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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

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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: sales@feedback-instruments.com

Website: www.feedback-instruments.com

Feedback reserves the right to change these specifications without notice

For further information on Feedback equipment please contact ...