A Cool Control Problem

Children on a Swing

The motion of the pendulum is controlled by two electric motors attached to the top pivot of the Swinging Blind Juggler (see figure here). Even though the machine is designed to juggle balls at a pendulum amplitude of up to 30 degrees, the maximum amplitude achieved so far is only 25 degrees because the motors are too weak. The motors have to accomplish two tasks: 1) They must ensure that the pendulum swings consistently at the desired amplitude; and 2) They must ensure that the pendulum motion remains synchronized with the ball motion. In other words, the paddle must be at the right position at the right time to strike the ball. Both tasks must be achieved in the presence of disturbances. The largest disturbance is the motion of the paddle, which affects the motion of the pendulum. This is similar to the physics that kids use to swing up higher and higher on swing sets by moving their bodies. Currently, when the Swinging Blind Juggler swings at an amplitude above 25 degrees, the disturbance from the paddle motion is too large and the ball falls off because the pendulum gets out of sync with the paddle motion.

We are working on turning the paddle motion from a disturbance to a useful control parameter. Just like kids on swings, we are investigating the control of the pendulum motion with the paddle motion. The only constraints on the paddle motion are the two striking motions at the peak angles of the pendulum. In between, we are free to design the motion of the paddle. We can use this short time window to apply a paddle motion that controls the pendulum motion.

For more information on how kids pump a swing and illustrating videos, visit the website of William Case, who authored a few scientific publications on the topic: http://www.grinnell.edu/academic/physics/faculty/case/swing/

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