SystemModeler – Uses and Examples of Wolfram SystemModeler

Wolfram SystemModeler

Uses and Examples of Wolfram SystemModeler

SystemModeler makes it easy to develop detailed, realistic models in any industry or application area. A core set of physical and logical components is built-in, and custom libraries can be developed to represent the key elements and processes in any domain. Modeling, simulation, visualization, and analysis with Mathematica are tightly integrated, dramatically reducing development time.

Controlling a Satellite Path

Model a satellite with a combination of 3D mechanics and block-based control logic. The satellite is launched from the Earth's surface with a launch sequence. Then a control logic subsystem adjusts altitude and velocity via thrusters. Mathematica is used to design the parameters of the control system.


  • Visualize the path of the satellite with and without controller adjustments.
  • Design the parameters of the altitude controller of the satellite in Mathematica.
  • Easily show the altitude and energy expenditure for different control parameters.


Driveline: Analyze a Drive Cycle

A model of a vehicle driveline can be used to evaluate performance measures. This example explores how the transmission control unit parameters affect fuel consumption.


  • Build up complex models in layers with separately testable and reusable subcomponents.
  • The EPA drive cycle is easily imported to the model with the link between Mathematica and SystemModeler.
  • Analyze the fuel consumption during the highway drivecycle.


Per Nobrant Driveline Modelling using MathModelica.
2001-02-27, Master Thesis performed in Vehicular Systems at Linköpings Institute of Technology.

Construction Equipment and Large Machine Simulation

Construction equipment is built in a wide variety of sizes and configurations to execute specific tasks. With SystemModeler, it is easy to try different design options before building the physical system. This example explores different scenarios, such as the reachable positions of the excavator bucket.


  • Use the built-in MultiBody library to model the excavator.
  • Quickly develop interfaces to generate simulation data in Mathematica and export to your simulation.
  • Add textures to the model and clearly see the real-world resemblance.
      CAD Animation


Active Damping: Control Diesel Engine Vibrations

Vibrations caused by heavy machinery can pose problems to structural integrity, especially if mounted on a steel structure or chassis. This model explores how to minimize vibrations in a diesel engine using a tuned mass damper.


  • Symbolically analyze the model equations in Mathematica to see how varying the parameters affects damping.
  • Do automatically parallelized parameter sweeps varying the spring damping constant and the damping mass.
  • Visualize the vibrations of the engine for different parameter combinations.
  • Interactively select the mass and spring constant of the tuned damper and instantly view the vibration displacement.
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Active Damping

Optimal Control for a Continuously Stirred Tank Reactor

Find an optimal control signal for a continuously stirred tank reactor (CSTR). The temperature in the tank influences a reaction rate, while the temperature in the cooling jacket acts as a control signal. The goal is to go from one concentration to another as quickly as possible while obeying safety limitations in temperature.


  • Get the equations governing tank behavior into Mathematica for in-depth analysis.
  • Use the optimization functionality in Mathematica to find an optimal cooling temperature.
  • Adjust the control signal interactively and instantly see how the system responds.
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Optimal Control for a Continuously Stirred Tank Reactor

Human Interface Design (HID): Design a Joystick

Exploring alternative product designs through modeling and simulation can be faster and cheaper than experimenting on physical prototypes. This model compares three designs for a spring-based recentering mechanism for an analog joystick.


  • Build up complex models in layers with separately testable and reusable subcomponents.
  • Compare the performance of different designs under test conditions.
  • The model is built using components from the mechanical MultiBody library, so 3D visualization of simulation results is automatic.
      3D Animation

Joystick Design

Simulation of Changing Refrigerator Temperatures

Real-world systems often exhibit rapid changes or discontinuities that must be resolved accurately during numerical simulation. This example simulates a household refrigerator freezer in several scenarios, correctly handling events such as the sudden triggering of a thermostat or the opening of a compartment door.


  • Correctly handle discontinuities associated with opening and closing compartment doors and with thermostats triggered by changing temperatures.
  • Compare performance under different conditions, such as the addition of hot food to a normally loaded versus a near-empty refrigerator compartment.
  • Combine different physical domains, including fluid heat flow (air circulation), thermal (food and insulation), and signal processing (thermostat).

Refrigerator Freezer

Electric Kettle: Controlled Heating Process

Controlled fluid heating processes are used in many industrial and residential applications, including boilers, petrochemical reactors, and more. This example simulates a controlled heating process in a water heater.


  • Combine components from different physical domains such as electrical (heating circuit), thermal (water), and logical (controller) units.
  • The link between Mathematica and SystemModeler makes it possible to optimize parameter settings to fit the model to measurement data.
  • Easily create realistic models and custom components with built-in electrical, magnetic, mechanical, and other libraries.

Electric Kettle

House Heating: Compare Energy Consumption

Models for heating and cooling of buildings are important to estimate power consumption, construct energy-efficient buildings, and minimize costs. This model compares power consumption for heating homes in different geographic locations.


  • Modeling the rooms and their subcomponents in a hierarchical way makes it easy to maintain or expand the model.
  • Plug data from your measurements or curated data from Mathematica into your model to compare house heating needs in different locations.
  • Compare the estimated power cost for different indoor temperatures.

House Heating

Insulin Signaling: Modeling a Biochemical Process

Insulin signaling in fat cells plays an important role in controlling the glucose level in the body. Insulin binding to receptors causes them to phosphorylate, transducing the insulin signal into the cells, controlling glucose uptake.


  • Model insulin signals with the included BioChem library.
  • Compare how different real-world parameter combinations affect IRS1 (Insulin Receptor Substrate 1) phosphorylation.
  • Easily identify the parameters that affect the phosphorylation most when changed.

Insulin Signaling

LEGO Segway: Controlling an Inverted Pendulum

Controlling inverted pendulums in different forms is common in engineering. They can be found in everything, from rockets during liftoff to skyscrapers and Segways. Build a control system for a Segway constructed out of LEGO Mindstorms NXT components.


  • Construct components for parts of the LEGO Segway using existing libraries.
  • Linearize the model around the upright stationary point.
  • Use Mathematica to find suitable controller gains to keep the Segway upright..
  • View the 3D animation that is automatically generated from the model.
      3D Animation

LEGO Segway

Bungee Jump: Simulate Multibody Systems

Easily model multibody systems, including springs, dampers, forces, joints, bodies, and more, using built-in libraries. Below is a simple model of a bungee jumper consisting of a mass attached to a platform by a spring and damper.


  • Get an accurate representation of the final system with automatically generated 3D animations.
  • See how changes in cord damping, inital speed, position of the jumper, and other factors affect the jump.
  • Use components from the built-in Multibody library to create the model by simple drag-and-drop functionality.

Bungee Jump

Bouncing Balls: Handle Events and Discontinuities

Model and simulate balls bouncing on the ground or in a box, taking advantage of powerful event handling in SystemModeler. Two models are used—one where a ball bounces on the ground and one where multiple balls are constrained in a two-dimensional box.


  • Simulate a bouncing ball several times for different parameters and initial values with a single command in Mathematica.
  • Event detection in Modelica allows changing of the model behavior when balls collide with a wall.
  • Visualize bouncing balls in a constrained 2D box with custom animations and plots.
  • Distribute simulation results as an interactive CDF document.
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Bouncing Balls

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