Ball on a Beam:
The ball-beam system is a frequently encountered example of a nonlinear
dynamical system. While the ideal ball-beam system is indeed nonlinear,
the physical implementation in t he lab has additional non-linearities,
including: deadband and backlash introduced by the DC motor and gearbox
configuration, discrete position sensing, and an uneven rolling surface.
The ball-beam system uses 32 phototransistors mounted within a slot on the
beam to sense the position of the ball; two light sources are used to illuminate
the beam from above. The angular position of the beam is sensed using a
potentiometer and 5 Volt power supply. A DC motor provides actuation of
the beam via a 50:1 gear ratio. The power system to drive the DC motor consists
of dual 24 Volt power supplies and a current amplifier. A PID controller
has been employed in an inner control loop as a motor position controller.
The PID parameters have been chosen such that the motor exhibits a fast
response, without overshoot. For a more complete description of the ball-beam
system see:
E. Laukonen and S. Yurkovich, "A Ball and Beam Testbed for Fuzzy Identification
and Control Design," The 1993 American Control Conference, San Francisco,
CA, June 1993.