Inverted Pendulum

Inverted Pendulum
Inverted Pendulum

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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 to swing up (self erecting) 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. 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 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 and visualisation.

The equipment set incorporates student experiments which can be carried out in a laboratory safely using safety extra-low voltage. Experiment instructions are contained in a manual in either printed or digital form.

A MATLAB™ license is required for this trial and is not included in the scope of delivery.
The equipment can require additional software modules.

Target Group

A training program made for the advanced training study programs at applied technology universities and technical universities. Knowledge of classic control engineering is a prerequisite.


Pendulum Model

  • Equations of motion
  • Non-linear model
  • Linear models
  • Static friction compensation
  • Running a real-time model
  • Dynamic model
  • Cart model identification
  • First model identification
  • Using MATLAB control (MATLAB not supplied)
  • Crane linear model identification
  • Inverted pendulum linear model

Pendulum set-up control

  • Plant control
  • PID controller
  • PID control of cart model position
  • 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 & hold
  • Up & down model

Components of equipment sets

1 33-005-PCI Set Digital Pendulum System FB
1 33-005I Digital Pendulum System (NCC) FB
1 33-936-SW MATLAB Models for Digital Pendulum System FB
1 PC with PCI interface and Windows 7/8/10/11 64-Bit
1 for Windows 7 Service Pack 1: MATLAB™ from Version R2015b (V8.6)  to R2017b (V9.3)
1 for Windows 10: MATLAB™  version R2019a (V9.6) or later
1 MATLAB™ Toolboxes (1): Simulink, Control System, System Identification
1 MATLAB™ Toolboxes (2): Simulink Desktop Real-Time, MATLAB Coder, Simulink Coder

Purchasing Options

  • 33-005-PCI, as described here, or
  • 33-005I, content as per 33-005-PCI except the 33-005I does not include the interface card
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