Ben Cazzolato

Wei Wang

Ball and Beam System

Ben S. Cazzolato and Wei Wang

The ball and beam system is a classic dynamic system used to illustrate control. It is inherently non-linear and unstable, and despite its simple nature, the cascaded dynamics of the system (with 3/4 integrators and an interconnection between rotational and translation subsystems) and are very similar to planar control of rockets.

The aim of this masters by course work project was to develop a ball and beam rig to illustrate control to our undergraduate students. It uses a very low backlash servo-motor to drive the beam, with the beam rotation measured using an encoder and the ball translational position measured using a resistive wire.

The deadzone of the motor was minimised using a fixed lookup table as a compensator. Three state control strategies were implemented, including full state LQR, LQR and LQG full state estimation, and LQR and LQG reduced order state estimation. All state controllers used an augmented structure to provide command tracking for the ball's position.

The image galleries at the bottom of this page show movies of the different controller structures in action.