Using Finite State Automata to Model Manufacturing Systems

1. Using Finite State Automata to Model Manufacturing Systems R. Wysk

2. Agenda – Systems Theory according to Wysk • Typical manufacturing systems • Modeling a manufacturing system as a state machine • What is a finite state machine? • Notation and variables • Examples

3. Basic types of systems • Continuous • Normally modeled as differential state based entities • Discrete (DES) • Not adequately modeled as differential or difference entities • Checkers, chess, many manufacturing systems

4. How about Starbucks?

5. The Concept of a Language • Every DES has an underlying event set, E associated with it. • The set E is thought of as the “alphabet” of a language. • The event sequences for a DES are thought of as “words” in the language. • Different modeling prospective can be taken for most DES

6. Model with respect to one piece Model with respect to one color Model with respect to all pieces Examples - chess

7. Model with respect to a part Model with respect to a machine Model with respect to all resources Examples - manufacturing 3 6 4 5 2 7 1 Machine 1 M1 Machine 2 M2 R 8 UL L

8. How about our machine?

9. Model with respect to one car (like a GPS) Model with respect to one highway Model with respect to all highways and cars Examples – Highway systems

10. How about driving to Crabtree Valley Mall?

11. Intent • Show what a finite state automata (FSA) is • Show how to formally model an FSA • Illustrate some uses for FSAs • Discuss “discrete event systems” modeling

12. Part Flow Through the Shop

13. Task Task Number Name 1 Pick L 2 Put M1 3 Process 1 4 Pick M1 5 Put M2 6 Process 2 7 Pick M2 8 Put UL Finite state view to IllustrateControl Simulation Requirements 3 6 4 5 2 7 1 Machine 1 M1 Machine 2 M2 R 8 UL L

14. Physical Model - Processing Workstation Process Process

15. Some Observations about this Perspective • Generic -- applies to any system • Other application specifics • Parts • Number • Routing • Buffers (none in our system)

16. Finite State Automata (FSA) • Consist of • Nodes – X • Events – E • Transition maps – f(m,n,e) • Starting state – q0 • Event transitions – F(X1, e) = X2

17. Modeling a state graph • States/nodes - X ( x , y, z ) • Events/transistions - E ( a , b, g ) • Graph construction • F (x ,a ) = x • F (y ,a ) = x • F (z ,b ) = z • F (x ,b ) = F (x ,g ) = z • F (y ,b ) = F (y ,g ) = y • F (z ,a ) = F (z ,g ) = y

18. The Graph looks like x y z

19. So FSAs • Formal way to model discrete systems • Can symbolically build complex systems • Capture lots of system detail • Provide the grain for modeling a system • So what about a DC?

20. Deterministic Automaton • A Deterministic Automaton, denoted by G, is a six-tuple G = (X,E, f, Γ, x0,Xm) where: X is the set of states E is the finite set of events associated with G f : X × E → X is the transition function: f(x, e) = y means that there is a transition labeled by event e from state x to state y; in general, f is a partial function on its domain Γ : X → 2Eis the active event function (or feasible event function); Γ(x) is the set of all events e for which f(x, e) is defined and it is called the active event set (or feasible event set) of G at x x0 is the initial state Xm ⊆ X is the set of marked states.

21. The words state machine and generator (which explains the notation G) are also often used to describe the above object. • If X is a finite set, we call G a deterministic finite-state automaton, often abbreviated as DFA. • The functions f and Γ are completely described by the state transition diagram of the automaton. • The automaton is said to be deterministic because f is a function from X × E to X, namely, there cannot be two transitions with the same event label out of a state. • In contrast, the transition structure of a nondeterministic automaton is defined by means of a function from X × E to 2X; in this case, there can be multiple transitions with the same event label out of a state. Note that by default, the word automaton will refer to deterministic automaton. • The fact that we allow the transition function f to be partially defined over its domain X × E is a variation over the usual definition of automaton in the computer science literature that is quite important in DES theory.

22. Planning, Scheduling, and Execution • PlanningDetermining what tasks thesystem needs to perform • SchedulingSequencing planned tasks • ExecutionPerforming the scheduledtasks at the appropriatetime

23. Shop Floor Controller Structure

24. Yard Example We can treat the Gate House as the “material handler” 3 1 2 Queue of trucks Gate House Dock 3

25. Dock 1 Depart Go to 1 Request Go to 2 Gate House Yard Dock 2 Go to 3 Truck Arrival Dock 3 System Model for the Yard

26. Build a formal model of the state graph • X (Yard, Gate, Docki) • E(Depart/Balk, Gate_serve,Traveli, Leave to gate, Return to yard) • You finish the FSA modeling

27. Some things not considered • Queue discipline • FIFO, SPT, … • Rules for assigning trucks to docks • Due date, SPT, …

29. A communicating automata • An FSA that interacts with a decision maker • Decision maker can be a person, algorithm, … • Messages create changes in the graph • Go_to_Dock #1  equivalent to the controller telling a driver to proceed to dock #1 • Input and Output messages • Input messages update the status of the graph • Output messages signal the start of an event

30. Dock 1 Depart Go to 1 Request Go to 2 Gate House Yard Dock 2 Go to 3 Truck Arrival Dock 3 Deterministic and non-deterministic FSAs

33. Some Observations about this Perspective • Generic -- applies to any discrete system • Other application specifics • Parts • Number • Routing • Buffers (none in our system)

34. RapidCIM Model • Message-based part state graph (MPSG) • Execution formalism based on finite automata • Mimic controller behavior from part point of view • Explicitly separate scheduling from execution • reference: Smith and Joshi, 1992 • web site: http://www.engr.psu.edu/cim/control.html

35. M2 Blocking attributes are set to 1: must be blocked 1 1 Robots Index R 1 Stations Index AS 1 M1 2 M2 3 M3 4 M1 R M3 1 Due to limited space, these two arrows are expanded in this figure 1 AS part_enter@1_sb rm_asrs@1_sb rm@1_bk at_loc@1_kb at_loc@1_bs I I O I O return_ok@1_bs ....... pick_ns#1@1_br pick_ns#1@1_sb delete@1 I O I T mv_to_asrs@1_sb arrive@1_bk arrive_ok@1_kb loc_ok@1_bs I O I O ....... put_ok#1@1_bs clear_ok#1@1_rb put_ns#1@1_br put_ns#1@1_sb O I O I Generated FSA Execution model -- based on the rules, but manual yet

36. RapidCIM Project • Built formal models for shop floor control (MPSG) • Developed a compiler to automatically generate code for control • Created Arena RT messaging • Used process plans to define part routes

37. Message-based Part State Graph (MPSG) • An MPSG is a deterministic finite automaton representing the processing protocol for a part. • An MPSG state provides information about the current processing state of the part that is needed to determine the behavior on subsequent events. • State transitions are caused by receiving messages about the part and by performing functions specified by the scheduler.

38. Mealy Machine • A Mealy machine is essentially a finite automaton with output. Formally, a Mealy machine M defined as follows: So, a Mealy machine is a finite automaton in which an output (defined by  and ) is generated during state transitions.

39. MPSG Definition

40. MPSG for Generic MP Equipment

41. MPSG Characteristics • Explicitly separate scheduling from execution. • Extensible at multiple levels to facilitate software development • Generic MPSG can be used unmodified. • Extraneous transitions can be removed. • Specified messages and tasks can be rearranged. • New messages and tasks can be specified. • Execution portion of the control software is automatically generated from the MPSG description.

42. Database Scheduler ARENA: real-time (Shop floor controller) Task Input Queue Task Output Queue Big Executor (Shop Level) ABB 140 Kardex AGVS M1 Hass VF 0E SL-20 ABB 240 Equipment Controllers Simulation-based SFCS

43. m p _ p u t c l e a r t o l o a d p a r t ? c l e a r e x e c u t e p r o g r a m c l o s e f i x t u r e t o l o a d p a r t e x e c u t e p r o g r a m t o c l o s e f i x t u r e f i x t u r e c l o s e d e x e c u t e p r o g r a m t o r e l e a s e p a r t a n d m o v e a w a y r o b o t c l e a r e x e c u t e p a r t p r o g r a m Equipment-level Device Interaction

44. Uses of FSAs • Can generate controllers automatically • Software can be created directly from this formal model • Can be used to define resources and events in a discrete system • Bernie Zeigler won the IEEE Gold Metal for his work on DEVS (2002) • Can be used to automatically generate simulation model • Son created both software controllers as well as simulation for messaging

45. Summary - Process a part 0 part_enter_sb 1 remove_kardex_sb 2 pick_ns_sb 3 return_sb move_to_mach_sb 7 move_to_kardex_sb 6 put_sb 5 move_to_mach_sb 4 put_ns_sb process_sb pick_sb 8 return_sb 9