Analysis & Design with Mathematica

Bring the full power of Mathematica to your model analysis. Programmatically control SystemModeler simulations and use built-in functions for finding model equilibria, linearizing models, and more. Perform model calibration and system optimization using Mathematica's symbolic and numerical features, and present your results with advanced graphics and interactivity.


Programmatic Simulation Control

Get complete control over SystemModeler simulations from within Mathematica's interactive notebook environment. Programmatically specify initial conditions, parameter values, and input signal functions. Sweeps of simulations across sets of parameter values automatically run in parallel.
Programmatic Simulation Control

Optimization & Design

Use Mathematica to help plan the geometry of 3D mechanical systems, prototype equation-based custom components, and more. Once the model is assembled in SystemModeler, use Mathematica to find optimal model parameters. Easily create custom user interfaces for manual exploration, numerical experimentation, and tuning.
Optimization & Design

Model & Equation Analysis

Access model equations and properties from Mathematica and use its symbolic mathematics functions to perform analyses on system equations such as finding closed form solutions, investigating approximate solutions, or solving for optimal parameter values or special states. Automatically perform constrained or unconstrained searches for equilibrium states.
Model & Equation Analysis

Control System Design

A full suite of control systems features is built in to Mathematica, including stability and frequency analysis, visualization, and controller design. Automatically linearize SystemModeler models into Mathematica's standard state-space representation for linear time-invariant (LTI) systems. Use numerical model linearization, or preserve named parameters for further symbolic analysis.
Control System Design
Related Examples:
LEGO Segway» | Satellite»

All of Mathematica

SystemModeler model equations and simulation results are accessible in Mathematica in a completely native form, immediately suitable for use with Mathematica's large collections of algorithms for symbolic and numerical mathematics. Mathematica is well-suited for model analysis with powerful statistics and data analysis, graphics, automatic interactivity, and thousands of other features.
All of Mathematica
 

Model Calibration

Fit free parameters by calibrating models against real-world data. Explore the parameter space by running SystemModeler simulations from Mathematica. Find the best-fitting parameter values using Mathematica's optimization features, and programmatically insert them back into the SystemModeler model.
Model Calibration
Related Examples:
Electric Kettle»
Documentation:
WSMSimulate» | Optimization»

Sensitivity Analysis

Simulate models while obtaining the sensitivity of system variables with respect to specified parameters. Sensitivity band plotting is built in. Discover which system variables are most sensitive to parameters of interest or which parameters have the greatest effect on system behavior.
Sensitivity Analysis

Plotting & Custom Visualization

Plot variables and sensitivity bands directly from simulation results. SystemModeler simulation results are immediately available in a standard interpolating function format, suitable for use in any of Mathematica's visualization functions. Create custom graphics, animations, and customizable user interfaces for running simulations and visualizing the results.
Plotting & Custom Visualization

Computable Data

Directly import Modelica model files and saved SystemModeler simulation results into Mathematica. Import and export data in any of 100+ formats natively supported by Mathematica, including input data formats of Modelica Standard Library components. Simulate models under realistic conditions by programmatically accessing Wolfram|Alpha's huge collection of data on weather, earthquakes, tides, and hundreds of other areas. Export graphics and animations in all standard image and multimedia formats.
Computable Data

Notebook Environment

The Mathematica environment is designed to make exploration and analysis as efficient as possible. Entering commands into a Mathematica notebook automatically creates a record of your work that can be shared with colleagues or reused and improved for future analyses. Notebooks combine code, data, explanatory text, plots and graphics, and interactive elements in a single platform-independent Computable Document Format (CDF).
Notebook Environment
Related Examples:
Bouncing Balls» | Active Damping»


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