# 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.

### Submodels

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

- Equivalent circuit model (ECM) for a battery
- ECM parameter estimation: synthetic data
- ECM parameter estimation: experimental data
- Data-driven modeling: Dynamic Mode Decomposition (DMD)
- Data-driven modeling: Extended DMD
- Data-driven modeling: SINDy with control
- Data-driven modeling: Neural Networks