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Page 1 of 2 10/2013
Digital Pendulum 33-005-PCI
The Digital Pendulum is a modern version of
a classical control problem; that of erecting
and balancing a free swinging pendulum in
its inverted position or moving a hanging
pendulum in a controlled manner.
The cart on the track is digitally controlled
using MATLAB™ software to swing up and to
balance the pendulum into an upright
sustained position or to move the cart with
pendulum in an unperturbed down position.
The cart track is of limited length, imposing
constraints on the control algorithm.
In pendulum mode the system is used to control the twin arm pendulum from an initial position, hanging at
rest with the cart in the centre of its travel along the track, to a final position with the pendulum upright and
the cart restored to its central position. In crane mode the control problem is to move the position of the
cart without undue movement of the pendulum. This problem is typical of that experienced when
controlling a gantry crane.
A guide is given for PID controller design, testing,
tuning and implementation on the model. Root locus
technique is used to illustrate the changes that PID
controller tuning inflicts on the control system
performance. The designed controllers are prepared
in SIMULINK™.
Screen showing MATLAB™ control software
Subject Areas
• MATLAB System Identification Toolbox
• Crane Linear Model Identification
• Inverted Pendulum Linear Model
• Pendulum Set-Up Control
• First Model Identification
• Plant Control
• PID Control of Cart Model
• Real-Time PID Control of Cart Position
• Real-Time Swing-Up Control
• Inverted Pendulum Control of Swing-Up
• Inverted Pendulum Stabilisation
• Crane Control
• Combined Control Techniques
• Swing-Up and Hold
• Up and Down Model
• Pendulum Model
• Equations of Motion
• Linear Models
• Model Identification - Static Friction
Compensation
• Running a Real-Time Model
• Dynamic Model
• Cart Model Identification
Page 2 of 2 10/2013
Digital Pendulum 33-005-PCI
The phenomenological process models are designed
in SIMULINK™ to provide initial models for the user to
test. Model linearization is then discussed and the uses
of simple dynamics analysis such as bode diagrams
and poles and zeros maps are introduced.
Features • Dual mode system - crane or inverted pendulum
• Self-erecting pendulum mode
• Extensive MATLAB toolboxes are available from The MathWorks Inc.
• An ideal vehicle for both undergraduate laboratory and project work
• Introduction to PID control
• Operates from either 110 V or 230 V, 50 Hz or 60 Hz
To obtain accurate models Identification procedures incorporating MATLAB™ functions are described. The user
has a chance to go step-by-step through the discrete models identification. One of the 'obtained models' is used
for the controllers design and PID control is explained. Using MATLAB™ together with the detailed training
manuals supplied by Feedback and an Advantech PCI card [which creates an impressive digital control system
development environment] the user is guided through the design process using the following:
• Phenomenological process models
• Dynamics analysis
• Discrete models identification
• Controller design
• Controller tests on the model
• Controller implementation in real-time
applications
• Implementation of various control strategies
• Data visualisation
Specification Power requirements
Line voltage: 200/250 V or 100/125 V, 50 or 60 Hz.
Consumption: 100 VA. Fuse: 4 A (110 V), 2 A (230 V).
Dimensions & Weight Length: 1710 mm, Height: 650 mm, Depth: 410 mm, Weight: 23 kg.
Tender Specification A MATLAB™ controlled digital pendulum model comprising a cart with a
free swinging dual arm pendulum attached and associated track.
Ordering information Order: Digital Pendulum 33-005-PCI — System with MATLAB™ interface card and cable
Order: Digital Pendulum 33-005I — System withoutwithoutwithoutwithout MATLAB™ interface card and cable
Feedback InstruFeedback InstruFeedback InstruFeedback Instrumentsmentsmentsments
5 & 6 Warren Court
Park Road, Crowborough
East Sussex, TN6 2QX
United Kingdom
Tel: +44 1892 653322
Sales: [email protected]
Website: www.feedback-instruments.com
Feedback reserves the right to change these specifications without notice
For further information on Feedback equipment please contact ...