Linear Flexible Inverted Pendulum

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Expand the Classic Inverted Pendulum Challenge

The Linear Flexible Inverted Pendulum is ideal to introduce intermediate and advanced control concepts and theories relevant to real-world challenges of stabilizing large lightweight structures.

The Linear Flexible Inverted Pendulum module is used attached to the Linear Servo Base Unit (IP02). This set up augments the classic inverted pendulum challenge by introducing a flexible link that requires balancing. Students learn how to:

  • obtain a state-space representation of the open-loop system
  • design and tune a LQR-based state-feedback controller
  • 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 fuzzy control, nonlinear control, adaptive control and intelligent control.

How It Works

The Linear Flexible Inverted Pendulum module is composed of a rigid 24-inch aluminum blue rod and a flexible link with an end weight mounted at the end. The module easily attaches to the front pendulum shaft on the Linear Servo Base Unit cart and is free to rotate 360 degrees. The angles of the pendulums are sensed using the Linear Servo pendulum shaft encoder. The deflection angle of the flexible link is measured using an analog strain gage sensor.

The balance control applies a voltage to the Linear Servo cart based on the rigid and flexible pendulum angles such that both the rigid and flexible pendulums are balanced in the upright, vertical position. The robustness of the system can be tested when the strain gage measurement is not used.

Quanser-develop Courseware Included

The Linear Flexible Inverted Pendulum comes with Quanser-developed courseware materials. 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.

  • High resolution optical encoders to sense pendulum angles
  • Strain gage to measure flexible pendulum deflection
  • 24-inch rigid blue pendulum and flexible link with end-weight
  • Easy-connect cables and connectors
  • Module easily attaches to front shaft of the Linear Servo Base Unit
  • 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
Rigid pendulum mass (with T-fitting) 0.230 kg
Rigid pendulum length (pivot to tip) 64.1 cm
Flexible pendulum mass (with T-fitting and weight) 0.458 kg
Flexible pendulum length (pivot to tip) 43.5 cm
Mass of flexible pendulum end weight 0.256 kg
Pendulum shaft encoder resolution (in quadrature) 4096 counts/rev
Strain gage measurement range ± 5 V
Strain gage sensitivity 2.54 cm/V
Flexible link stiffness 2.64 N.m/rad


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

To set up your Linear Flexible 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 Q2-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 myRIO with 1x Quanser Terminal Board for NI myRIO, or
  - 1x NI CompactRIO controller² with 1x Quanser Q1-CRIO module, or
  - 1x NI M- or X-series data acquisition device³ with 1x Quanser NI Terminal Board

¹ alternatively, you can use Q8-USB, 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 DAQ device must be supported by Quanser RCP toolkit. Alternatively, you can use Quanser Q2-USBQ8-USB, or QPIDe

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Linear Double Inverted Pendulum
High Fidelity Linear Cart System
Linear Flexible Joint
Rotary Flexible Link
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