# 1 M. Teixeira, José E.R. Cury and Max H. de Queiroz Local.

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

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

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

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

5 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Manufacturing Line Subsystems Modeling M1: G1 M2: G2 R: G4 TU: G3 1 1 1 1

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.

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 =? 1 1 1 1

8 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Distinguishing z t r M1: M2: TU: 1 1 1 1 R: w

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 =? 1 1 1 1

10 Local Modular Supervisory Control of DES with Distinguisher – ETFA’11 Distinguishers Modeling H  = Hz || Hw || Ht || Hr 1 1 1 1...

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:

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

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 11222414 520 262129 31523025 41523020 512 214 508468 660 480 672032 DLMC (i)Gd loc_i Ed ioc_i Kd loc_i Sd loc_i ‖ i  I Sd loc i 13362 108 520 23362532232 31680233602880 41680233602160 5336 2 508468 61680 4 67202880

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 11222414 262129 31523025 41523020 DLMC (i  I’) Gd loc_i Ed ioc_i Kd loc_i Sd loc_i 5336 2 508468 61680 4 67202880 520

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

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

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