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 Discrete (DES)
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. Examples - chess Model with respect to one piece
Model with respect to one color
Model with respect to all pieces

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

8. How about our machine?

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

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. Finite state view to Illustrate Control Simulation Requirements8 2 3 4 5 6 7 1
Machine 1 M1
Machine 2 M2 R L UL
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

14. Physical Model - Processing Workstation

15. Resource Acquisition: Simulation for Real-time Control
Task
Number
Name M1 M2 R 1
Pick L Ö 2
Put M1 3
Process 1 4
Pick M1 5
Put M2 6
Process 2 7
Pick M2 8
Put U
MH tasks are represented explicitly like MP tasks
Resource management is significantly complex

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

17. 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

18. 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

19. The Graph looks like x y z

20. 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?

21. 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 → 2E is 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.

22. 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.

23. Planning, Scheduling, and Execution
Planning Determining what tasks the system needs to perform
Scheduling Sequencing planned tasks
Execution Performing the scheduled tasks at the appropriate time

24. Shop Floor Controller Structure

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

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

27. 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

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

30. 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

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

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

35. 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:

36. Generated FSA Execution model -- based on the rules, but manual yet1 R M2 M3 AS
Due to limited space, these two arrows are expanded in this figure I O T
Robots Index
R 1
Stations Index
AS 1
M1 2
M2 3
M3 4
Blocking attributes are set to 1: must be blocked M1

37. 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

38. 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.

39. 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.

40. MPSG Definition

41. MPSG for Generic MP Equipment

42. 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.

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

44. Equipment-level Device Interactionb t c l e a x u p g m s f i d ? n v w y _

45. 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

46. Summary - Process a part
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