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1 M. Teixeira, José E.R. Cury and Max H. de Queiroz Local Modular Supervisory Control of DES with Distinguishers Departamento de Automação e Sistemas Universidade Federal de Santa Catarina Florianópolis, SC, Brasil

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2 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 LMC, an extension of the SCT, is computationally efficient for implementing supervisors in DES; (QUEIROZ and CURY, 2000) However, modeling some control requirements can be very difficult or even impossible, in practice; DISTINGUISHERS can make the difference! (BOUZON, CURY and QUEIROZ, 2009) Motivation

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3 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Presentation Outline Preliminaries: LMC (Local Modular Control) Distinguishers Example Manufacturing line control problem Proposal Distinguishers in LMC: Distinguished Local Mmmm(DLMC) Drawbacks of the DLMC Combining LMC and DLMC Over the same SCP Contributions Conclusions References

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4 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Preliminaries Distinguishers D(L) = 2 * 2 * Refine each original event Into a new nonempty set ≠ The refinements are driven by information received from a distinguisher model D(L) = -1 (L) ∩ L It identifies particular instances of execution, facilitating the modeling of specifications Moving back: LMC E1E1 E2E2 Complexity Supervision System Plants Specifications Local Plants

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5 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Manufacturing Line Subsystems Modeling M1: G1 M2: G2 R: G4 TU: G

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6 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Specifications Controlling the buffers overflow and underflow: E1 : avoids overflow and underflow of the Buffer 1; E2 : avoids overflow and underflow of the Buffer 2; E3 : avoids overflow and underflow of the Buffer 3; E4 : avoids overflow and underflow of the Buffer 4; Controlling the number of reworks: E5 : limits the number of reworks (at most 2 for each part) Distributing the manufactured parts on the output conveyor: E6 : considers the quality (number of reworks), where: q0 : without rework; q1 : first rework; q2 : second rework; qd : rejected parts.

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7 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Specifications Modeling E 1 = Buffer 1E 2 = Buffer 2E 3 = Buffer 3 E 4 = Buffer 4 E 6 =? E 5 =?

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8 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Distinguishing z t r M1: M2: TU: R: w

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9 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Distinguished Specifications E 1 = Buffer 1E 2 = Buffer 2E 3 = Buffer 3 E 4 = Buffer 4 ? = E 6 E 5 =?

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10 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Distinguishers Modeling H = Hz || Hw || Ht || Hr

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11 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Distinguishers in LMC DLMC LMC E1E1 E2E2 Global Problem Complexity Ed 1 Ed 2 Global Problem Proposition:

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12 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Combined Synthesis DLMC LMC E1E1 E6E6 Original Global Solution Complexity Ed 1 Ed 6 Refined Global Solution Combined Global Solution

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13 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Comparing LMC and DLMC results LMC (i)G loc_i E ioc_i K loc_i S loc_i ‖ i I S loc i DLMC (i)Gd loc_i Ed ioc_i Kd loc_i Sd loc_i ‖ i I Sd loc i

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14 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Combined Local Modular Results LMC (i I’’) G loc_i E ioc_i K loc_i S loc_i DLMC (i I’) Gd loc_i Ed ioc_i Kd loc_i Sd loc_i

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15 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Conclusions: Control Solution Conclusions and Prospects Control Problem Distinguishers LMC DLMC Simple Control Problems Complex Control Problems CLMC Computational Savings DLMC

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16 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Thank you all! I'm available for questions. Acknowledgments

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