Linear Flexible Joint with Inverted Pendulum

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Introduce Control Concepts Related to Vibration Analysis and Resonance

The Linear Flexible Joint with Inverted Pendulum system is ideal to introduce intermediate control concepts related to vibration analysis and resonance. You can use it to demonstrate real-world control challenges encountered, for example, in elastic linkages and mechanical transmissions. The Linear Flexible Joint with Inverted Pendulum module is used paired with the Linear Servo Base Unit (IP02). With this setup students learn how to:

  • obtain a state-space representation of the open-loop system
  • design and tune an LQR-based state-feedback controller that can balance an inverted pendulum mounted on the linear flexible joint cart while minimizing the spring deflection
  • using the designed state-feedback control, simulate the system and ensure it is stabilized
  • implement the state-feedback controller on the actual system and evaluate its performance

In addition to teaching intermediate control concepts, Linear Flexible Joint with Inverted Pendulum can be used for research in various areas, including system inversion and time optimization.

How It Works

The Linear Flexible Joint with Inverted Pendulum consists of a Linear Flexible Joint module with a passive linear cart coupled to a Linear Servo Base Unit through a linear spring and a pendulum mounted on the output cart.

The Linear Flexible Joint is made of solid aluminum and uses linear bearings to slide along the Linear Servo Base Unit ground stainless steel shaft. The cart position is measured using a rotary optical encoder whose shaft meshes with the track via a pinion. The system is supplied with two additional masses that can be mounted atop the cart.

As the Linear Servo Base Unit moves back and forth, the Linear Flexible Joint cart will naturally tend to oscillate. Using feedback control, one can attempt to attenuate these motions.

The passive cart is equipped with a rotary joint, the joint’s axis of rotation is perpendicular to the direction of the cart’s motion. A free-swinging rod can be attached to the joint, suspended in front of the cart. This rod can function as an inverted pendulum, as well as a regular pendulum. The angle of the rod is measured using a rotary optical encoder

Two different pendulum rods are supplied : a 12-inch "medium" pendulum and a 24-inch "long" pendulum.

Quanser-develop Courseware Included

The Linear Flexible Joint with 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.

  • High quality aluminum and precision-crafted parts
  • High resolution optical encoders to sense cart position and the pendulum angle
  • Pendulum easily attaches to the front shaft of a Linear Flexible Joint module
  • Two different pendulum lengths supplied
  • Easy-connect cables and connectors
  • Fully compatible with MATLAB®/Simulink® and LabVIEW™
  • Fully documented system models and parameters provided for MATLAB®, Simulink®, LabVIEWand Maple™
  • Open architecture design, allowing users to design their own controller
Linear Flexible Joint with Inverted Pendulum cart mass 0.24 kg
Weight mass  0.12 kg
Pendulum fixture mass  0.135 kg
Spring stiffness 160 N/m
Spring assembly mass 0.145 kg
Spring length 29.0 cm
Long pendulum length (from pivot to tip) 64.1 cm
Long pendulum mass (with T-fitting)  0.23 kg
Medium pendulum length (from pivot to tip)  33.6 cm
Medium pendulum mass (with T-fitting) 0.127 kg
Cart encoder resolution (in quadrature) 4096 counts/rev
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
  • Parameter estimation
  • Model validation

Control Topics

  • Linear-quadratic regulator (LQR)
  • State-feedback control
  • Vibration control

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

To set up your Linear Flexible Joint with 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 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 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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