Manufacturing Example 2

Manufacturing Systems: Multitasking Supervisory Control




• Description
  
  
• The Flexible Manufacturing System (FMS) presented in the above figure produces two types of products from raw blocks and raw pegs: a block with a conical pin on top (Product A) and a block with a cylindrical painted pin (Product B). The FMS consists of eight devices: three conveyors (C₁, C₂ and C₃), a Mill, a Lathe, a Robot, a Painting Device (PD) and an Assembly Machine (AM). The devices are connected through buffers B_i, i = 1, . . . , 8, each with capacity for one part. The arrows in the figure indicate the events representing the flow of unfinished parts through the FMS. The controllable events are labeled with odd numbers.



• System Models
  
  
• The open loop behavior of the FMS is modeled by the synchronous composition of the set of eight colored marking generators (CMG) in the figure below. The manufacture of one Product A and of one Product B is respectively indicated by the tasks a and b in the model for the AM. The task o represents the simultaneous operation of the Lathe and the Mill. The synchronous composition of the eight CMG leads to a CMG G with 3456 states and color set C = {a, b, o}.




• Behavior Specifications
  
  
• The control logic to be synthesized must give the maximal degree of freedom to the FMS while avoiding overflow or underflow of parts in the buffers. As liveness specifications, the supervisor should not prevent the manufacture of Product A and Product B and the Lathe from operating simultaneously with the Mill. Further it should not prevent the buffers B_i, i = 1, . . . ,6 from becoming empty and the buffers B₇ and B₈ from becoming simultaneously empty. The restrictions can be modularly expressed by a set of generic specifications, which are given by colored behaviors defined on a particular subset of events from the alphabet of the plant. The generic specifications M_gen,i, i = 1, . . . , 8, for avoiding overflow and underflow in the buffers B_i, i = 1, . . . , 8, respectively, are generated by the CMG in the figure below.





• The tasks ei, i = 1, . . . , 6, defined in the specifications M_gen,i indicate when the respective buffers are empty. The task e, indicating that buffers B₇ and B₈ are simultaneously empty, is defined by M_gen,7 and M_gen,8. The synchronous composition M of all generic specifications has color set E = {e1, e2, e3, e4, e5, e6, e}. The global specification is then obtained from A_D = M || Λ_C(G), which can be modeled by a CMG with 812544 states. Consequently, in order to respect all the safety and liveness specifications, the controlled system must respect A_D and be strongly nonblocking with respect to the color set D = {a, b, o, e1, e2, e3, e4, e5, e6, e}.

• Computation of Supervisor
  
  
• For a regular specification A_D and a finite-state G, SupCSNB(A_D, G, D) can be computed by the iterative elimination of uncontrollable or not strongly coreachable states of a CMG modeling A_D (See section 3.2 of the referenced publication for details). Following this algorithm, the optimal colored behavior SupCSNB(A_D, G, D) can be ensured by a coloring supervisor with 45504 states.

• For more information on this example:

de Queiroz, M. H., Cury, J. E. R., and Wonham, W. M. "Multitasking Supervisory Control of Discrete-Event Systems." Discrete Event Dynamic Systems: Theory and Applications, 15, 390-393, 2005.