Two-Pusher Example

Our system is depicted in Figure 1 below. It consists simply of two pushers, each of which has two ``degrees'' of extension: half-extended, and fully-extended. When Pusher 1 is fully extended, the workpiece in position 1 has moved to position 2. If there is a workpiece in position 2 and Pusher 2 fully extends, then the workpiece moves to position 3. Notice that the uncontrolled plant allows both pushers to move freely, back and forth, regardless of the position of the workpiece.

  
Figure 1: Two-Pusher Example

We consider two different sets of specifications:

• Specifications I
  (i) It is forbidden for both pushers to be fully extended at the same time.
  (ii) The following task must be accomplished: a workpiece must follow positions 1, 2, 3.
• Specifications II
  (i) Only one pusher at a time is allowed to leave its basic position.
  (ii) The same task as above must be accomplished.