Manufacturing Example 1

Manufacturing Systems: Centralized Supervisory Control




• Description
• This manufacturing system has two machines (Machine 1 and Machine 2) and a buffer of size one. The machines are initially idle and the buffer is empty. They cannot overflow or underflow, machine 1 (M1) cannot be working if there is something in the buffer, and machine 2 (M2) cannot start working unless there is something in the buffer. Also, M2 will always be repaired and returned to service first over M1 if both are down at the same time.



• Modeling Plants
  
  
• Machine One (M1)
• Events: M1 starts operation (s1), M1 finishes operation (f1), M1 breaks down (b1), M1 is repaired and returned to service (r1).
• States: M1 is idle (I1), M1 is working (W1), M1 is down (D1).


Note that events s1 and r1 are controllable, whereas b1 and f1 are uncontrollable.

• Machine Two (M2)
• Events: M2 starts operation (s2), M2 finishes operation (f2), M2 breaks down (b2), M2 is repaired and returned to service (r2).
• States: M2 is idle (I2), M2 is working (W2), M2 is down (D2).


Note that events s2 and r2 are controllable, whereas b2 and f2 are uncontrollable.





• Behavior Specifications
  
  
• Buffer Behavioral Specifications
• Events: M1 finishes operations (f1), M2 starts operation (s2).
• States: buffer is empty (E), buffer is full (F).

• Breakdown Behavioral Specifications
• Events: M1 is repaired and returns to service (r1), M2 breaks down (b2), M2 is repaired and returns to service (r2).
• States: M2 is working correctly (OK), M2 is down (KO).

• Synthesization of Control Law and Supervisor
• In order to make sure that the system above behaves according to the given specifications, we must synthesize a control law that will carry out these desired behaviors. This is achieved by taking control law, and the parallel composition of the above machines and behavior automata and implementing a computer program that will provide the information whether it is possible for the machines to stay within these conditions, output the supervisor that represents the maximally permissive controlled behavior of the machines that still follow the specifications, and the corresponding control law. In other words, the control law and supervisor are coded into a program that will ensure that the desired behavior occurs.
  
  
  
  Everytime an event occurs, this information will be sent to the program to update the supervisor's state and make sure that the right event sequence occurs by sending out controls according to the control law. The program works by disabling any events that absolutely cannot occur and letting the automata choose from the remaining events accordingly.

The table above represents all the state components of the parallel composition our component automata (machines and behavior automata). For example, State 1 (initial state of the parallel composition) is {I1,I2,E,OK} which is the initial state of all the smaller automata (M1, M2, buffer, repair/breakdown specification).

• For more information on this example:

Brandin, B.A. "The Real-Time Supervisory Control of an Experimental Manufacturing Cell." IEEE Transactions on Robotics and Automaton. 12.1(1996): 1-14.