems with both *continuous and discrete dynamics*. +* **Gradient-Enabled Simulation:** Provides built-in *automatic differentiation* for sensitivity analysis and integration with gradient-based optimization or machine learning frameworks. +* **Unified Framework for Diverse Dynamics:** Offers a wide range of solvers, including implicit methods (ESDIRK, BDF/GEAR) for *stiff systems*. * **Extensibility in Python:** Leverages the scientific Python ecosystem with minimal dependencies. Its architecture allows straightforward creation and integration of custom blocks. -PathSim provides a powerful, flexible, and extensible open-source tool for simulating complex dynamical systems in Python. +PathSim provides a powerful, flexible, and extensible open-source tool for simulating complex dynamical systems with minimal dependencies in Python. + +# Comparison to Existing Tools + +Several Python tools exist for simulating dynamical systems. Standard ODE solvers like `scipy.integrate.solve_ivp` [@virtanen2020scipy] offer robust integration but lack a structured framework for modeling complex, interconnected systems or handling discrete events natively. Libraries like `SimuPy` [@Margolis2017; @SimuPyRepo] provide a block-based modeling approach similar to PathSim, leveraging SymPy for symbolic definition and SciPy solvers for integration. Other frameworks like `Collimator` [@pycollimator] offer graphical interfaces and JAX-based acceleration but introduce dependencies beyond the standard scientific Python stack. `bdsim` [@bdsimRepo] also provides block diagram simulation with a graphical editor, focusing often on robotics. PathSim differentiates itself by offering a purely script-based block-diagram interface with a *decentralized architecture*, *native integration* of both automatic differentiation and discrete event handling, and a *built-in library* of independently implemented and verified ODE solvers (beyond wrapping SciPy), all while maintaining *minimal core dependencies*. # Architecture and Design @@ -45,14 +49,11 @@ PathSim employs a decentralized, object-oriented design centered around three pr 2. **Connections (`Connection`):** Define the explicit data flow pathways between block output ports and input ports, mirroring the connections in a block diagram. 3. **Simulation (`Simulation`):** Coordinates the overall simulation process. It maintains the list of blocks and connections. During each time step, it manages a fixed-point iteration loop. In this loop, `Connection.update()` propagates output values to inputs, and `Block.update()` computes algebraic outputs based on current inputs and states. This iterative process resolves algebraic loops and ensures consistency across interconnected blocks. The `Simulation` object then triggers the `step` (for explicit solvers) or `solve` (for implicit solvers) methods of the blocks' engines to advance their internal states. It also manages the event handling system. -This decentralized design promotes modularity, as blocks are largely self-contained. It simplifies adding new block types without altering the core simulation loop and provides flexibility in configuring individual block behaviors. +This decentralized design promotes modularity, as blocks are fully self-contained. It simplifies adding new block types without altering the core simulation loop and provides flexibility in configuring individual block behaviors. Additionaly this opens up integration with other simulation environments, or hardware in the loop (HiL) setups through encapsulation within blocks. # Example Usage -The following examples demonstrate PathSims core functionalities and features. - - -## Continuous Nonlinear Dynamics - Pendulum +The following example of a nonlinear pendulum demonstrate PathSims core system modeling and simulation flow. ```python import numpy as np @@ -74,28 +75,22 @@ amp = Amplifier(-g/l) fnc = Function(np.sin) sco = Scope(labels=[r"$\omega$", r"$\varphi$"]) -#connections between the blocks -connections = [ - Connection(in1, in2, sco[0]), - Connection(in2, fnc, sco[1]), - Connection(fnc, amp), - Connection(amp, in1) - ] - #simulation instance from the blocks and connections sim = Simulation( - blocks, - connections, - dt=0.1, - Solver=RKBS32, - tolerance_lte_rel=1e-6, - tolerance_lte_abs=1e-8 + blocks=[in1, in2, amp, fnc, sco], + connections=[ + Connection(in1, in2, sco[0]), + Connection(in2, fnc, sco[1]), + Connection(fnc, amp), + Connection(amp, in1) + ], + Solver=RKBS32 ) #run the simulation for 15 seconds sim.run(duration=15) -#read the results directly from the scope +#read the results directly from the scope for postprocessing time, [omega, phi] = sco.read() #plot the results for quick visualization @@ -103,71 +98,7 @@ sco.plot(".-") sco.plot2D() ``` - -## Stiff Systems and Subsystems - Van der Pol - -```python -from pathsim import Simulation, Connection, Interface, Subsystem -from pathsim.blocks import Integrator, Scope, Function -from pathsim.solvers import ESDIRK43 - -#initial conditions -x1_0, x2_0 = 2, 0 - -#van der Pol parameter -mu = 1000 - -#blocks that define the system -sco = Scope() - -#subsystem with two separate integrators to emulate ODE block -ifx = Interface() -in1 = Integrator(x1_0) -in2 = Integrator(x2_0) -fnc = Function(lambda x1, x2: mu*(1 - x1**2)*x2 - x1) - -sub_blocks = [ifx, in1, in2, fnc] -sub_connections = [ - Connection(in2, in1, fnc[1], ifx[1]), - Connection(in1, fnc, ifx), - Connection(fnx, in2) - ] - -#the subsystem acts just like a normal block -vdp = Subsystem(sub_blocks, sub_connections) - -#blocks of the main system -blocks = [vdp, sco] - -#the connections between the blocks in the main system -connections = [ - Connection(vdp, sco) - ] - -#initialize simulation with the blocks and connections -sim = Simulation( - blocks, - connections, - Solver=ESDIRK43, - tolerance_lte_abs=1e-6, - tolerance_lte_rel=1e-3, - tolerance_fpi=1e-9 - ) - -#run the simulation -sim.run(3*mu) - -#quickly visualize the results -sco.plot(".-") -``` - - -## Event Handling - Bouncing Ball - - -## Sensitivity Analysis - PID Controler - - +This code shows block instantiation, connection definition, simulation setup (including solver selection), execution, and result visualization. Full examples demonstrating event handling, stiff systems, and sensitivity analysis are available in the software repository [@PathSimRepo] and documentation [@PathSimDocs]. # References From b84e1545c5bb611d592176e7dc5a8bd23917829a Mon Sep 17 00:00:00 2001 From: milanofthe Date: Wed, 23 Apr 2025 14:18:55 +0200 Subject: [PATCH 05/33] adding figures to paper --- paper/assets/pendulum_block_diagram.svg | 1 + paper/assets/pendulum_result_phasespace.svg | 583 ++++++++ paper/assets/pendulum_result_timeseries.svg | 1313 +++++++++++++++++++ paper/paper.md | 14 +- 4 files changed, 1907 insertions(+), 4 deletions(-) create mode 100644 paper/assets/pendulum_block_diagram.svg create mode 100644 paper/assets/pendulum_result_phasespace.svg create mode 100644 paper/assets/pendulum_result_timeseries.svg diff --git a/paper/assets/pendulum_block_diagram.svg b/paper/assets/pendulum_block_diagram.svg new file mode 100644 index 00000000..b72919b9 --- /dev/null +++ b/paper/assets/pendulum_block_diagram.svg @@ -0,0 +1 @@ +ScopeIntegrator 1ω0Integrator 2φ0φ(t)ω(t)lφ0gFunctionsinAmpg/l \ No newline at end of file diff --git a/paper/assets/pendulum_result_phasespace.svg b/paper/assets/pendulum_result_phasespace.svg new file mode 100644 index 00000000..109845f9 --- /dev/null +++ b/paper/assets/pendulum_result_phasespace.svg @@ -0,0 +1,583 @@ + + + + + + + + 2025-04-23T13:59:18.992063 + image/svg+xml + + + Matplotlib v3.8.3, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/paper/assets/pendulum_result_timeseries.svg b/paper/assets/pendulum_result_timeseries.svg new file mode 100644 index 00000000..a5b10f53 --- /dev/null +++ b/paper/assets/pendulum_result_timeseries.svg @@ -0,0 +1,1313 @@ + + + + + + + + 2025-04-23T13:59:26.295443 + image/svg+xml + + + Matplotlib v3.8.3, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/paper/paper.md b/paper/paper.md index 55a1d296..5c4c6d2f 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -16,7 +16,7 @@ authors: orcid: 0009-0006-5964-6115 affiliation: 1 affiliations: - - name: University of Technology Braunschweig + - name: Technische Universität Braunschweig index: 1 date: 23 april 2025 bibliography: paper.bib @@ -49,18 +49,20 @@ PathSim employs a decentralized, object-oriented design centered around three pr 2. **Connections (`Connection`):** Define the explicit data flow pathways between block output ports and input ports, mirroring the connections in a block diagram. 3. **Simulation (`Simulation`):** Coordinates the overall simulation process. It maintains the list of blocks and connections. During each time step, it manages a fixed-point iteration loop. In this loop, `Connection.update()` propagates output values to inputs, and `Block.update()` computes algebraic outputs based on current inputs and states. This iterative process resolves algebraic loops and ensures consistency across interconnected blocks. The `Simulation` object then triggers the `step` (for explicit solvers) or `solve` (for implicit solvers) methods of the blocks' engines to advance their internal states. It also manages the event handling system. -This decentralized design promotes modularity, as blocks are fully self-contained. It simplifies adding new block types without altering the core simulation loop and provides flexibility in configuring individual block behaviors. Additionaly this opens up integration with other simulation environments, or hardware in the loop (HiL) setups through encapsulation within blocks. +The decentralized design promotes modularity, as blocks are fully self-contained. It simplifies adding new block types without altering the core simulation loop and provides flexibility in configuring individual block behaviors. Additionaly this opens up integration with other simulation environments (co-simulation), or hardware in the loop (HiL) setups through encapsulation within blocks. # Example Usage The following example of a nonlinear pendulum demonstrate PathSims core system modeling and simulation flow. +![Mechanical model and block diagram of nonlinear pendulum.](assets/pendulum_block_diagram.svg) + ```python import numpy as np from pathsim import Simulation, Connection from pathsim.blocks import Integrator, Amplifier, Function, Adder, Scope -from pathsim.solvers import RKBS32 +from pathsim.solvers import RKCK54 #initial angle and angular velocity phi0, omega0 = 0.9*np.pi, 0 @@ -84,7 +86,9 @@ sim = Simulation( Connection(fnc, amp), Connection(amp, in1) ], - Solver=RKBS32 + Solver=RKCK54, + tolerance_lte_rel=1e-6, + tolerance_lte_abs=1e-8 ) #run the simulation for 15 seconds @@ -98,6 +102,8 @@ sco.plot(".-") sco.plot2D() ``` +![Time series results from `Scope.plot()` ](assets/pendulum_result_timeseries.svg) ![2D phase portrait from `Scope.plot2D()`](assets/pendulum_result_phasespace.svg) + This code shows block instantiation, connection definition, simulation setup (including solver selection), execution, and result visualization. Full examples demonstrating event handling, stiff systems, and sensitivity analysis are available in the software repository [@PathSimRepo] and documentation [@PathSimDocs]. From bcfc7e46f0f91bbc24d9517eabeae7ef9e5159f9 Mon Sep 17 00:00:00 2001 From: milanofthe Date: Wed, 23 Apr 2025 14:52:48 +0200 Subject: [PATCH 06/33] updated paper title --- paper/paper.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 5c4c6d2f..1364ad91 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -1,5 +1,5 @@ --- -title: 'PathSim: A Decentralized Python Framework for Dynamical System Simulation' +title: 'PathSim - A Decentralized System Simulation Framework' tags: - Python - system simulation @@ -24,7 +24,7 @@ bibliography: paper.bib # Summary -PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems using an object-oriented and decentralized architecture. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features like automatic differentiation for sensitivity analysis or gradient based optimization, discrete event handling for hybrid systems, automatic linearization, hierarchical subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries: NumPy [@harris2020array], SciPy [@virtanen2020scipy], and Matplotlib [@hunter2007matplotlib]. +PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems using an object-oriented and decentralized architecture. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features i.e. automatic differentiation for sensitivity analysis or gradient based optimization, discrete event handling for hybrid systems, automatic system- or block-level linearization, hierarchical modeling through subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries: NumPy [@harris2020array], SciPy [@virtanen2020scipy], and Matplotlib [@hunter2007matplotlib]. # Statement of Need From 1ec2a0bc4098c1f219b67edb38c213f9bd221fc3 Mon Sep 17 00:00:00 2001 From: milanofthe Date: Wed, 23 Apr 2025 15:09:54 +0200 Subject: [PATCH 07/33] changed figure for paper to unified flow --- paper/assets/pathsim_flow.svg | 1 + paper/paper.md | 55 ++--------------------------------- 2 files changed, 4 insertions(+), 52 deletions(-) create mode 100644 paper/assets/pathsim_flow.svg diff --git a/paper/assets/pathsim_flow.svg b/paper/assets/pathsim_flow.svg new file mode 100644 index 00000000..3de67af9 --- /dev/null +++ b/paper/assets/pathsim_flow.svg @@ -0,0 +1 @@ +import numpy as np import matplotlib.pyplot as plt from pathsim import Simulation, Connection from pathsim.blocks import Integrator, Function, Amplifier, Scope from pathsim.solvers import RKCK54 #initial angle and angular velocity phi0, omega0 = 0.9*np.pi, 0 #parameters (gravity, length) g, l = 9.81, 1 #blocks that define the system in1 = Integrator(omega0) in2 = Integrator(phi0) amp = Amplifier(-g/l) fnc = Function(np.sin) sco = Scope(labels=[r"$\omega$", r"$\varphi$"]) #simulation instance from the blocks and connections sim = Simulation( blocks=[in1, in2, amp, fnc, sco], connections=[ Connection(in1, in2, sco[0]), Connection(in2, fnc, sco[1]), Connection(fnc, amp), Connection(amp, in1) ], Solver=RKCK54, tolerance_lte_rel=1e-6, tolerance_lte_abs=1e-8 ) #run the simulation for 15 seconds sim.run(15) #read the results directly from the scope for postprocessing time, [omega, phi] = sco.read() #plot the results for quick visualization sco.plot(".-") sco.plot2D() PathSimScopeIntegrator 1ω0Integrator 2φ0φ(t)ω(t)lφ0gFunctionsinAmpg/lto Block Diagramto PathSimResults \ No newline at end of file diff --git a/paper/paper.md b/paper/paper.md index 1364ad91..1d5b80b5 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -51,60 +51,11 @@ PathSim employs a decentralized, object-oriented design centered around three pr The decentralized design promotes modularity, as blocks are fully self-contained. It simplifies adding new block types without altering the core simulation loop and provides flexibility in configuring individual block behaviors. Additionaly this opens up integration with other simulation environments (co-simulation), or hardware in the loop (HiL) setups through encapsulation within blocks. -# Example Usage +# PathSim Modeling Flow -The following example of a nonlinear pendulum demonstrate PathSims core system modeling and simulation flow. +![Example dynamical system modeling flow using PathSim](assets/pathsim_flow.svg) -![Mechanical model and block diagram of nonlinear pendulum.](assets/pendulum_block_diagram.svg) - -```python -import numpy as np - -from pathsim import Simulation, Connection -from pathsim.blocks import Integrator, Amplifier, Function, Adder, Scope -from pathsim.solvers import RKCK54 - -#initial angle and angular velocity -phi0, omega0 = 0.9*np.pi, 0 - -#parameters (gravity, length) -g, l = 9.81, 1 - -#blocks that define the system -in1 = Integrator(omega0) -in2 = Integrator(phi0) -amp = Amplifier(-g/l) -fnc = Function(np.sin) -sco = Scope(labels=[r"$\omega$", r"$\varphi$"]) - -#simulation instance from the blocks and connections -sim = Simulation( - blocks=[in1, in2, amp, fnc, sco], - connections=[ - Connection(in1, in2, sco[0]), - Connection(in2, fnc, sco[1]), - Connection(fnc, amp), - Connection(amp, in1) - ], - Solver=RKCK54, - tolerance_lte_rel=1e-6, - tolerance_lte_abs=1e-8 - ) - -#run the simulation for 15 seconds -sim.run(duration=15) - -#read the results directly from the scope for postprocessing -time, [omega, phi] = sco.read() - -#plot the results for quick visualization -sco.plot(".-") -sco.plot2D() -``` - -![Time series results from `Scope.plot()` ](assets/pendulum_result_timeseries.svg) ![2D phase portrait from `Scope.plot2D()`](assets/pendulum_result_phasespace.svg) - -This code shows block instantiation, connection definition, simulation setup (including solver selection), execution, and result visualization. Full examples demonstrating event handling, stiff systems, and sensitivity analysis are available in the software repository [@PathSimRepo] and documentation [@PathSimDocs]. + # References From b4756522467a46d4c6bf2f791a8a4ee86062a449 Mon Sep 17 00:00:00 2001 From: milanofthe Date: Wed, 23 Apr 2025 15:15:13 +0200 Subject: [PATCH 08/33] updated paper figure --- paper/assets/pathsim_flow.png | Bin 0 -> 327660 bytes paper/assets/pathsim_flow.svg | 1 - paper/assets/pendulum_block_diagram.svg | 1 - paper/assets/pendulum_result_phasespace.svg | 583 -------- paper/assets/pendulum_result_timeseries.svg | 1313 ------------------- paper/paper.md | 2 +- 6 files changed, 1 insertion(+), 1899 deletions(-) create mode 100644 paper/assets/pathsim_flow.png delete mode 100644 paper/assets/pathsim_flow.svg delete mode 100644 paper/assets/pendulum_block_diagram.svg delete mode 100644 paper/assets/pendulum_result_phasespace.svg delete mode 100644 paper/assets/pendulum_result_timeseries.svg diff --git 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z2Z891EXm*NqGz0lPN;Df3i8VyM*AC-VzEGQx<&JNz|`Rf!aL@2v&#P+p$fE8NS4XW zYA7EFEE3**1#>wYxMfSIpGn>?j9m*~ zc|*SH7hvv?$OBbFF}ofC0Y|3&eU`3D(AA=85nJp5-ct48quN*j$b=xIW^~D$0nf4x z_?pNy^x<6r+4m1T=-p?Q%1v^JWIXbFacqL?yXtoAD$9y|Do6$D#lcjpQ{7X+@<3`) zUKPQxD&B(WJOAPJ0fO;^e+q(K5Cq`WbHq%+daj=P|MwShn5#H83A^U>CJn4934xq8 LKWA2Gg1G%}f%!)z From f9d0ee4cd2882489c04b809fe79d648f1b190abc Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Wed, 23 Apr 2025 17:36:00 +0200 Subject: [PATCH 13/33] updated paper.md and references --- paper/paper.bib | 41 ++++++++++++----------------------------- paper/paper.md | 5 +++-- 2 files changed, 15 insertions(+), 31 deletions(-) diff --git a/paper/paper.bib b/paper/paper.bib index a74ab34d..94fe4283 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -1,21 +1,3 @@ -@misc{PathSimRepo, - author = {Milan Rother}, - title = {PathSim - A System Simulation Framework}, - howpublished = {\url{https://github.com/milanofthe/pathsim}}, - month = {September}, - year = {2024}, - note = {Source Code Repository} -} - -@misc{PathSimDocs, - author = {Milan Rother}, - title = {PathSim - A System Simulation Framework}, - howpublished = {\url{https://pathsim.readthedocs.io/en/latest/}}, - month = {February}, - year = {2024}, - note = {Package Documentation} -} - @misc{pycollimator, author = {Collimator.ai}, title = {Collimator.ai core simulation engine and API client}, @@ -25,17 +7,6 @@ @misc{pycollimator note = {Package Distribution on PyPi} } -@software{PathSimZenodo, - author = {Milan Rother}, - title = {PathSim - A System Simulation Framework}, - month = {April}, - year = {2025}, - publisher = {Zenodo}, - version = {v0.6.6}, - doi = {10.5281/zenodo.14992799}, - url = {https://doi.org/10.5281/zenodo.14992799} -} - @misc{bdsimRepo, author = {Peter Corke}, title = {bdsim: Simulate dynamic systems expressed in block diagram form using Python}, @@ -142,3 +113,15 @@ @Article{harris2020array publisher = {Springer Science and Business Media {LLC}}, url = {https://doi.org/10.1038/s41586-020-2649-2} } + + +@INPROCEEDINGS{pythoncontrol, + author={Fuller, Sawyer and Greiner, Ben and Moore, Jason and Murray, Richard and van Paassen, René and Yorke, Rory}, + booktitle={2021 60th IEEE Conference on Decision and Control (CDC)}, + title={The Python Control Systems Library (python-control)}, + year={2021}, + volume={}, + number={}, + pages={4875-4881}, + keywords={Machine learning;Software systems;Libraries;Stability analysis;Robustness;Time factors;Standards}, + doi={10.1109/CDC45484.2021.9683368}} diff --git a/paper/paper.md b/paper/paper.md index 1166a43a..f98ebf5c 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -39,7 +39,9 @@ PathSim provides a powerful, flexible, and extensible open-source tool for simul # Comparison to Existing Tools -Several Python tools exist for simulating dynamical systems. Standard ODE solvers like `scipy.integrate.solve_ivp` [@virtanen2020scipy] offer robust integration but lack a structured framework for modeling complex, interconnected systems or handling discrete events natively. Libraries like `SimuPy` [@Margolis2017; @SimuPyRepo] provide a block-based modeling approach similar to PathSim, leveraging SymPy for symbolic definition and SciPy solvers for integration. Other frameworks like `Collimator` [@pycollimator] offer graphical interfaces and JAX-based acceleration but introduce dependencies beyond the standard scientific Python stack. `bdsim` [@bdsimRepo] also provides block diagram simulation with a graphical editor, focusing often on robotics. PathSim differentiates itself by offering a purely script-based block-diagram interface with a *decentralized architecture*, *native integration* of both automatic differentiation and discrete event handling, and a *built-in library* of independently implemented and verified ODE solvers (beyond wrapping SciPy), all while maintaining *minimal core dependencies*. +Several Python tools exist for simulating dynamical systems. Standard ODE solvers like `scipy.integrate.solve_ivp` [@virtanen2020scipy] offer robust integration but lack a structured framework for modeling complex, interconnected systems or handling discrete events natively. The *Python Control Systems Library* [@pythoncontrol] is a popular package for modeling and optimizing dynamical systems from the control engineering perspective primarily. Libraries like `SimuPy` [@Margolis2017; @SimuPyRepo] provide a block-based modeling approach similar to PathSim, leveraging SymPy for symbolic definition and SciPy solvers for integration. Other frameworks like `Collimator` [@pycollimator] offer graphical interfaces and JAX-based acceleration but require compilation and introduce dependencies beyond the standard scientific Python stack. `bdsim` [@bdsimRepo] also provides block diagram simulation, focusing on robotics. + +PathSim differentiates itself by offering a purely script-based block-diagram interface with a *decentralized architecture*, native integration of both *automatic differentiation* and *discrete event handling*, and a *built-in library* of independently implemented and verified ODE solvers (beyond wrapping SciPy), all while maintaining *minimal core dependencies*. # Architecture and Design @@ -57,7 +59,6 @@ The figure below shows the modeling and simulation flow with PathSim. Once the d ![Exemplary dynamical system modeling and simulation flow using PathSim](assets/pathsim_flow.png) -Full examples demonstrating event handling, stiff systems, and sensitivity analysis are available in the software repository [@PathSimRepo] and documentation [@PathSimDocs]. # References From 8511081625c270301e2fb8ab70f64b8a1c82f853 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Wed, 23 Apr 2025 17:38:22 +0200 Subject: [PATCH 14/33] updated paper.md --- paper/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index f98ebf5c..4818e8c2 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -24,7 +24,7 @@ bibliography: paper.bib # Summary -PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems using an object-oriented and decentralized architecture. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features i.e. automatic differentiation for sensitivity analysis or gradient based optimization, discrete event handling for hybrid systems, automatic system- or block-level linearization, hierarchical modeling through subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries: NumPy [@harris2020array], SciPy [@virtanen2020scipy], and Matplotlib [@hunter2007matplotlib]. +PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems, similar to Matlab Simulink [@Matlab; @Simulink] using an object-oriented and decentralized architecture. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features i.e. automatic differentiation for sensitivity analysis or gradient based optimization, discrete event handling for hybrid systems, automatic system- or block-level linearization, hierarchical modeling through subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries: NumPy [@harris2020array], SciPy [@virtanen2020scipy], and Matplotlib [@hunter2007matplotlib]. # Statement of Need From 8fcd827cf4d4eb8fc295aca9b23169a922399cdc Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Wed, 23 Apr 2025 17:40:09 +0200 Subject: [PATCH 15/33] updated paper --- paper/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index 4818e8c2..d570e142 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -24,7 +24,7 @@ bibliography: paper.bib # Summary -PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems, similar to Matlab Simulink [@Matlab; @Simulink] using an object-oriented and decentralized architecture. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features i.e. automatic differentiation for sensitivity analysis or gradient based optimization, discrete event handling for hybrid systems, automatic system- or block-level linearization, hierarchical modeling through subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries: NumPy [@harris2020array], SciPy [@virtanen2020scipy], and Matplotlib [@hunter2007matplotlib]. +PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems, similar to Matlab Simulink [@Matlab; @Simulink] using an object-oriented and decentralized architecture. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features i.e. (forward mode) automatic differentiation for sensitivity analysis or gradient based optimization, discrete event handling for hybrid systems, automatic system- or block-level linearization, hierarchical modeling through subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries: NumPy [@harris2020array], SciPy [@virtanen2020scipy], and Matplotlib [@hunter2007matplotlib]. # Statement of Need From 588d93fd1caffc78e43d9a8491a9aa3bede2d499 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Wed, 23 Apr 2025 21:33:31 +0200 Subject: [PATCH 16/33] fixed capital P for Python in paper.bib, added country to affiliation in paper.md --- paper/paper.bib | 10 +++++----- paper/paper.md | 6 ++++-- 2 files changed, 9 insertions(+), 7 deletions(-) diff --git a/paper/paper.bib b/paper/paper.bib index 94fe4283..fdec1305 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -9,7 +9,7 @@ @misc{pycollimator @misc{bdsimRepo, author = {Peter Corke}, - title = {bdsim: Simulate dynamic systems expressed in block diagram form using Python}, + title = {bdsim: Simulate dynamic systems expressed in block diagram form using {P}ython}, howpublished = {\url{https://github.com/petercorke/bdsim}}, month = {May}, year = {2020}, @@ -34,7 +34,7 @@ @article{Margolis2017 number = {17}, pages = {396}, author = {Benjamin W. l. Margolis}, - title = {SimuPy: A Python framework for modeling and simulating dynamical systems}, + title = {SimuPy: A {P}ython framework for modeling and simulating dynamical systems}, journal = {Journal of Open Source Software} } @@ -65,7 +65,7 @@ @ARTICLE{virtanen2020scipy Ribeiro, Ant{\^o}nio H. and Pedregosa, Fabian and {van Mulbregt}, Paul and {SciPy 1.0 Contributors}}, title = {{{SciPy} 1.0: Fundamental Algorithms for Scientific - Computing in Python}}, + Computing in {P}ython}}, journal = {Nature Methods}, year = {2020}, volume = {17}, @@ -82,7 +82,7 @@ @Article{hunter2007matplotlib Volume = {9}, Number = {3}, Pages = {90--95}, - abstract = {Matplotlib is a 2D graphics package used for Python for + abstract = {Matplotlib is a 2D graphics package used for {P}ython for application development, interactive scripting, and publication-quality image generation across user interfaces and operating systems.}, publisher = {IEEE COMPUTER SOC}, @@ -118,7 +118,7 @@ @Article{harris2020array @INPROCEEDINGS{pythoncontrol, author={Fuller, Sawyer and Greiner, Ben and Moore, Jason and Murray, Richard and van Paassen, René and Yorke, Rory}, booktitle={2021 60th IEEE Conference on Decision and Control (CDC)}, - title={The Python Control Systems Library (python-control)}, + title={The {P}ython {C}ontrol {S}ystems {L}ibrary (python-control)}, year={2021}, volume={}, number={}, diff --git a/paper/paper.md b/paper/paper.md index d570e142..63afe0d6 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -16,7 +16,7 @@ authors: orcid: 0009-0006-5964-6115 affiliation: 1 affiliations: - - name: Technische Universität Braunschweig + - name: Technische Universität Braunschweig, Germany index: 1 date: 23 april 2025 bibliography: paper.bib @@ -28,7 +28,9 @@ PathSim is a flexible, block-based, time-domain dynamical system simulation fram # Statement of Need -Modeling and simulating dynamical systems is vital across many disciplines. PathSim meets the need for a Python-native framework combining a programmatic block-diagram approach with advanced features. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), easier extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis, Cosimulation and Hardware in the Loop (HiL) testing. PathSim specifically addresses: +Modeling and simulating dynamical systems is vital across many disciplines such as control engineering, chemical process engineering, or general system engineering. Challenges are often the interplay of multiple *coupled* subsystems which have to be simulated and synchronized concurrently. + +PathSim meets the need for a Python-native framework combining a programmatic block-diagram approach with advanced features. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), easier extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis, Cosimulation and Hardware in the Loop (HiL) testing. PathSim specifically addresses: * **Accessible Hybrid System Simulation:** Integrates event detection (zero-crossing, scheduled) directly into the block-diagram paradigm, simplifying the modeling of systems with both *continuous and discrete dynamics*. * **Gradient-Enabled Simulation:** Provides built-in *automatic differentiation* for sensitivity analysis and integration with gradient-based optimization or machine learning frameworks. From 916e74b84eac7d8f67a62afca2473fbdda8060b1 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Wed, 23 Apr 2025 21:40:48 +0200 Subject: [PATCH 17/33] edited Statement of Need to be more detailed and explicit about use cases --- paper/paper.md | 12 +++++------- 1 file changed, 5 insertions(+), 7 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 63afe0d6..d6a600a0 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -28,22 +28,22 @@ PathSim is a flexible, block-based, time-domain dynamical system simulation fram # Statement of Need -Modeling and simulating dynamical systems is vital across many disciplines such as control engineering, chemical process engineering, or general system engineering. Challenges are often the interplay of multiple *coupled* subsystems which have to be simulated and synchronized concurrently. +Modeling and simulating dynamical systems is vital across many disciplines such as control engineering, chemical process engineering, or mixed signal engineering. Challenges are often the interplay of multiple *coupled* subsystems with their distinct dynamics and behaviors which have to be solved and synchronized concurrently to advance the full system simulation. -PathSim meets the need for a Python-native framework combining a programmatic block-diagram approach with advanced features. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), easier extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis, Cosimulation and Hardware in the Loop (HiL) testing. PathSim specifically addresses: +PathSim meets the need for a simulation framework in the block-diagram paradigm, which integrates seemlessly into the Python ecosystem. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), easier extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis. Additionaly this opens up integration with other simulation environments (co-simulation) and hardware in the loop (HiL) setups through encapsulation within blocks, as well as integration into machine-learning pipelines. + +Specifically PathSim offers: * **Accessible Hybrid System Simulation:** Integrates event detection (zero-crossing, scheduled) directly into the block-diagram paradigm, simplifying the modeling of systems with both *continuous and discrete dynamics*. * **Gradient-Enabled Simulation:** Provides built-in *automatic differentiation* for sensitivity analysis and integration with gradient-based optimization or machine learning frameworks. * **Unified Framework for Diverse Dynamics:** Offers a wide range of solvers, including implicit methods (ESDIRK, BDF/GEAR) for *stiff systems*. * **Extensibility in Python:** Leverages the scientific Python ecosystem with minimal dependencies. Its architecture allows straightforward creation and integration of custom blocks. -PathSim provides a powerful, flexible, and extensible open-source tool for simulating complex dynamical systems with minimal dependencies in Python. - # Comparison to Existing Tools Several Python tools exist for simulating dynamical systems. Standard ODE solvers like `scipy.integrate.solve_ivp` [@virtanen2020scipy] offer robust integration but lack a structured framework for modeling complex, interconnected systems or handling discrete events natively. The *Python Control Systems Library* [@pythoncontrol] is a popular package for modeling and optimizing dynamical systems from the control engineering perspective primarily. Libraries like `SimuPy` [@Margolis2017; @SimuPyRepo] provide a block-based modeling approach similar to PathSim, leveraging SymPy for symbolic definition and SciPy solvers for integration. Other frameworks like `Collimator` [@pycollimator] offer graphical interfaces and JAX-based acceleration but require compilation and introduce dependencies beyond the standard scientific Python stack. `bdsim` [@bdsimRepo] also provides block diagram simulation, focusing on robotics. -PathSim differentiates itself by offering a purely script-based block-diagram interface with a *decentralized architecture*, native integration of both *automatic differentiation* and *discrete event handling*, and a *built-in library* of independently implemented and verified ODE solvers (beyond wrapping SciPy), all while maintaining *minimal core dependencies*. +PathSim differentiates itself by offering a script-based block-diagram interface with a *decentralized architecture*, native integration of both *automatic differentiation* and *discrete event handling* into the full simulation loop, and a *built-in library* of independently implemented and verified ODE solvers (beyond wrapping SciPy), all while maintaining *minimal core dependencies*. # Architecture and Design @@ -53,8 +53,6 @@ PathSim employs a decentralized, object-oriented design centered around three pr 2. **Connections (`Connection`):** Define the explicit data flow pathways between block output ports and input ports, mirroring the connections in a block diagram. 3. **Simulation (`Simulation`):** Coordinates the overall simulation process. It maintains the list of blocks and connections. During each time step, it manages a fixed-point iteration loop. In this loop, `Connection.update()` propagates output values to inputs, and `Block.update()` computes algebraic outputs based on current inputs and states. This iterative process resolves algebraic loops and ensures consistency across interconnected blocks. The `Simulation` object then triggers the `step` (for explicit solvers) or `solve` (for implicit solvers) methods of the blocks' engines to advance their internal states. It also manages the event handling system. -The decentralized design promotes modularity, as blocks are fully self-contained. It simplifies adding new block types without altering the core simulation loop and provides flexibility in configuring individual block behaviors. Additionaly this opens up integration with other simulation environments (co-simulation), or hardware in the loop (HiL) setups through encapsulation within blocks. - # PathSim Modeling Flow The figure below shows the modeling and simulation flow with PathSim. Once the dynamical system is translated to the block-diagram paradigm, it can be built from PathSim blocks and connections. The code to the right shows block instantiation, connection definition, simulation setup (including solver and tolerance selection), execution, and result visualization. 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It enables the modeling and simulation of complex interconnected systems, similar to Matlab Simulink [@Matlab; @Simulink] using an object-oriented and decentralized architecture. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features i.e. (forward mode) automatic differentiation for sensitivity analysis or gradient based optimization, discrete event handling for hybrid systems, automatic system- or block-level linearization, hierarchical modeling through subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries: NumPy [@harris2020array], SciPy [@virtanen2020scipy], and Matplotlib [@hunter2007matplotlib]. +PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems from their signal flow graphs, similar to Mathworks Simulink [@Simulink] using an object-oriented and decentralized architecture. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features i.e. (forward mode) automatic differentiation for sensitivity analysis or gradient based optimization, discrete event handling for hybrid systems, automatic system- or block-level linearization, hierarchical modeling through subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries: NumPy [@harris2020array], SciPy [@virtanen2020scipy], and Matplotlib [@hunter2007matplotlib]. # Statement of Need -Modeling and simulating dynamical systems is vital across many disciplines such as control engineering, chemical process engineering, or mixed signal engineering. Challenges are often the interplay of multiple *coupled* subsystems with their distinct dynamics and behaviors which have to be solved and synchronized concurrently to advance the full system simulation. +Modeling and simulating dynamical systems is vital across many disciplines such as control engineering, chemical process engineering, and mixed signal engineering. Challenges are often the interplay of multiple *coupled* subsystems with their distinct dynamics and behaviors which have to be solved and synchronized concurrently to advance the full system simulation. -PathSim meets the need for a simulation framework in the block-diagram paradigm, which integrates seemlessly into the Python ecosystem. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), easier extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis. Additionaly this opens up integration with other simulation environments (co-simulation) and hardware in the loop (HiL) setups through encapsulation within blocks, as well as integration into machine-learning pipelines. +PathSim meets the need for an open source simulation framework in the block-diagram paradigm with minimal dependencies, which integrates seamlessly into the Python ecosystem. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), easier extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis. Additionaly this opens up block level solver optimizations, integration with other simulation environments (co-simulation) and hardware in the loop (HiL) setups through encapsulation within blocks, as well as integration into machine-learning pipelines. Specifically PathSim offers: +* **Open Source Alternative:** An open source alternative to legacy block-diagram system simulation frameworks. * **Accessible Hybrid System Simulation:** Integrates event detection (zero-crossing, scheduled) directly into the block-diagram paradigm, simplifying the modeling of systems with both *continuous and discrete dynamics*. * **Gradient-Enabled Simulation:** Provides built-in *automatic differentiation* for sensitivity analysis and integration with gradient-based optimization or machine learning frameworks. * **Unified Framework for Diverse Dynamics:** Offers a wide range of solvers, including implicit methods (ESDIRK, BDF/GEAR) for *stiff systems*. @@ -41,7 +42,7 @@ Specifically PathSim offers: # Comparison to Existing Tools -Several Python tools exist for simulating dynamical systems. Standard ODE solvers like `scipy.integrate.solve_ivp` [@virtanen2020scipy] offer robust integration but lack a structured framework for modeling complex, interconnected systems or handling discrete events natively. The *Python Control Systems Library* [@pythoncontrol] is a popular package for modeling and optimizing dynamical systems from the control engineering perspective primarily. Libraries like `SimuPy` [@Margolis2017; @SimuPyRepo] provide a block-based modeling approach similar to PathSim, leveraging SymPy for symbolic definition and SciPy solvers for integration. Other frameworks like `Collimator` [@pycollimator] offer graphical interfaces and JAX-based acceleration but require compilation and introduce dependencies beyond the standard scientific Python stack. `bdsim` [@bdsimRepo] also provides block diagram simulation, focusing on robotics. +Several Python tools for simulating dynamical systems have emerged over the years. Standard ODE solvers like `scipy.integrate.solve_ivp` [@virtanen2020scipy] offer robust integration but lack a structured framework for modeling complex, interconnected systems or handling discrete events natively Uses have to manually derive the govering system equations. The *Python Control Systems Library* [@pythoncontrol] is a popular package for modeling and optimizing dynamical systems from the control engineering perspective primarily. Libraries like `SimuPy` [@Margolis2017; @SimuPyRepo] provide a block-based modeling approach similar to PathSim, leveraging SymPy for symbolic definition and SciPy solvers for integration. Other frameworks like `Collimator` [@pycollimator] offer graphical interfaces and JAX-based acceleration but require compilation and introduce dependencies beyond the standard scientific Python stack. `bdsim` [@bdsimRepo] also provides block diagram simulation, focusing on robotics. PathSim differentiates itself by offering a script-based block-diagram interface with a *decentralized architecture*, native integration of both *automatic differentiation* and *discrete event handling* into the full simulation loop, and a *built-in library* of independently implemented and verified ODE solvers (beyond wrapping SciPy), all while maintaining *minimal core dependencies*. @@ -49,16 +50,65 @@ PathSim differentiates itself by offering a script-based block-diagram interface PathSim employs a decentralized, object-oriented design centered around three primary components: -1. **Blocks (`Block`):** Represent individual system components or operations. They encapsulate their parameters and, if stateful (like `Integrator` or `ODE`), manage their own internal state via a dedicated numerical integration engine (`engine`) instance. This contrasts with centralized approaches where a single solver manages all system states. Blocks define `update` methods for algebraic computations within a timestep and `step`/`solve` methods for interacting with their `engine` for state evolution. +1. **Blocks (`Block`):** Represent individual system components or operations. They encapsulate their parameters and, if stateful (like `Integrator`, `StateSpace` or `ODE`), manage their own internal state via a dedicated numerical integration engine (`engine`) instance. This contrasts with centralized approaches where a single solver manages all system states. Blocks define `update` methods for algebraic computations within a timestep and `step`/`solve` methods for interacting with their `engine` for state evolution. 2. **Connections (`Connection`):** Define the explicit data flow pathways between block output ports and input ports, mirroring the connections in a block diagram. -3. **Simulation (`Simulation`):** Coordinates the overall simulation process. It maintains the list of blocks and connections. During each time step, it manages a fixed-point iteration loop. In this loop, `Connection.update()` propagates output values to inputs, and `Block.update()` computes algebraic outputs based on current inputs and states. This iterative process resolves algebraic loops and ensures consistency across interconnected blocks. The `Simulation` object then triggers the `step` (for explicit solvers) or `solve` (for implicit solvers) methods of the blocks' engines to advance their internal states. It also manages the event handling system. +3. **Simulation (`Simulation`):** Coordinates the overall simulation process. It maintains the list of blocks and connections. It assembles directed graphs of the block dependencies that is used to evaluate the algebraic parts of the global system function. `Connection.update()` propagates output values to inputs, and `Block.update()` computes algebraic outputs based on current inputs and states. Algebraic loop blocks are stored in a separate graph and resolved iteratively in a second stage. The `Simulation` object then triggers the `step` (for explicit solvers) or `solve` (for implicit solvers) methods of the blocks' engines to advance their internal states. It also manages the event handling system. # PathSim Modeling Flow -The figure below shows the modeling and simulation flow with PathSim. Once the dynamical system is translated to the block-diagram paradigm, it can be built from PathSim blocks and connections. The code to the right shows block instantiation, connection definition, simulation setup (including solver and tolerance selection), execution, and result visualization. +PathSim is a script based modelling framework. Therefore it makes sense to start from the block diagram of the system to be modelled. The figure below shows the mechanical representation of the harmonic oscillator to the left and its block diagram to the right. + +![Mechanical representation of the harmonic oscillator to the left and its block diagram to the right](assets/harmonic_oscillator_g.png) + +Translating it to PathSim involves importing the blocks from the block library, instantiating them with their correct parameters, connecting them with the `Connection` object and passing everything to the `Simulation`. + +```python +from pathsim import Simulation, Connection +from pathsim.blocks import Integrator, Amplifier, Adder, Scope + +#initial position and velocity +x0, v0 = 2, 5 + +#parameters (mass, damping, spring constant) +m, c, k = 0.8, 0.2, 1.5 + +#blocks that define the system +I1 = Integrator(v0) # integrator for velocity +I2 = Integrator(x0) # integrator for position +A1 = Amplifier(-c/m) +A2 = Amplifier(-k/m) +P1 = Adder() +Sc = Scope(labels=["velocity", "position"]) + +blocks = [I1, I2, A1, A2, P1, Sc] + +#connections between the blocks +connections = [ + Connection(I1, I2, A1, Sc), + Connection(I2, A2, Sc[1]), + Connection(A1, P1), + Connection(A2, P1[1]), + Connection(P1, I1) + ] + +#create a simulation instance from the blocks and connections +Sim = Simulation(blocks, connections) + +#run the simulation for some time +Sim.run(25) + +#plot the results directly from the scope +Sc.plot() + +#or read them out for postprocessing +time, [vel, pos] = Sc.read() +``` + +The `Scope` block enables fast plotting of the simulation results as well as their retrieval. + +![Simulation results plotted from the PathSim `Scope` for the harmonic oscillator example](assets/harmonic_oscillator_result_g.png) + -![Exemplary dynamical system modeling and simulation flow using PathSim](assets/pathsim_flow.png) - # References From ff3894132a8ca6bd98d3eb70e36d381ed1f7e2d7 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Sun, 4 May 2025 20:50:20 +0200 Subject: [PATCH 19/33] updated paper.md, added references for tbcontrol, improved Simulink citation, added more context around subsystems --- paper/paper.bib | 24 ++++++++++++++---------- paper/paper.md | 7 ++++--- 2 files changed, 18 insertions(+), 13 deletions(-) diff --git a/paper/paper.bib b/paper/paper.bib index fdec1305..bc20288c 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -16,6 +16,15 @@ @misc{bdsimRepo note = {Source Code Repository} } +@misc{tbcontrol, + author = {Carl Sandrock}, + title = {A {P}ython library for solving textbook control problems}, + howpublished = {\url{https://github.com/alchemyst/Dynamics-and-Control}}, + month = {May}, + year = {2019}, + note = {Source Code Repository} +} + @misc{SimuPyRepo, author = {Benjamin W. l. Margolis}, title = {SimuPy: A framework for modeling and simulating dynamical systems}, @@ -38,16 +47,11 @@ @article{Margolis2017 journal = {Journal of Open Source Software} } -@software{Simulink, - author = {{The MathWorks, Inc.}}, - title = {Simulink - Simulation and model-based design}, - url = {https://www.mathworks.com/products/simulink.html} -} - -@software{Matlab, - author = {{The MathWorks, Inc.}}, - title = {Matlab - The language of technical computing}, - url = {https://www.mathworks.com/products/matlab.html} +@manual{Simulink, + title={{Simulink, Simulation and Model-Based Design, Version R2025a}}, + organization={The MathWorks, Inc.}, + address={Natick, Massachusetts}, + year={2025} } @ARTICLE{virtanen2020scipy, diff --git a/paper/paper.md b/paper/paper.md index 01a99331..8632acf8 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -30,21 +30,22 @@ PathSim is a flexible, block-based, time-domain dynamical system simulation fram Modeling and simulating dynamical systems is vital across many disciplines such as control engineering, chemical process engineering, and mixed signal engineering. Challenges are often the interplay of multiple *coupled* subsystems with their distinct dynamics and behaviors which have to be solved and synchronized concurrently to advance the full system simulation. -PathSim meets the need for an open source simulation framework in the block-diagram paradigm with minimal dependencies, which integrates seamlessly into the Python ecosystem. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), easier extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis. Additionaly this opens up block level solver optimizations, integration with other simulation environments (co-simulation) and hardware in the loop (HiL) setups through encapsulation within blocks, as well as integration into machine-learning pipelines. +PathSim meets the need for an open source simulation framework in the block-diagram paradigm with minimal dependencies, which integrates seamlessly into the Python ecosystem. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), easier extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis. Additionally this opens up block level solver optimizations, integration with other simulation environments (co-simulation) and hardware in the loop (HiL) setups through encapsulation within blocks, as well as integration into machine-learning pipelines. Specifically PathSim offers: * **Open Source Alternative:** An open source alternative to legacy block-diagram system simulation frameworks. * **Accessible Hybrid System Simulation:** Integrates event detection (zero-crossing, scheduled) directly into the block-diagram paradigm, simplifying the modeling of systems with both *continuous and discrete dynamics*. +* **Hierarchical Modeling:** Subsystem blocks that encapsulate their own blocks and connections to *manage model complexity*. * **Gradient-Enabled Simulation:** Provides built-in *automatic differentiation* for sensitivity analysis and integration with gradient-based optimization or machine learning frameworks. * **Unified Framework for Diverse Dynamics:** Offers a wide range of solvers, including implicit methods (ESDIRK, BDF/GEAR) for *stiff systems*. * **Extensibility in Python:** Leverages the scientific Python ecosystem with minimal dependencies. Its architecture allows straightforward creation and integration of custom blocks. # Comparison to Existing Tools -Several Python tools for simulating dynamical systems have emerged over the years. Standard ODE solvers like `scipy.integrate.solve_ivp` [@virtanen2020scipy] offer robust integration but lack a structured framework for modeling complex, interconnected systems or handling discrete events natively Uses have to manually derive the govering system equations. The *Python Control Systems Library* [@pythoncontrol] is a popular package for modeling and optimizing dynamical systems from the control engineering perspective primarily. Libraries like `SimuPy` [@Margolis2017; @SimuPyRepo] provide a block-based modeling approach similar to PathSim, leveraging SymPy for symbolic definition and SciPy solvers for integration. Other frameworks like `Collimator` [@pycollimator] offer graphical interfaces and JAX-based acceleration but require compilation and introduce dependencies beyond the standard scientific Python stack. `bdsim` [@bdsimRepo] also provides block diagram simulation, focusing on robotics. +Several Python tools for simulating dynamical systems have emerged over the years. Standard ODE solvers like `scipy.integrate.solve_ivp` [@virtanen2020scipy] offer robust integration but lack a structured framework for modeling complex, interconnected systems or handling discrete events natively Uses have to manually derive the govering system equations. The *Python Control Systems Library* [@pythoncontrol] is a popular package for modeling and optimizing dynamical systems from the control engineering perspective primarily. The package `tbcontrol` [@tbcontrol] similarly focuses on control systems. Libraries like `SimuPy` [@Margolis2017; @SimuPyRepo] provide a block-based modeling approach similar to PathSim, leveraging SymPy for symbolic definition and SciPy solvers for integration. Other frameworks like `Collimator` [@pycollimator] offer graphical interfaces and JAX-based acceleration but require compilation and introduce dependencies beyond the standard scientific Python stack. `bdsim` [@bdsimRepo] also provides block diagram simulation, based on Scipy solvers, with a strong focus on robotics but without event handling. -PathSim differentiates itself by offering a script-based block-diagram interface with a *decentralized architecture*, native integration of both *automatic differentiation* and *discrete event handling* into the full simulation loop, and a *built-in library* of independently implemented and verified ODE solvers (beyond wrapping SciPy), all while maintaining *minimal core dependencies*. +PathSim differentiates itself by offering a script-based block-diagram interface with a *decentralized architecture*, native integration of both *automatic differentiation* and *discrete event handling* into the full simulation loop, capable of handling *algebraic loops*, and a *built-in library* of independently implemented and verified ODE solvers (beyond wrapping SciPy), all while maintaining *minimal core dependencies*. # Architecture and Design From 90557fc33842d47c542ce83050ade4b55918d6f0 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Sun, 4 May 2025 20:57:20 +0200 Subject: [PATCH 20/33] paper.md, fixed typo --- paper/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index 8632acf8..760853ac 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -24,7 +24,7 @@ bibliography: paper.bib # Summary -PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems from their signal flow graphs, similar to Mathworks Simulink [@Simulink] using an object-oriented and decentralized architecture. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features i.e. (forward mode) automatic differentiation for sensitivity analysis or gradient based optimization, discrete event handling for hybrid systems, automatic system- or block-level linearization, hierarchical modeling through subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries: NumPy [@harris2020array], SciPy [@virtanen2020scipy], and Matplotlib [@hunter2007matplotlib]. +PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems from their signal flow graphs, similar to MathWorks Simulink [@Simulink] using an object-oriented and decentralized architecture. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features i.e. (forward mode) automatic differentiation for sensitivity analysis or gradient based optimization, discrete event handling for hybrid systems, automatic system- or block-level linearization, hierarchical modeling through subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries: NumPy [@harris2020array], SciPy [@virtanen2020scipy], and Matplotlib [@hunter2007matplotlib]. # Statement of Need From 2448950fb52c397ac27faf2c3178735a9657e06f Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Wed, 7 May 2025 17:07:33 +0200 Subject: [PATCH 21/33] updated joss paper --- paper/assets/bouncing_ball_g.png | Bin 0 -> 107468 bytes .../assets/bouncing_ball_result_events_g.png | Bin 0 -> 44634 bytes paper/assets/harmonic_oscillator_g.png | Bin 140926 -> 145640 bytes paper/assets/vanderpol_g.png | Bin 0 -> 123917 bytes paper/assets/vanderpol_result_g.png | Bin 0 -> 28321 bytes paper/paper.bib | 9 + paper/paper.md | 195 +++++++++++++++++- 7 files changed, 196 insertions(+), 8 deletions(-) create mode 100644 paper/assets/bouncing_ball_g.png create mode 100644 paper/assets/bouncing_ball_result_events_g.png create mode 100644 paper/assets/vanderpol_g.png create mode 100644 paper/assets/vanderpol_result_g.png diff --git 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z7bSmb?1PEXmj`GEK%(uZ4sD|cJUuS#s&(5(pLSq0$8o(&ii_2uUm7{tPBVS~mFd&a zw9=OOUM#JnDSoW*Lw|pumwK!vsJCBfh4W36DiQr^<39>!SJFk4J8y*sP)GO zzfh^(@!a|(W@m42@5ENL!2@(q(w18^GzNev?xNXIsr5faml-Q9iv0b??0#UBn|bZh zxJZgI!#2q08HiL&s2&t@h#c8yUU>C)VC9XS?=!Pk$}0wTG<+mgT&h+NKBzH9Wl_YK z=>6*jL~FMQqlM8q2vaxJ{d!r5omYd3^uApVKb?U3XdN{Qo;*X}W?OHAdmgWgcjyNC zCDg5+A`1*%PL7b@&@aB@Tf+)(MYb^a+;BcR3$tIcaANlKCTRp`< z18DJEJx^ecR9kcSx&$JIAmnY@ZV-;>UHFJKS!PT-G%|=KwqE4rsM>p*>_z*_h5csW z`L7cafK^?Sl9Hm3=IOQujbi2C;smVg(2#y4ih)9E9U6&7Fl$F1kgi|8q8j*qeaHQD z2J07mm2?~rO4W|S>1qNL{_Tnr)9@m5?cN2_1DOB1B)MsmDox`d>+eV`KmT From dc91169332a360184584b0b29365b48f5b9f7019 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Tue, 13 May 2025 14:47:45 +0200 Subject: [PATCH 29/33] paper figure captions --- paper/paper.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 7483eb31..bbaa8d66 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -115,11 +115,11 @@ The `Scope` block enables fast plotting of the simulation results as well as the There are more *examples* of dynamical system simulations present in the **PathSim** repository and, with further explanations, in the documentation. The examples cover all features **PathSim** has to offer, including hierarchical modelling through *subsystems*, examples of *stiff dynamics* with implicit solver and discrete dynamics with *event handling*. -The figures below show a variety of systems and simulation results obtained with **PathSim**. +The figures below showcase more dynamical systems and simulation results obtained with **PathSim**. -![Visualization of the *Van der Pol* system built from distinct components as a block diagram and the simulation results for a very stiff case ($\\mu=1000$). This example is available in the repository.](assets/vanderpol_g.png) +![Visualization of the *Van der Pol* system built from distinct components as a block diagram and the simulation results for a very stiff case ($\mu=1000$). This example showcases PathSims ability to handle stiff systems, it is available in the repository.](assets/vanderpol_g.png) -![Visualization of the *bouncing ball*, a classical example for discrete event handling. This example is available in the repository.](assets/bouncing_ball_g.png) +![Visualization of the *bouncing ball*, a classical example for discrete event handling. This example showcases Pathsims event handling mechanism for detecting and resolving discrete events (*zero-crossings* in this case). It is available in the repository.](assets/bouncing_ball_g.png) # References From a4bad6cd789ec42f285a41d229619771048b19c9 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Tue, 13 May 2025 14:51:17 +0200 Subject: [PATCH 30/33] paper figure captions --- paper/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index bbaa8d66..c719a64b 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -117,7 +117,7 @@ There are more *examples* of dynamical system simulations present in the **PathS The figures below showcase more dynamical systems and simulation results obtained with **PathSim**. -![Visualization of the *Van der Pol* system built from distinct components as a block diagram and the simulation results for a very stiff case ($\mu=1000$). This example showcases PathSims ability to handle stiff systems, it is available in the repository.](assets/vanderpol_g.png) +![Visualization of the *Van der Pol* system built from distinct components as a block diagram and the simulation results for a very stiff case ($\mu=1000$) using one of PathSims implicit ODE solvers (`ESDIRK43`). This example showcases PathSims ability to handle stiff systems, it is available in the repository.](assets/vanderpol_g.png) ![Visualization of the *bouncing ball*, a classical example for discrete event handling. This example showcases Pathsims event handling mechanism for detecting and resolving discrete events (*zero-crossings* in this case). It is available in the repository.](assets/bouncing_ball_g.png) From 6c854707611585b9f3cdc87c208acea9481fc376 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Tue, 13 May 2025 16:00:52 +0200 Subject: [PATCH 31/33] fixed typos in paper --- paper/paper.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index c719a64b..26fd6538 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -47,7 +47,7 @@ MathWorks Simulink [@Simulink] is the defacto industry standard for system model Several Python tools for simulating dynamical systems have emerged over the years. Standard ODE solvers like `scipy.integrate.solve_ivp` [@virtanen2020scipy] offer robust integration but lack a structured framework for modeling complex, interconnected systems or handling discrete events natively Uses have to manually derive the govering system equations. The *Python Control Systems Library* [@pythoncontrol] is a popular package for modeling and optimizing dynamical systems from the control engineering perspective primarily. The package `tbcontrol` [@tbcontrol] similarly focuses on control systems. Libraries like `SimuPy` [@Margolis2017; @SimuPyRepo] provide a block-based modeling approach similar to PathSim, leveraging SymPy for symbolic definition and SciPy solvers for integration. Other frameworks like `Collimator` [@pycollimator] offer graphical interfaces and JAX-based acceleration but require compilation and introduce dependencies beyond the standard scientific Python stack. `bdsim` [@bdsimRepo] also provides block diagram simulation, based on Scipy solvers, with a strong focus on robotics but without event handling. -PathSim differentiates itself by offering a script-based block-diagram interface with a *decentralized architecture*, native integration of both *automatic differentiation* and *discrete event handling* into the full simulation loop, capable of handling *algebraic loops*, and a *built-in library* of independently implemented and verified ODE solvers (beyond wrapping SciPy). Its fully open under *MIT-License* with *minimal core dependencies*. +PathSim differentiates itself by offering a script-based block-diagram interface with a *decentralized architecture*, native integration of both *automatic differentiation* and *discrete event handling* into the full simulation loop, capable of handling *algebraic loops*, and a *built-in library* of independently implemented and verified ODE solvers (beyond wrapping SciPy). It is fully open under *MIT-License* with *minimal core dependencies*. # Architecture and Design @@ -59,7 +59,7 @@ PathSim employs a decentralized, object-oriented design centered around three pr # PathSim Modelling Flow -PathSim is a script based modelling framework with no built in graphical user interface. Therefore it makes sense to start from the block diagram of the system to be modelled. This section demonstrates PathSims modelling and simulation flow on a classical example dynamical system, the *harmonic oscillator*. +PathSim is a script based modelling framework with no built in graphical user interface. Therefore it makes sense to start from the block diagram of the system to be modelled. This section demonstrates PathSim's modelling and simulation flow on a classical example dynamical system, the *harmonic oscillator*. The figure below shows the mechanical representation of the harmonic oscillator to the left and its block diagram to the right. @@ -117,9 +117,9 @@ There are more *examples* of dynamical system simulations present in the **PathS The figures below showcase more dynamical systems and simulation results obtained with **PathSim**. -![Visualization of the *Van der Pol* system built from distinct components as a block diagram and the simulation results for a very stiff case ($\mu=1000$) using one of PathSims implicit ODE solvers (`ESDIRK43`). This example showcases PathSims ability to handle stiff systems, it is available in the repository.](assets/vanderpol_g.png) +![Visualization of the *Van der Pol* system built from distinct components as a block diagram and the simulation results for a very stiff case ($\mu=1000$) using one of PathSim's implicit ODE solvers (`ESDIRK43`). This example showcases PathSim's ability to handle stiff systems, it is available in the repository.](assets/vanderpol_g.png) -![Visualization of the *bouncing ball*, a classical example for discrete event handling. This example showcases Pathsims event handling mechanism for detecting and resolving discrete events (*zero-crossings* in this case). It is available in the repository.](assets/bouncing_ball_g.png) +![Visualization of the *bouncing ball*, a classical example for discrete event handling. This example showcases PathSim's event handling mechanism for detecting and resolving discrete events (*zero-crossings* in this case). It is available in the repository.](assets/bouncing_ball_g.png) # References From 3f2a65be0f0c8eb412390afa418dbbfec81005c9 Mon Sep 17 00:00:00 2001 From: "Daniel S. Katz" Date: Tue, 13 May 2025 09:26:23 -0500 Subject: [PATCH 32/33] small changes in paper.md --- paper/paper.md | 20 ++++++++++---------- 1 file changed, 10 insertions(+), 10 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 26fd6538..c7ca1ac5 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -24,13 +24,13 @@ bibliography: paper.bib # Summary -PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems from their signal flow graphs, similar to MathWorks Simulink [@Simulink] using an object-oriented and decentralized architecture. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features i.e. (forward mode) automatic differentiation for sensitivity analysis or gradient based optimization, discrete event handling for hybrid systems, automatic system- or block-level linearization, hierarchical modeling through subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries: NumPy [@harris2020array], SciPy [@virtanen2020scipy], and Matplotlib [@hunter2007matplotlib]. +PathSim is a flexible, block-based, time-domain dynamical system simulation framework implemented in Python. It enables the modeling and simulation of complex interconnected systems from their signal flow graphs, similar to MathWorks Simulink [@Simulink] using an object-oriented and decentralized architecture. This architectural choice distinguishes PathSim by distributing state and computation across individual `Block` components, promoting modularity, extensibility, and flexibility. Core components include user-defined or built-in `Block` objects encapsulating specific behaviors, `Connection` objects defining explicit data flow, and a `Simulation` object managing time evolution and coordination. Dynamic blocks possess their own numerical solver instances (`engine`) for state integration. PathSim incorporates advanced features: (forward mode) automatic differentiation for sensitivity analysis or gradient based optimization, discrete event handling for hybrid systems, automatic system- or block-level linearization, hierarchical modeling through subsystems, and a comprehensive suite of ODE solvers suitable for stiff problems. It requires only core scientific Python libraries: NumPy [@harris2020array], SciPy [@virtanen2020scipy], and Matplotlib [@hunter2007matplotlib]. # Statement of Need -Modeling and simulating dynamical systems is vital across many disciplines such as control engineering, chemical process engineering, and mixed signal engineering. Challenges are often the interplay of multiple *coupled* subsystems with their distinct dynamics and behaviors which have to be solved and synchronized concurrently to advance the full system simulation. +Modeling and simulating dynamical systems is vital across many disciplines such as control engineering, chemical process engineering, and mixed signal engineering. Challenges are often the interplay of multiple *coupled* subsystems with their distinct dynamics and behaviors that have to be solved and synchronized concurrently to advance the full system simulation. -PathSim meets the need for an open source simulation framework in the block-diagram paradigm with minimal dependencies, which integrates seamlessly into the Python ecosystem. Traditional simulation tools often rely on centralized solvers, proprietary file formats or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), straight forward extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis. Additionally this opens up block level solver optimizations, integration with other simulation environments (co-simulation) and hardware in the loop (HiL) setups through encapsulation within blocks, as well as integration into machine-learning pipelines. +PathSim meets the need for an open source simulation framework in the block-diagram paradigm with minimal dependencies, which integrates seamlessly into the Python ecosystem. Traditional simulation tools often rely on centralized solvers, proprietary file formats, or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), straight forward extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis. Additionally this opens up block level solver optimizations, integration with other simulation environments (co-simulation), and hardware in the loop (HiL) setups through encapsulation within blocks, as well as integration into machine-learning pipelines. Specifically PathSim offers: @@ -43,11 +43,11 @@ Specifically PathSim offers: # Comparison to Existing Tools -MathWorks Simulink [@Simulink] is the defacto industry standard for system modeling in the block diagram paradigm. Its a proprietary tool with significant licensing costs. Besides that, other equation based modeling frameworks such as `Modelica` [@ModelicaRepo] with its own model description language are also used but not as widely adopted. +MathWorks Simulink [@Simulink] is the de facto industry standard for system modeling in the block diagram paradigm. It's a proprietary tool with significant licensing costs. Besides that, other equation based modeling frameworks such as `Modelica` [@ModelicaRepo] with its own model description language are also used but not as widely adopted. -Several Python tools for simulating dynamical systems have emerged over the years. Standard ODE solvers like `scipy.integrate.solve_ivp` [@virtanen2020scipy] offer robust integration but lack a structured framework for modeling complex, interconnected systems or handling discrete events natively Uses have to manually derive the govering system equations. The *Python Control Systems Library* [@pythoncontrol] is a popular package for modeling and optimizing dynamical systems from the control engineering perspective primarily. The package `tbcontrol` [@tbcontrol] similarly focuses on control systems. Libraries like `SimuPy` [@Margolis2017; @SimuPyRepo] provide a block-based modeling approach similar to PathSim, leveraging SymPy for symbolic definition and SciPy solvers for integration. Other frameworks like `Collimator` [@pycollimator] offer graphical interfaces and JAX-based acceleration but require compilation and introduce dependencies beyond the standard scientific Python stack. `bdsim` [@bdsimRepo] also provides block diagram simulation, based on Scipy solvers, with a strong focus on robotics but without event handling. +Several Python tools for simulating dynamical systems have emerged over the years. Standard ODE solvers like `scipy.integrate.solve_ivp` [@virtanen2020scipy] offer robust integration but lack a structured framework for modeling complex, interconnected systems, or handling discrete events natively. Users have to manually derive the govering system equations. The *Python Control Systems Library* [@pythoncontrol] is a popular package for modeling and optimizing dynamical systems, primarily from the control engineering perspective. The package `tbcontrol` [@tbcontrol] similarly focuses on control systems. Libraries like `SimuPy` [@Margolis2017; @SimuPyRepo] provide a block-based modeling approach similar to PathSim, leveraging SymPy for symbolic definition and SciPy solvers for integration. Other frameworks like `Collimator` [@pycollimator] offer graphical interfaces and JAX-based acceleration but require compilation and introduce dependencies beyond the standard scientific Python stack. `bdsim` [@bdsimRepo] also provides block diagram simulation, based on Scipy solvers, with a strong focus on robotics but without event handling. -PathSim differentiates itself by offering a script-based block-diagram interface with a *decentralized architecture*, native integration of both *automatic differentiation* and *discrete event handling* into the full simulation loop, capable of handling *algebraic loops*, and a *built-in library* of independently implemented and verified ODE solvers (beyond wrapping SciPy). It is fully open under *MIT-License* with *minimal core dependencies*. +PathSim differentiates itself by offering a script-based block-diagram interface with a *decentralized architecture*, native integration of both *automatic differentiation* and *discrete event handling* into the full simulation loop, capable of handling *algebraic loops*, and a *built-in library* of independently implemented and verified ODE solvers (beyond wrapping SciPy). It is fully open under the *MIT License* with *minimal core dependencies*. # Architecture and Design @@ -57,15 +57,15 @@ PathSim employs a decentralized, object-oriented design centered around three pr 2. **Connections (`Connection`):** Define the explicit data flow pathways between block output ports and input ports, mirroring the connections in a block diagram. 3. **Simulation (`Simulation`):** Coordinates the overall simulation process. It maintains the list of blocks and connections. It assembles directed graphs of the block dependencies that is used to evaluate the algebraic parts of the global system function. `Connection.update()` propagates output values to inputs, and `Block.update()` computes algebraic outputs based on current inputs and states. Algebraic loop blocks are stored in a separate graph and resolved iteratively in a second stage. The `Simulation` object then triggers the `step` (for explicit solvers) or `solve` (for implicit solvers) methods of the blocks' engines to advance their internal states. It also manages the event handling system. -# PathSim Modelling Flow +# PathSim Modeling Flow -PathSim is a script based modelling framework with no built in graphical user interface. Therefore it makes sense to start from the block diagram of the system to be modelled. This section demonstrates PathSim's modelling and simulation flow on a classical example dynamical system, the *harmonic oscillator*. +PathSim is a script based modeling framework with no built-in graphical user interface. Therefore it makes sense to start from the block diagram of the system to be modeled. This section demonstrates PathSim's modeling and simulation flow on a classical example dynamical system, the *harmonic oscillator*. The figure below shows the mechanical representation of the harmonic oscillator to the left and its block diagram to the right. ![Mechanical representation of the harmonic oscillator to the left and its block diagram to the right as a schematic viasualization to help with the assembly of the system im PathSim (PathSim is purely script based)](assets/harmonic_oscillator_g.png) -Translating it to PathSim involves importing the blocks from the block library, instantiating them with their correct parameters, connecting them with the `Connection` object and passing everything to the `Simulation`. +Translating it to PathSim involves importing the blocks from the block library, instantiating them with their correct parameters, connecting them with the `Connection` object, and passing everything to the `Simulation`. ```python from pathsim import Simulation, Connection @@ -113,7 +113,7 @@ The `Scope` block enables fast plotting of the simulation results as well as the ![Simulation results plotted directly from the PathSim `Scope` block for the harmonic oscillator example.](assets/harmonic_oscillator_result_g.png) -There are more *examples* of dynamical system simulations present in the **PathSim** repository and, with further explanations, in the documentation. The examples cover all features **PathSim** has to offer, including hierarchical modelling through *subsystems*, examples of *stiff dynamics* with implicit solver and discrete dynamics with *event handling*. +There are more *examples* of dynamical system simulations present in the **PathSim** repository and, with further explanations, in the documentation. The examples cover all features **PathSim** has to offer, including hierarchical modeling through *subsystems*, examples of *stiff dynamics* with implicit solver, and discrete dynamics with *event handling*. The figures below showcase more dynamical systems and simulation results obtained with **PathSim**. From f5f5187c5ca84195e5a96d76c9e41f5e7f9ace26 Mon Sep 17 00:00:00 2001 From: "Daniel S. Katz" Date: Tue, 13 May 2025 09:28:09 -0500 Subject: [PATCH 33/33] minor change in paper.bib --- paper/paper.bib | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/paper/paper.bib b/paper/paper.bib index c5a5025d..a641beaa 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -77,8 +77,8 @@ @ARTICLE{virtanen2020scipy Harris, Charles R. and Archibald, Anne M. and Ribeiro, Ant{\^o}nio H. and Pedregosa, Fabian and {van Mulbregt}, Paul and {SciPy 1.0 Contributors}}, - title = {{{SciPy} 1.0: Fundamental Algorithms for Scientific - Computing in {P}ython}}, + title = {{SciPy} 1.0: Fundamental Algorithms for Scientific + Computing in {P}ython}, journal = {Nature Methods}, year = {2020}, volume = {17},

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retrieval. -![Simulation results plotted from the PathSim `Scope` for the harmonic oscillator example.](assets/harmonic_oscillator_result_g.png) +![Simulation results plotted directly from the PathSim `Scope` block for the harmonic oscillator example.](assets/harmonic_oscillator_result_g.png) + +There are more *examples* of dynamical system simulations present in the **PathSim** repository and, with further explanations, in the documentation. The examples cover all features **PathSim** has to offer, including hierarchical modelling through *subsystems*, examples of *stiff dynamics* with implicit solver and discrete dynamics with *event handling*. + +The figures below show a variety of systems and simulation results obtained with **PathSim**. + +![Visualization of the *Van der Pol* system built from distinct components as a block diagram and the simulation results for a very stiff case ($\\mu=1000$). This example is available in the repository.](assets/vanderpol_g.png) + +![Visualization of the *bouncing ball*, a classical example for discrete event handling. This example is available in the repository.](assets/bouncing_ball_g.png) -There more *examples* of dynamical system simulations present in the PathSim repository and, with further explanations, in the documentation. The examples cover all features PathSim has to offer, including hierarchical modelling through *subsystems*, examples of *stiff dynamics* with implicit solver and discrete dynamics with *event handling*. # References From c4f0bdd4c900b3c0bbea28719bc8ca05aa124e82 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Tue, 13 May 2025 14:42:15 +0200 Subject: [PATCH 28/33] updated figure of harmonic oscillator result to fit better --- paper/assets/harmonic_oscillator_result_g.png | Bin 182473 -> 186089 bytes 1 file changed, 0 insertions(+), 0 deletions(-) diff --git a/paper/assets/harmonic_oscillator_result_g.png b/paper/assets/harmonic_oscillator_result_g.png index b8f6ceb9ed62fe9b806be213926f217898f20e09..146719fde97ab413b93dc46f78970f4eb45d3f8a 100644 GIT binary patch literal 186089 zcmeFZXH=70)HNFQ*p8wUDT<0jih>Y2A|*!*BGN=aKza*OL+>FRMY;P=DM zHw@e$5c$99|MqOMeYy|cyyC8;@2-tPx_g-E(($cDn+DIsUps80BgMi+9y`1&m8xuw0e`#B418(SxNesWbU|2bPLd44@fbrE&vYu5K{Z}_@eYx`>GSo+#q%2@Hk 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zCs()9<$-C^xBB+y>{ddCo9>`!|0;`};x@=gBnc9B;djqR##NA&M>nXF)F6~$&M;q= zSY7puD0IUjBu9f6OJQ1`c9)O-N`6nGk(FUiB#+f=kSf4msm>cgmsSrj&H~p>Gzd2o z^E;xb^$Em!2CZc!vSxf6Sdn-DwQG_(RiC_ldh4)G+X_3|E&tJZtx82Oft-CM|MvU& vlp%5P`#JzLg71eaZeMa2hX2nWM03QO+fHgv2pTmb;E#!s`7h55Tz~s7e=4&` literal 0 HcmV?d00001 diff --git a/paper/paper.bib b/paper/paper.bib index bc20288c..ebe20c2e 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -54,6 +54,15 @@ @manual{Simulink year={2025} } +@misc{ModelicaRepo, + title = {Free (standard conforming) library to model mechanical (1D/3D), electrical (analog, digital, machines), magnetic, thermal, fluid, control systems and hierarchical state machines. Also numerical functions and functions for strings, files and streams are included.}, + organization = {Modelica Association}, + howpublished = {\url{https://github.com/modelica/ModelicaStandardLibrary}}, + month = {December}, + year = {1999}, + note = {Source Code Repository, created 2017} +} + @ARTICLE{virtanen2020scipy, author = {Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and Haberland, Matt and Reddy, Tyler and Cournapeau, David and diff --git a/paper/paper.md b/paper/paper.md index 760853ac..aa17bb23 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -30,7 +30,7 @@ PathSim is a flexible, block-based, time-domain dynamical system simulation fram Modeling and simulating dynamical systems is vital across many disciplines such as control engineering, chemical process engineering, and mixed signal engineering. Challenges are often the interplay of multiple *coupled* subsystems with their distinct dynamics and behaviors which have to be solved and synchronized concurrently to advance the full system simulation. -PathSim meets the need for an open source simulation framework in the block-diagram paradigm with minimal dependencies, which integrates seamlessly into the Python ecosystem. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), easier extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis. Additionally this opens up block level solver optimizations, integration with other simulation environments (co-simulation) and hardware in the loop (HiL) setups through encapsulation within blocks, as well as integration into machine-learning pipelines. +PathSim meets the need for an open source simulation framework in the block-diagram paradigm with minimal dependencies, which integrates seamlessly into the Python ecosystem. Traditional simulation tools often rely on centralized solvers, proprietary file formats or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), straight forward extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis. Additionally this opens up block level solver optimizations, integration with other simulation environments (co-simulation) and hardware in the loop (HiL) setups through encapsulation within blocks, as well as integration into machine-learning pipelines. Specifically PathSim offers: @@ -43,23 +43,29 @@ Specifically PathSim offers: # Comparison to Existing Tools +MathWorks Simulink [@Simulink] is the defacto industry standard for system modeling in the block diagram paradigm. Its a proprietary tool with significant licensing costs. Besides that, other equation based modeling frameworks such as `Modelica` [@ModelicaRepo] with its own model description language are also used but not as widely adopted. + Several Python tools for simulating dynamical systems have emerged over the years. Standard ODE solvers like `scipy.integrate.solve_ivp` [@virtanen2020scipy] offer robust integration but lack a structured framework for modeling complex, interconnected systems or handling discrete events natively Uses have to manually derive the govering system equations. The *Python Control Systems Library* [@pythoncontrol] is a popular package for modeling and optimizing dynamical systems from the control engineering perspective primarily. The package `tbcontrol` [@tbcontrol] similarly focuses on control systems. Libraries like `SimuPy` [@Margolis2017; @SimuPyRepo] provide a block-based modeling approach similar to PathSim, leveraging SymPy for symbolic definition and SciPy solvers for integration. Other frameworks like `Collimator` [@pycollimator] offer graphical interfaces and JAX-based acceleration but require compilation and introduce dependencies beyond the standard scientific Python stack. `bdsim` [@bdsimRepo] also provides block diagram simulation, based on Scipy solvers, with a strong focus on robotics but without event handling. -PathSim differentiates itself by offering a script-based block-diagram interface with a *decentralized architecture*, native integration of both *automatic differentiation* and *discrete event handling* into the full simulation loop, capable of handling *algebraic loops*, and a *built-in library* of independently implemented and verified ODE solvers (beyond wrapping SciPy), all while maintaining *minimal core dependencies*. +PathSim differentiates itself by offering a script-based block-diagram interface with a *decentralized architecture*, native integration of both *automatic differentiation* and *discrete event handling* into the full simulation loop, capable of handling *algebraic loops*, and a *built-in library* of independently implemented and verified ODE solvers (beyond wrapping SciPy). Its fully open under *MIT-License* with *minimal core dependencies*. # Architecture and Design PathSim employs a decentralized, object-oriented design centered around three primary components: -1. **Blocks (`Block`):** Represent individual system components or operations. They encapsulate their parameters and, if stateful (like `Integrator`, `StateSpace` or `ODE`), manage their own internal state via a dedicated numerical integration engine (`engine`) instance. This contrasts with centralized approaches where a single solver manages all system states. Blocks define `update` methods for algebraic computations within a timestep and `step`/`solve` methods for interacting with their `engine` for state evolution. -2. **Connections (`Connection`):** Define the explicit data flow pathways between block output ports and input ports, mirroring the connections in a block diagram. +1. **Blocks (`Block`):** Represent individual system components or operations. They encapsulate their parameters and, if stateful (like `Integrator`, `StateSpace` or `ODE`), manage their own internal state via a dedicated numerical integration engine (`engine`) instance. This contrasts with centralized approaches where a single solver manages all system states. Blocks define `update` methods for algebraic computations within a timestep and `step`/`solve` methods for interacting with their `engine` for state evolution. The `Subsystem` class shares the same interface as the base `Block` and is treated by the main simulation loop as such. This enables arbitrary encapsulation and nesting. +2. **Connections (`Connection`):** Define the explicit data flow pathways between block output ports and input ports, mirroring the connections in a block diagram. 3. **Simulation (`Simulation`):** Coordinates the overall simulation process. It maintains the list of blocks and connections. It assembles directed graphs of the block dependencies that is used to evaluate the algebraic parts of the global system function. `Connection.update()` propagates output values to inputs, and `Block.update()` computes algebraic outputs based on current inputs and states. Algebraic loop blocks are stored in a separate graph and resolved iteratively in a second stage. The `Simulation` object then triggers the `step` (for explicit solvers) or `solve` (for implicit solvers) methods of the blocks' engines to advance their internal states. It also manages the event handling system. -# PathSim Modeling Flow +# PathSim Modelling Flow + +PathSim is a script based modelling framework, with no built in graphical user interface. Therefore it makes sense to start from the block diagram of the system to be modelled. The following sections demonstrate PathSims modelling and simulation flow. The examples cover classical dynamical systems such as the *harmonic oscillator*, the *bouncing ball* (to showcase the event handling system) and the *Van der Pol* system (as a stiff subsystem). + +## Harmonic Oscillator -PathSim is a script based modelling framework. Therefore it makes sense to start from the block diagram of the system to be modelled. The figure below shows the mechanical representation of the harmonic oscillator to the left and its block diagram to the right. +The figure below shows the mechanical representation of the harmonic oscillator to the left and its block diagram to the right. -![Mechanical representation of the harmonic oscillator to the left and its block diagram to the right](assets/harmonic_oscillator_g.png) +![Mechanical representation of the harmonic oscillator to the left and its block diagram to the right.](assets/harmonic_oscillator_g.png) Translating it to PathSim involves importing the blocks from the block library, instantiating them with their correct parameters, connecting them with the `Connection` object and passing everything to the `Simulation`. @@ -107,9 +113,182 @@ time, [vel, pos] = Sc.read() The `Scope` block enables fast plotting of the simulation results as well as their retrieval. -![Simulation results plotted from the PathSim `Scope` for the harmonic oscillator example](assets/harmonic_oscillator_result_g.png) +![Simulation results plotted from the PathSim `Scope` for the harmonic oscillator example.](assets/harmonic_oscillator_result_g.png) + + +## Bouncing Ball + +The classical example for demonstrating event handling is the bouncing ball. The ball accelerates downward due to gravity and onece it hits the floor, it bounces back. The dynamics of this system are discontinuous due to the jump in velocity (sign change) exactly at the bounce. This is called a discrete event, specifically a zero-crossing event. Systems like this require the location and resolution of discrete events within the timestep and are not easily solved with standard numerical ODE solvers. **PathSim** implements an event management system, that can track the system state and locate and resolve specified events. + +![Schematic of the bouncing ball dynamics to the left and the corresponding block diagram with two distinct integrators and the event handler to the righ.](assets/bouncing_ball_g.png) + +The following code block defines the bouncing ball system in PathSim, utilizing the `ZeroCrossing` event manager to track the height of the ball and trigger the jump in velocity. + +```python +from pathsim import Simulation, Connection +from pathsim.blocks import Integrator, Constant, Scope +from pathsim.events import ZeroCrossing #event manager +from pathsim.solvers import RKBS32 #adaptive solver + +#elasticity of bounce and gravitational acceleration +b, g = 0.9, 9.81 + +#initial conditions +x0, v0 = 1, 5 + +#blocks that define the system +Ix = Integrator(x0) # v -> x +Iv = Integrator(v0) # a -> v +Cn = Constant(-g) # gravitational acceleration +Sc = Scope(labels=["x", "v"]) + +blocks = [Ix, Iv, Cn, Sc] + +#the connections between the blocks +connections = [ + Connection(Cn, Iv), + Connection(Iv, Ix), + Connection(Ix, Sc[0]) + ] + +#event function for zero crossing detection +def func_evt(t): + *_, x = Ix() #get block outputs and states + return x + +#action function for state transformation +def func_act(t): + *_, x = Ix() + *_, v = Iv() + Ix.engine.set(abs(x)) + Iv.engine.set(-b*v) + +#events (zero crossing) +E1 = ZeroCrossing( + func_evt=func_evt, + func_act=func_act, + tolerance=1e-4 + ) + +events = [E1] + +#initialize simulation from blocks, connections and events +Sim = Simulation( + blocks, + connections, + events, + dt=0.01, + dt_max=0.04, + Solver=RKBS32 + ) + +#run the simulation +Sim.run(10) + +#read the recordings from the scope direclty +time, [data_x] = Sc.read() + +#plot the recordings from the scope +fig, ax = Sc.plot() + +#add detected events to scope plot +for t in E1: + ax.axvline(t, ls="--", c="k") + +``` + +The results (plotted from the `Scope`) show the evolution of ball accross time. The dashed lines indicate the locations of the bounces (detected events): + +![Simulation results plotted from the PathSim `Scope` for the bouncing ball dynamics, including the detected events.](assets/bouncing_ball_result_events_g.png) + + +## Van der Pol System + +Another classic dynamical system is the *Van der Pol* oscillator, which is described by the second order nonlinear ODE + +```math +\begin{eqnarray} + \dot{x}_1 &= x_2 \\ + \dot{x}_2 &= \mu (1 - x_1^2) x_2 - x_1 +\end{eqnarray} +``` + +where the parameter $\\mu$ controls the *stiffness*. Stiffness in dynamical systems typically arises when the (local) internal time constants (eigenvalues of the Jacobian) are on vastly different scales, or when very steep gradients are encountered. This forces explicit integrators to take extremely small timesteps in order for the discretized system to be stable. Implicit solvers have larger areas of stability and are therefore a better choice for stiff problems like the *Van der Pol* system for large $\\mu$. In this example, we select the parameter $\\mu = 1000$ as a torture test do demonstrate PathSim's ability to handle severe stiffness. + +![Block diagram representation of the *Van der Pol* ODE built from distinct PathSim blocks. Schematic visualization of the encapsulation into a `Subsystem`.](assets/vanderpol_g.png) + +The following code implements the *Van der Pol* system with the basic **PathSim** blocks and encapsulates it into a `Subsystem`. + +```python + +from pathsim import Simulation, Connection, Interface, Subsystem +from pathsim.blocks import Integrator, Scope, Adder, Multiplier, Amplifier, Function +from pathsim.solvers import ESDIRK43 # <- implicit solver for stiff systems + +#initial condition +x1_0 = 2 +x2_0 = 0 + +#van der Pol parameter +mu = 1000 # <- very stiff + +#subsystem to emulate the ODE +If = Interface() +I1 = Integrator(x1_0) +I2 = Integrator(x2_0) +Fn = Function(lambda a: 1 - a**2) +Pr = Multiplier() +Ad = Adder("-+") +Am = Amplifier(mu) + +sub_blocks = [If, I1, I2, Fn, Pr, Ad, Am] +sub_connections = [ + Connection(I2, I1, Pr[0], If[1]), + Connection(I1, Fn, Ad[0], If[0]), + Connection(Fn, Pr[1]), + Connection(Pr, Am), + Connection(Am, Ad[1]), + Connection(Ad, I2) + ] + +#the subsystem acts just like a normal block +VDP = Subsystem(sub_blocks, sub_connections) +``` + +The subsystem `VDP` can now be treated like a regular block and included in the main simulation: + +```python +#scope for plotting +Sco = Scope(labels=["$x_1$"]) + +#blocks of the main system +blocks = [VDP, Sco] + +#the connections between the blocks in the main system +connections = [ + Connection(VDP, Sco) + ] + +#initialize simulation with the blocks, connections, and implicit solver +Sim = Simulation( + blocks, + connections, + Solver=ESDIRK43, + tolerance_lte_abs=1e-5, + tolerance_lte_rel=1e-3, + tolerance_fpi=1e-8 + ) + +#run the simulation +Sim.run(4*mu) + +#plot results from scope +Sco.plot(".-") +``` +Again, visualizing the results directy from the `Scope` block. +![Simulation results plotted from the PathSim `Scope` for the bouncing ball dynamics, including the detected events.](assets/vanderpol_result_g.png) # References From a7cd16485afd9e34ab511bab30d6859ef2f756f4 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Wed, 7 May 2025 17:10:40 +0200 Subject: [PATCH 22/33] fixed typo --- paper/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index aa17bb23..23685a8f 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -213,7 +213,7 @@ Another classic dynamical system is the *Van der Pol* oscillator, which is descr \end{eqnarray} ``` -where the parameter $\\mu$ controls the *stiffness*. Stiffness in dynamical systems typically arises when the (local) internal time constants (eigenvalues of the Jacobian) are on vastly different scales, or when very steep gradients are encountered. This forces explicit integrators to take extremely small timesteps in order for the discretized system to be stable. Implicit solvers have larger areas of stability and are therefore a better choice for stiff problems like the *Van der Pol* system for large $\\mu$. In this example, we select the parameter $\\mu = 1000$ as a torture test do demonstrate PathSim's ability to handle severe stiffness. +where the parameter $\\mu$ controls the *stiffness*. Stiffness in dynamical systems typically arises when the (local) internal time constants (eigenvalues of the Jacobian) are on vastly different scales, or when very steep gradients are encountered. This forces explicit integrators to take extremely small timesteps in order for the discretized system to be stable. Implicit solvers have larger areas of stability and are therefore a better choice for stiff problems like the *Van der Pol* system for large $\\mu$. In this example, we select the parameter $\\mu = 1000$ as a torture test to demonstrate PathSim's ability to handle severe stiffness. ![Block diagram representation of the *Van der Pol* ODE built from distinct PathSim blocks. Schematic visualization of the encapsulation into a `Subsystem`.](assets/vanderpol_g.png) From f37c45c0fde54d9d5bbc68f00170364e348da9be Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Wed, 7 May 2025 17:17:21 +0200 Subject: [PATCH 23/33] updated joss paper, fixed typos --- paper/paper.bib | 2 +- paper/paper.md | 8 ++++---- 2 files changed, 5 insertions(+), 5 deletions(-) diff --git a/paper/paper.bib b/paper/paper.bib index ebe20c2e..c5a5025d 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -55,7 +55,7 @@ @manual{Simulink } @misc{ModelicaRepo, - title = {Free (standard conforming) library to model mechanical (1D/3D), electrical (analog, digital, machines), magnetic, thermal, fluid, control systems and hierarchical state machines. Also numerical functions and functions for strings, files and streams are included.}, + title = {Modelica Standard Library}, organization = {Modelica Association}, howpublished = {\url{https://github.com/modelica/ModelicaStandardLibrary}}, month = {December}, diff --git a/paper/paper.md b/paper/paper.md index 23685a8f..703518fb 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -206,14 +206,14 @@ The results (plotted from the `Scope`) show the evolution of ball accross time. Another classic dynamical system is the *Van der Pol* oscillator, which is described by the second order nonlinear ODE -```math +$$ \begin{eqnarray} \dot{x}_1 &= x_2 \\ \dot{x}_2 &= \mu (1 - x_1^2) x_2 - x_1 \end{eqnarray} -``` +$$ -where the parameter $\\mu$ controls the *stiffness*. Stiffness in dynamical systems typically arises when the (local) internal time constants (eigenvalues of the Jacobian) are on vastly different scales, or when very steep gradients are encountered. This forces explicit integrators to take extremely small timesteps in order for the discretized system to be stable. Implicit solvers have larger areas of stability and are therefore a better choice for stiff problems like the *Van der Pol* system for large $\\mu$. In this example, we select the parameter $\\mu = 1000$ as a torture test to demonstrate PathSim's ability to handle severe stiffness. +where the parameter $\mu$ controls the *stiffness*. Stiffness in dynamical systems typically arises when the (local) internal time constants (eigenvalues of the Jacobian) are on vastly different scales, or when very steep gradients are encountered. This forces explicit integrators to take extremely small timesteps in order for the discretized system to be stable. Implicit solvers have larger areas of stability and are therefore a better choice for stiff problems like the *Van der Pol* system for large $\mu$. In this example, we select the parameter $\mu = 1000$ as a torture test to demonstrate PathSim's ability to handle severe stiffness. ![Block diagram representation of the *Van der Pol* ODE built from distinct PathSim blocks. Schematic visualization of the encapsulation into a `Subsystem`.](assets/vanderpol_g.png) @@ -288,7 +288,7 @@ Sco.plot(".-") Again, visualizing the results directy from the `Scope` block. -![Simulation results plotted from the PathSim `Scope` for the bouncing ball dynamics, including the detected events.](assets/vanderpol_result_g.png) +![Simulation results plotted from the PathSim `Scope` for *Van der Pol* Subsystem.](assets/vanderpol_result_g.png) # References From 6889d227a7f817c57dc874a3339f2e084d1e4b42 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Wed, 7 May 2025 17:25:57 +0200 Subject: [PATCH 24/33] fixed math display --- paper/paper.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 703518fb..a4d18159 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -206,12 +206,12 @@ The results (plotted from the `Scope`) show the evolution of ball accross time. Another classic dynamical system is the *Van der Pol* oscillator, which is described by the second order nonlinear ODE -$$ -\begin{eqnarray} + +$$\begin{eqnarray} \dot{x}_1 &= x_2 \\ \dot{x}_2 &= \mu (1 - x_1^2) x_2 - x_1 -\end{eqnarray} -$$ +\end{eqnarray}$$ + where the parameter $\mu$ controls the *stiffness*. Stiffness in dynamical systems typically arises when the (local) internal time constants (eigenvalues of the Jacobian) are on vastly different scales, or when very steep gradients are encountered. This forces explicit integrators to take extremely small timesteps in order for the discretized system to be stable. Implicit solvers have larger areas of stability and are therefore a better choice for stiff problems like the *Van der Pol* system for large $\mu$. In this example, we select the parameter $\mu = 1000$ as a torture test to demonstrate PathSim's ability to handle severe stiffness. From 461d8bc5896206a0b8e8d7f7692fcd43c139f29f Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Wed, 7 May 2025 17:29:24 +0200 Subject: [PATCH 25/33] fixed typo --- paper/paper.md | 7 +------ 1 file changed, 1 insertion(+), 6 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index a4d18159..700501a1 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -206,12 +206,7 @@ The results (plotted from the `Scope`) show the evolution of ball accross time. Another classic dynamical system is the *Van der Pol* oscillator, which is described by the second order nonlinear ODE - -$$\begin{eqnarray} - \dot{x}_1 &= x_2 \\ - \dot{x}_2 &= \mu (1 - x_1^2) x_2 - x_1 -\end{eqnarray}$$ - +$$\ddot{x} = \mu (1 - x^2) \dot{x} - x$$ where the parameter $\mu$ controls the *stiffness*. Stiffness in dynamical systems typically arises when the (local) internal time constants (eigenvalues of the Jacobian) are on vastly different scales, or when very steep gradients are encountered. This forces explicit integrators to take extremely small timesteps in order for the discretized system to be stable. Implicit solvers have larger areas of stability and are therefore a better choice for stiff problems like the *Van der Pol* system for large $\mu$. In this example, we select the parameter $\mu = 1000$ as a torture test to demonstrate PathSim's ability to handle severe stiffness. From f00f6997da93141f59ce1bcb794f05a76fc8cb98 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Fri, 9 May 2025 16:21:16 +0200 Subject: [PATCH 26/33] updated paper, only one example now --- paper/paper.md | 176 +------------------------------------------------ 1 file changed, 3 insertions(+), 173 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 700501a1..b36534c9 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -59,13 +59,11 @@ PathSim employs a decentralized, object-oriented design centered around three pr # PathSim Modelling Flow -PathSim is a script based modelling framework, with no built in graphical user interface. Therefore it makes sense to start from the block diagram of the system to be modelled. The following sections demonstrate PathSims modelling and simulation flow. The examples cover classical dynamical systems such as the *harmonic oscillator*, the *bouncing ball* (to showcase the event handling system) and the *Van der Pol* system (as a stiff subsystem). - -## Harmonic Oscillator +PathSim is a script based modelling framework with no built in graphical user interface. Therefore it makes sense to start from the block diagram of the system to be modelled. This section demonstrates PathSims modelling and simulation flow on a classical example dynamical system, the *harmonic oscillator*. The figure below shows the mechanical representation of the harmonic oscillator to the left and its block diagram to the right. -![Mechanical representation of the harmonic oscillator to the left and its block diagram to the right.](assets/harmonic_oscillator_g.png) +![Mechanical representation of the harmonic oscillator to the left and its block diagram to the right as a schematic viasualization to help with the assembly of the system im PathSim (PathSim is purely script based)](assets/harmonic_oscillator_g.png) Translating it to PathSim involves importing the blocks from the block library, instantiating them with their correct parameters, connecting them with the `Connection` object and passing everything to the `Simulation`. @@ -115,175 +113,7 @@ The `Scope` block enables fast plotting of the simulation results as well as the ![Simulation results plotted from the PathSim `Scope` for the harmonic oscillator example.](assets/harmonic_oscillator_result_g.png) - -## Bouncing Ball - -The classical example for demonstrating event handling is the bouncing ball. The ball accelerates downward due to gravity and onece it hits the floor, it bounces back. The dynamics of this system are discontinuous due to the jump in velocity (sign change) exactly at the bounce. This is called a discrete event, specifically a zero-crossing event. Systems like this require the location and resolution of discrete events within the timestep and are not easily solved with standard numerical ODE solvers. **PathSim** implements an event management system, that can track the system state and locate and resolve specified events. - -![Schematic of the bouncing ball dynamics to the left and the corresponding block diagram with two distinct integrators and the event handler to the righ.](assets/bouncing_ball_g.png) - -The following code block defines the bouncing ball system in PathSim, utilizing the `ZeroCrossing` event manager to track the height of the ball and trigger the jump in velocity. - -```python -from pathsim import Simulation, Connection -from pathsim.blocks import Integrator, Constant, Scope -from pathsim.events import ZeroCrossing #event manager -from pathsim.solvers import RKBS32 #adaptive solver - -#elasticity of bounce and gravitational acceleration -b, g = 0.9, 9.81 - -#initial conditions -x0, v0 = 1, 5 - -#blocks that define the system -Ix = Integrator(x0) # v -> x -Iv = Integrator(v0) # a -> v -Cn = Constant(-g) # gravitational acceleration -Sc = Scope(labels=["x", "v"]) - -blocks = [Ix, Iv, Cn, Sc] - -#the connections between the blocks -connections = [ - Connection(Cn, Iv), - Connection(Iv, Ix), - Connection(Ix, Sc[0]) - ] - -#event function for zero crossing detection -def func_evt(t): - *_, x = Ix() #get block outputs and states - return x - -#action function for state transformation -def func_act(t): - *_, x = Ix() - *_, v = Iv() - Ix.engine.set(abs(x)) - Iv.engine.set(-b*v) - -#events (zero crossing) -E1 = ZeroCrossing( - func_evt=func_evt, - func_act=func_act, - tolerance=1e-4 - ) - -events = [E1] - -#initialize simulation from blocks, connections and events -Sim = Simulation( - blocks, - connections, - events, - dt=0.01, - dt_max=0.04, - Solver=RKBS32 - ) - -#run the simulation -Sim.run(10) - -#read the recordings from the scope direclty -time, [data_x] = Sc.read() - -#plot the recordings from the scope -fig, ax = Sc.plot() - -#add detected events to scope plot -for t in E1: - ax.axvline(t, ls="--", c="k") - -``` - -The results (plotted from the `Scope`) show the evolution of ball accross time. The dashed lines indicate the locations of the bounces (detected events): - -![Simulation results plotted from the PathSim `Scope` for the bouncing ball dynamics, including the detected events.](assets/bouncing_ball_result_events_g.png) - - -## Van der Pol System - -Another classic dynamical system is the *Van der Pol* oscillator, which is described by the second order nonlinear ODE - -$$\ddot{x} = \mu (1 - x^2) \dot{x} - x$$ - -where the parameter $\mu$ controls the *stiffness*. Stiffness in dynamical systems typically arises when the (local) internal time constants (eigenvalues of the Jacobian) are on vastly different scales, or when very steep gradients are encountered. This forces explicit integrators to take extremely small timesteps in order for the discretized system to be stable. Implicit solvers have larger areas of stability and are therefore a better choice for stiff problems like the *Van der Pol* system for large $\mu$. In this example, we select the parameter $\mu = 1000$ as a torture test to demonstrate PathSim's ability to handle severe stiffness. - -![Block diagram representation of the *Van der Pol* ODE built from distinct PathSim blocks. Schematic visualization of the encapsulation into a `Subsystem`.](assets/vanderpol_g.png) - -The following code implements the *Van der Pol* system with the basic **PathSim** blocks and encapsulates it into a `Subsystem`. - -```python - -from pathsim import Simulation, Connection, Interface, Subsystem -from pathsim.blocks import Integrator, Scope, Adder, Multiplier, Amplifier, Function -from pathsim.solvers import ESDIRK43 # <- implicit solver for stiff systems - -#initial condition -x1_0 = 2 -x2_0 = 0 - -#van der Pol parameter -mu = 1000 # <- very stiff - -#subsystem to emulate the ODE -If = Interface() -I1 = Integrator(x1_0) -I2 = Integrator(x2_0) -Fn = Function(lambda a: 1 - a**2) -Pr = Multiplier() -Ad = Adder("-+") -Am = Amplifier(mu) - -sub_blocks = [If, I1, I2, Fn, Pr, Ad, Am] -sub_connections = [ - Connection(I2, I1, Pr[0], If[1]), - Connection(I1, Fn, Ad[0], If[0]), - Connection(Fn, Pr[1]), - Connection(Pr, Am), - Connection(Am, Ad[1]), - Connection(Ad, I2) - ] - -#the subsystem acts just like a normal block -VDP = Subsystem(sub_blocks, sub_connections) -``` - -The subsystem `VDP` can now be treated like a regular block and included in the main simulation: - -```python -#scope for plotting -Sco = Scope(labels=["$x_1$"]) - -#blocks of the main system -blocks = [VDP, Sco] - -#the connections between the blocks in the main system -connections = [ - Connection(VDP, Sco) - ] - -#initialize simulation with the blocks, connections, and implicit solver -Sim = Simulation( - blocks, - connections, - Solver=ESDIRK43, - tolerance_lte_abs=1e-5, - tolerance_lte_rel=1e-3, - tolerance_fpi=1e-8 - ) - -#run the simulation -Sim.run(4*mu) - -#plot results from scope -Sco.plot(".-") -``` - -Again, visualizing the results directy from the `Scope` block. - -![Simulation results plotted from the PathSim `Scope` for *Van der Pol* Subsystem.](assets/vanderpol_result_g.png) +There more *examples* of dynamical system simulations present in the PathSim repository and, with further explanations, in the documentation. The examples cover all features PathSim has to offer, including hierarchical modelling through *subsystems*, examples of *stiff dynamics* with implicit solver and discrete dynamics with *event handling*. # References From 7ffd726deff659517c51e21fe74c897de41bf4f8 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Tue, 13 May 2025 14:40:09 +0200 Subject: [PATCH 27/33] updated figures of paper --- paper/assets/bouncing_ball_g.png | Bin 107468 -> 274203 bytes .../assets/bouncing_ball_result_events_g.png | Bin 44634 -> 0 bytes paper/assets/harmonic_oscillator_result_g.png | Bin 44123 -> 182473 bytes paper/assets/vanderpol_g.png | Bin 123917 -> 202649 bytes paper/assets/vanderpol_result_g.png | Bin 28321 -> 0 bytes paper/paper.md | 11 +++++++++-- 6 files changed, 9 insertions(+), 2 deletions(-) delete mode 100644 paper/assets/bouncing_ball_result_events_g.png delete mode 100644 paper/assets/vanderpol_result_g.png diff --git a/paper/assets/bouncing_ball_g.png b/paper/assets/bouncing_ball_g.png 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Function(np.sin) sco = Scope(labels=[r"$\omega$", r"$\varphi$"]) #simulation instance from the blocks and connections sim = Simulation( blocks=[in1, in2, amp, fnc, sco], connections=[ Connection(in1, in2, sco[0]), Connection(in2, fnc, sco[1]), Connection(fnc, amp), Connection(amp, in1) ], Solver=RKCK54, tolerance_lte_rel=1e-6, tolerance_lte_abs=1e-8 ) #run the simulation for 15 seconds sim.run(15) #read the results directly from the scope for postprocessing time, [omega, phi] = sco.read() #plot the results for quick visualization sco.plot(".-") sco.plot2D() PathSimScopeIntegrator 1ω0Integrator 2φ0φ(t)ω(t)lφ0gFunctionsinAmpg/lto Block Diagramto PathSimResults \ No newline at end of file diff --git a/paper/assets/pendulum_block_diagram.svg b/paper/assets/pendulum_block_diagram.svg deleted file mode 100644 index b72919b9..00000000 --- a/paper/assets/pendulum_block_diagram.svg +++ /dev/null @@ -1 +0,0 @@ -ScopeIntegrator 1ω0Integrator 2φ0φ(t)ω(t)lφ0gFunctionsinAmpg/l \ No newline at end of file diff --git a/paper/assets/pendulum_result_phasespace.svg b/paper/assets/pendulum_result_phasespace.svg deleted file mode 100644 index 109845f9..00000000 --- a/paper/assets/pendulum_result_phasespace.svg +++ /dev/null @@ -1,583 +0,0 @@ - - - - - - - - 2025-04-23T13:59:18.992063 - image/svg+xml - - - Matplotlib v3.8.3, https://matplotlib.org/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/paper/assets/pendulum_result_timeseries.svg b/paper/assets/pendulum_result_timeseries.svg deleted file mode 100644 index a5b10f53..00000000 --- a/paper/assets/pendulum_result_timeseries.svg +++ /dev/null @@ -1,1313 +0,0 @@ - - - - - - - - 2025-04-23T13:59:26.295443 - image/svg+xml - - - Matplotlib v3.8.3, https://matplotlib.org/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/paper/paper.md b/paper/paper.md index 1d5b80b5..3623511a 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -53,7 +53,7 @@ The decentralized design promotes modularity, as blocks are fully self-contained # PathSim Modeling Flow -![Example dynamical system modeling flow using PathSim](assets/pathsim_flow.svg) +![Example dynamical system modeling flow using PathSim](assets/pathsim_flow.png) From 864a78c9881633b8cc1e6c469c82e6630a319bb0 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Wed, 23 Apr 2025 17:06:31 +0200 Subject: [PATCH 09/33] updated paper.md --- paper/paper.md | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 3623511a..c74016ba 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -28,7 +28,7 @@ PathSim is a flexible, block-based, time-domain dynamical system simulation fram # Statement of Need -Simulating dynamical systems is vital across many disciplines. PathSim meets the need for a Python-native framework combining a programmatic block-diagram approach with advanced features. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), easier extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis, Cosimulation and Hardware in the Loop (HiL) testing. PathSim specifically addresses: +Modeling and simulating dynamical systems is vital across many disciplines. PathSim meets the need for a Python-native framework combining a programmatic block-diagram approach with advanced features. Traditional simulation tools often rely on centralized solvers or compiled code, which can limit flexibility and extensibility within the Python ecosystem. PathSim's decentralized architecture offers distinct advantages: enhanced modularity (blocks are self-contained units), easier extensibility (new blocks integrate naturally without core modification), and greater flexibility in model composition and analysis, Cosimulation and Hardware in the Loop (HiL) testing. PathSim specifically addresses: * **Accessible Hybrid System Simulation:** Integrates event detection (zero-crossing, scheduled) directly into the block-diagram paradigm, simplifying the modeling of systems with both *continuous and discrete dynamics*. * **Gradient-Enabled Simulation:** Provides built-in *automatic differentiation* for sensitivity analysis and integration with gradient-based optimization or machine learning frameworks. @@ -53,10 +53,11 @@ The decentralized design promotes modularity, as blocks are fully self-contained # PathSim Modeling Flow -![Example dynamical system modeling flow using PathSim](assets/pathsim_flow.png) - - +The figure below shows the modeling and simulation flow with PathSim. Once the dynamical system is translated to the block-diagram paradigm, it can be built from PathSim blocks and connections. The code to the right shows block instantiation, connection definition, simulation setup (including solver and tolerance selection), execution, and result visualization. +![Exemplary dynamical system modeling and simulation flow using PathSim](assets/pathsim_flow.png) + +Full examples demonstrating event handling, stiff systems, and sensitivity analysis are available in the software repository [@PathSimRepo] and documentation [@PathSimDocs]. # References From 796390c1605d9c51e0644336d2fccfd70b1d8175 Mon Sep 17 00:00:00 2001 From: Milan Rother Date: Wed, 23 Apr 2025 17:13:05 +0200 Subject: [PATCH 10/33] updated paper.md --- paper/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index c74016ba..1166a43a 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -1,5 +1,5 @@ --- -title: 'PathSim - A Decentralized System Simulation Framework' +title: 'PathSim - A System Simulation Framework' tags: - Python - system simulation From 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