 # Inverted Pendulum Controls Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

The problem is to move the cart supporting a rod so that the rod does not fall, or—even better—so that the rod stays vertical. This classic problem appears in the control of the Segway invented by Dean Kamen. The solution shown here uses a proportional derivative controller. Other parameters can be examined using this example, but at some point it becomes too complicated for a simple visualization. You can vary several parameters to demonstrate the stability of the device, which can be instructive. The problem includes free body diagrams and variables that can be included in future versions.

Contributed by: Stephen Wilkerson (Towson University) and Nathan Slegers (University of Alabama, Huntsville) with contributions by Franz Brandhuber (March 2011)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

Here are the equations used:  Control law: glossary of terms: is the length of the pendulum is the small mass on top of the pendulum is the mass of the sled is the force applied to the sled to keep the pendulum in the vertical position is the force on the small mass (here 0) is the rotation of the pendulum is the rotation rate of the pendulum is the rotational acceleration of the pendulum is the displacement of the sled is the velocity of the sled is the acceleration of the sled is the acceleration due to gravity is the angular damping of inverted pendulum shaft is the initial angle of the pendulum is the initial angle rate assumed as zero is the initial displacement of the sled assumed at zero is the initial velocity of the sled assumed at zero is the proportional displacement gain is the proportional angle gain is the derivative displacement gain is the derivative angle gain

## Permanent Citation

Stephen Wilkerson (Towson University) and Nathan Slegers (University of Alabama, Huntsville) with contributions by Franz Brandhuber

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send