Linear Double Inverted Pendulum

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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.

  • 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
Mass of linear double pendulum assembly  0.364 kg
Medium pendulum mass (with T-fitting)  0.127 kg
Medium pendulum length (pivot to tip)  33.65 cm
Short pendulum mass (with T-fitting)  0.097 kg
Short pendulum length (pivot to tip) 20.0 cm
Mass of encoder hinge  0.141 kg
Pendulum encoder resolution (in quadrature) 4096 counts/rev


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.

To set up your Linear Double Inverted Pendulum workstation, you need additional components. Quanser engineers recommend:

for MATLAB®/Simulink® users for LabVIEW™ users
1x Linear Servo Base Unit 1x Linear Servo Base Unit
1x Q8-USB data acquisition device¹ 1x VoltPAQ-X1 linear voltage amplifier
1x VoltPAQ-X1 linear voltage amplifier Quanser Rapid Control Prototyping toolkit software
QUARC real-time control software and one of the following options:
  - 1x NI CompactRIO controller² with 2x Quanser Q1-CRIO module
  - 1x NI M- or X-series data acquisition device³ with 1x Quanser NI Terminal Board

¹ alternatively, you can use QPIDe or any equivalent NI DAQ device supported by QUARC
² NI cRIO-9074, or NI cRIO-9024 with cRIO-9113 or cRIO-9114 chassis
³ NI PCIe-6351 or other NI DAQ device with 4 encoders supported by Quanser RCP toolkit. Alternatively, you can use Quanser Q8-USB, or QPIDe

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Linear Flexible Inverted Pendulum
High Fidelity Linear Cart System
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