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Example notebooks

Introductory examples

If you haven't already, check out the tutorials, which explain how to build and simulate models in Collimator.

Primitive blocks and composability

Shows how to build systems with primitive blocks and how to compose them into larger diagrams.

Bouncing ball

Shows hybrid dynamics modeling of a bouncing ball.

Linear Quadratic Regulator (LQR)

Demonstrates the LQR for a pendulum and a planar quadrotor model.

Energy shaping and LQR stabilization

Demonstrates energy shaping control to swing a pendulum to the vertically 'up' orientation and then stabilize it in the 'up' orientation via LQR.

Linear Model Predictive Control (MPC)

Demonstrates MPC on a linearized model of the Cessna Citation aircraft and a pendulum model.

Interacting with the Dashboard

Demonstrates how to interact with Collimator's Dashboard to upload your local models, import Dashboard models and run simulations on the cloud.

Advanced examples

Trajectory optimization and stabilization

Shows trajectory optimization for the problem of swinging an Acrobot to the vertically 'up' orientation and then stabilizing the trajectory via finite-horizon LQR.

Automatic tuning of a PID controller

Demonstrates automatic differentiation and optimization capabilities of Collimator to automatically tune the gains of a discrete-time PID controller.

Finding limit cycles

Demonstrates how to find limit cycles and assess their stability by leveraging the automatic differentiation capabilities of Collimator.

Nonlinear MPC

See thematic series on modeling and control of 3D quadcopter below, which showcases trajectory tracking by nonlinear MPC.


Demonstrates how to download a submodel defined in the Dashboard, incorporate it in a local model to run an optimization workflow and upload the result to the Dashboard.

Thematic examples

Battery modeling

  1. Equivalent circuit model (ECM) for a battery
  2. ECM parameter estimation: synthetic data
  3. ECM parameter estimation: experimental data
  4. Data-driven modeling: Dynamic Mode Decomposition (DMD)
  5. Data-driven modeling: Extended DMD
  6. Data-driven modeling: SINDy with control
  7. Data-driven modeling: Neural Networks

3D quadcopter modeling and control

  1. 3D quadcopter modelling
  2. Trajectory generation through differentially flat outputs
  3. Control with nonlinear MPC