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4. Petri Nets

• These are like state diagrams, except multiple states can be active at the same time.

• Other techniques, such as GRAFCET, are based on Petri nets.

• Ideal for parallel control problems

• Basic logic functions are shown below,

• We can model various logic functions with Petri nets,

• Reachability allows us to determine if a state (set of places) is possible given an initial condition.

• Boundedness determines whether the number of states will be controlled, or grow/shrink.

• Deadlock and liveliness: will the controller find itself unable to continue.

• The procedure for producing ladder logic and other programs from the Petri Nets, is identical to producing Ladder Logic for SFC diagrams.

• Petri nets have been used for the modeling, control and validation of the control model [Teng and Black, 1988]

4.1 Implementation for a PLC
• Consider the example of a parts buffer. Parts enter the buffer and are added to the top of the stack. The part at the bottom of the stack is checked and sorted (ejected differently) based on a quality check.

• This can be implemented in ladder logic, but unlike the sequential techniques, there may be multiple tokens in the places, so counters are used to keep track of token counts.

Problem 4.1 Turn the coffee machine petri net diagram into ladder logic

4.2 Problems
Problem 4.2 Develop a Petri net to control a part sorting station. Parts enter on a conveyor belt and are detected by a proximity sensor. The part can then be checked with a vision system that will signal to the PLC that the part is good/bad. There are then two cylinders that can eject the part into a good or bad bin.