High Fidelity Linear Cart System

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A Platform That Takes You from Single to Triple Inverted Pendulum

The High Fidelity Linear Cart (HFLC) system is ideally suited to introduce advanced control concepts and theories relevant to real world applications of servomotors, taking the classic inverted pendulum challenge to the next level with an array of experiments including double, dual and triple inverted pendulums. Students learn how to:

  • find a transfer function that describes the linear motion of the cart
  • develop a feedback system to control the position and speed of the cart
  • design a state-feedback control system to track a desired cart position while minimizing the swing of a suspended single pendulum / double pendulum / triple pendulum
  • design a state-feedback control systems that keeps the inverted pendulum / two independent single inverted pendulums / a double inverted pendulum / a triple inverted pendulum balanced and tracks the cart to a commanded position
  • design a switching mode control system to swing up a single pendulum and balance it in the upright position
  • implement the controllers on the actual system and evaluate its performance

Adding More Complexity with a Flexible Joint

I addition to five different pendulums provided with the HFLC system (three single pendulums of different length, one double pendulum and one triple pendulum), an optional Linear Flexible Joint can be connected to the actuated High Fidelity Linear Cart to create experiments of increased complexity. Students learn how to design a state feedback control system that regulates the position of the High Fidelity Linear Cart and the Linear Flexible Joint cart to a desired setpoint while dampening the spring.

High Fidelity Linear Cart with Single Pendulum High Fidelity Linear Cart with Dual Pendulum High Fidelity Linear Cart with Double Pendulum High Fidelity Linear Cart System with Triple Pendulum High Fidelity Linear Cart System with Linear Flexible Joint
HFLC single pendulum setup HFLC dual pendulum setup HFLC double pendulum set up HFLC triple pendulum setup HFLC Linear Flexible Joint setup

How It Works

The High Fidelity Linear Cart (HFLC) system consists of a precisely machined solid aluminum cart driven by a high-power 3-phase brushless DC motor. The cart slides along two high precision, ground hardened steel guide rails with self-aligning linear bearings for true linear motion. The motor shaft has a pinion gear that rides on a track permitting the cart to move in a linear fashion. Both rack and pinion are made of hardened steel and mesh with a tight tolerance. The rack-and-pinion mechanism eliminates undesirable effects found in belt-driven and free wheel systems, such as slippage or belt stretching, ensuring consistent and continuous traction.

The complete assembly rests on a solid aluminum base to ensure straightness, increased rigidity and support. With this design, the linear positioning system can obtain high speed, high acceleration and repeatability.

The cart is also equipped with two unactuated rotary joints with ball bearings for attaching of free-turning pendulum rods. The rods can be controlled individually or in combination to perform a variety of experiments with increasing complexity. One pendulum can be mounted directly on the cart, the rotation of the cart joint is mechanically limited to ± 30.9 degrees around its “inverted” vertical posture. The second pendulum can be suspended in front of the cart through an extended pivot shaft and can be used to perform self-erecting and gantry experiments.

The motor shaft is coupled to a high-resolution optical encoder that accurately measures the position of the cart. The angles of both pendulums are also measured by the optical encoders, allowing for multiple turns and continuous measurement over the entire range of motion.

The HFLC system comes with five different pendulums: three single pendulum rods of different lengths, one double and one triple pendulum. More experimental combinations can be created by adding an unactuated cart connected to the actuated High Fidelity Linear cart with a single linear flexible joint.

Quanser-develop Courseware Included

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

  • Precisely machined solid aluminum cart
  • High-power 3-phase brushless DC motor
  • Rack-and-pinion mechanism for consistent and continuous traction
  • Five different pendulums provided with the system: three single pendulums of different length, one double and one triple pendulum
  • Optional Linear Flexible Joint module (can be purchased separately)
  • High resolution optical encoders to sense position and angles
  • Easy-connect cables and connectors
  • Fully compatible with MATLAB®/Simulink®
  • Fully documented system models and parameters provided for MATLAB®, Simulink® and Maple™
  • Open architecture design, allowing users to design their own controller
Rack dimensions (L x W x H)  1.1 m x 0.31 m x 0.18 m
Cart system mass 3.22 kg
Motor current-torque constant 0.36 N.m/A
Motor armature resistance  2.94 W
Motor peak torque 4.82 N.m
Motor peak current 15.6 A
Motor maximum mechanical speed 838 rad/s
Rotor moment of inertia 2.7 x 10-5 kg.m²
Motor pinion radius 1.11 x 10-³ m
Cart encoder linear position sensitivity  8.523 x 10-6 m/count
Cart encoder resolution (in quadrature) 8192 counts/rev
Pendulum encoder resolution (in quadrature)   4096 counts/rev
Rear pendulum mechanical range ± 30.9 deg
Short pendulum length (pivot to tip)  20.96 cm
Short pendulum mass 0.072 kg
Medium pendulum length (pivot to tip) 33.65 cm
Medium pendulum mass 0.127 kg
Long pendulum length (pivot to tip) 64.13 cm
Long pendulum mass 0.230 kg
Mini pendulum length (pivot to tip) 0.0953 cm
Mini pendulum mass  0.0257 kg

Topics Included in the Quanser-developed courseware:

  • Derivation of dynamic model from first-principles
  • Derivation of dynamic model using Lagrange
  • Transfer function representation
  • State-space representation
  • Model validation
  • PID control
  • State-feedback / LQR control
  • Swing-up / balance control
  • Vibration control (with Linear Flexible Joint)
The HFLC system can be also used to teach other topics that are not included in the Quanser-developed courseware.

To set up your High Fidelity Linear Cart workstation, you need additional components. Quanser engineers recommend:

for MATLAB®/Simulink® users  
1x Q8 data acquisition device  
1x UPM-180-25B amplifier  
QUARC real-time control software  

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Linear Servo Base Unit with Inverted Pendulum
Linear Double Inverted Pendulum
Rotary Inverted Pendulum
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