Control of Flexible Manufacturing Systems: Automata Based Approaches

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Control of Flexible Manufacturing
SystemsAutomata Based Approaches

• Nebil Buyurgan
• Can Saygin
• April 22, 2002

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Flexible Manufacturing Systems

• Automated and computer controlled manufacturing
  systems
• Physical Components
• Computer controlled machine
• tools capable of performing different
• operations
• Automated material handling system

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Control Structure of FMS

• Generally have hierarchical control structure
• The (low) machine-level control
• Machines are modeled as a
• continuous system
• The (high) system-level control
• System is controlled as a
• discrete event system

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Discrete Event Systems

• Dynamic systems with state changes driven by the
  occurrence of individual events.
• Main features
• The state space is an infinite discrete set.
• The state transitions are forced by events from a
  discrete and finite set.

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Main Modeling Techniques

• Automata models
• Petri net models
• Finitely recursive process models
• Temporal logic models
• Markov process models
• Queuing network models
• Semi-Markov process models

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Automata Theory

• Based on the concept of language models
• Language model concept
• Events in a system are mapped to a symbol
• Symbols are included in a finite, nonempty set
  (Alphabet)
• A string is a finite sequence of symbols (events)
• A language is a set of finite length strings that
  are formed from the symbols in an alphabet.

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Example

• Let E a, b, c
• e (empty string) with zero length
• a, b, c with 1 length
• aa, ab, ac, ba, bb, bc, ca, cb, cc with 2 length
• aaa, aab, aac, aba, abcetc. with 3 length
• Lall possible strings of length 3 starting with
  a
• Laaa, aab, aac, aba, abb, abc, aca, acb, acc

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Automata

• State Transition Diagram

Transition Function f (x, b) z f (x, c) x f
(z, a) f (z, c) y f (y, a) x, y
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Generator

• Generator, G (Q, S, d, q0, Qm)
• where
• Q The set of states of q
• S The alphabet or set symbols of s
• d The transition function
• d(s, q1) q2 d S ? Q ?? Q
• d(ss, q) d(s, d(s, q))
• q0 The initial state q0 ? Q
• Qm The set of final (marked) states Qm ? Q

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Example

• d(ba, x) d(a, d(b, x)) d(a, z)

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FMS Control Example
System Layout
This example was taken from Yalcin, A.,
Boucher, T. O., Deadlock Avoidance in Flexible
Manufacturing Systems Using Finite Automata,
IEEE Transactions on Robotics and Automation,
Vol. 16, No. 4, August 2000
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FMS Control Example

• Part Processes

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FMS Control Example

• Transition Graph For The System

Qiii, iib, bii, ibi, bib, ibb, bbi Qm
iii qo iii S I1R1, R1O1, R1M1, M1R1, R1M2,
M2R1 d(I1R1, iii) iib etc.
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FMS Control Example

• Transition Graphs For The Parts

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FMS Control Example

• For Part A
• Qai, a1, a2, a3, a4, a5, a6, a7, a8, af
• Qm af
• qo ai
• S I1R1, R1O1, R1M1, M1R1, R1M2, M2R1
• d(I1R1, iii) iib etc.

• For Part B
• Qbi, b1, b2, b3, b4, b5, bf
• Qm bf
• qo bi
• S I1R1, R1O1, R1M1, M1R1, R1M2, M2R1
• d(I1R1, iii) iib etc.

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FMS Control Example

• Transition Graph of the Shuffle of the Parts

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FMS Control Example

• Supervisor, S (S, ?)
• where S (X, S, ?, x0, Xm )
• ? S ? X ?? (0 Disable, 1 Enable)
• ?(s, x) 0 or 1 if s ? Sc and 1 if s ? Su
• X The set of states of x
• S The alphabet or set symbols of s
• ? The transition function
• x0 The initial state x0 ? X
• Xm The set of final (marked) states Xm ? X

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FMS Control Example

• The Coupled Supervised Discrete Event Process
• S/G (Q x X, S, d x ?, q0 x x0, Xm x Qm)

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FMS Control Example

• Transition Graph Coupled Model

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FMS Control Example

• Supervisory Control Pattern

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Advantages of Automata

• High expressive power for formulation and
  representation
• Fundamental features that guarantee the control
  strategy to be correct by construction
• Ability to avoid the repeated trial-analysis-redes
  ign cycle during the implementation of control
  model

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Disadvantages of Automata

• Computational complexity
• State space grows exponentially
• Number of machines
• Machine features (Capacity of machines)
• Indirect material handling systems
• Buffers
• More part types
• Different operation routes for parts

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Questions