• Description

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, Data visualisation.

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 - like bode diagrams poles and zeros maps are introduced.

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. 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™.


  • 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 laboratory and project work

Subject Area

  • Using the MATLAB System Identification Toolbox
  • Crane Linear Model Identification
  • Inverted Pendulum Linear Model
  • Pendulum Set-Up Control
  • First Model Identification
  • Plant Control
  • PID Controller
  • 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