Linear Double Inverted Pendulum


Take the Classic Inverted Pendulum Challenge to the Next Level

The Linear Double Inverted Pendulum module is ideal to introduce intermediate and advanced control concepts, taking the classic single inverted pendulum challenge to the next level of complexity. You can use it to demonstrate real-world control challenges related, for example, to takeoff stabilization of a multi-stage rocket

The Linear Double Inverted Pendulum module is used attached to the Linear Servo Base Unit. With this setup students learn how to:

  • obtain a state-space representation of the open-loop system
  • design a state-feedback controller to balance a double pendulum, while tracking the linear servo cart position
  • simulate the system and use the designed state-feedback controller to ensure the system is stabilized
  • implement the controller and evaluate the system’s performance

In addition to teaching intermediate control concepts, the Linear Flexible Inverted Pendulum can be used for research in various areas, including robust and optimal control.

How It Works

The Double Inverted Pendulum module consists of two aluminum, precision-machined blue rods; one seven inches long and the other 12 inches long. The module easily attaches to the front pendulum shaft on the Linear Servo Base Unit cart and is free to rotate 360 degrees. The short link angle is sensed using the Linear Servo pendulum shaft encoder, while the medium length link is measured using the middle encoder mounted on the Linear Double Inverted Pendulum itself.

Based on the cart position and the pendulum angles, the balance control computes a voltage that is applied to the cart motor. The cart moves back and forth to balances the two pendulums and keep them in the upright, vertical position.

Quanser-developed Courseware Included

The Linear Double Inverted Pendulum comes with Quanser-developed courseware. The Laboratory Guide, together with quick start resources, a comprehensive User Manual, pre-designed controllers and a system model allow you to get your lab running faster, saving months of time typically required to develop lab materials.

Click here to view the Demonstration Video


  • Module easily attaches to front shaft of Linear Servo Base Unit
  • Two pendulum sizes supplied: medium and long
  • High resolution optical encoders to sense pendulum angle
  • Easy-connect cable and connectors
  • High quality aluminum and precision-crafted parts
  • Fully compatible with MATLAB®/Simulink® and LabVIEW™
  • Fully documented system models and parameters provided for MATLAB®, Simulink®, LabVIEW™ and Maple™
  • Open architecture design, allowing users to design their own controller

Curriculum Topics Provided

Topics included in the Quanser-developed courseware:

Modeling Topics

  • Derivation of dynamic model using Lagrange
  • State-space representation
  • Linearization

Control Topics

  • Linear-quadratic regulator (LQR)

The Linear Double Inverted Pendulum can be also used to teach other topics that are not included in the Quanser-developed courseware.

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