Local Modular Supervisory Control
of DES with Distinguishers
M. Teixeira, José E.R. Cury and Max H. de Queiroz
[email protected], [email protected], [email protected]
Departamento de Automação e Sistemas
Universidade Federal de Santa Catarina
Florianópolis, SC, Brasil
1
Motivation
 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)
Local Modular Supervisory Control of DES with Distinguisher – ETFA’11
2
Presentation Outline
 Preliminaries:
 LMC (Local Modular Control)
 Proposal
 Distinguishers in LMC:
 Distinguished Local Mmmm(DLMC)
 Distinguishers
 Drawbacks of the DLMC
 Example
 Manufacturing line control
problem
 Combining LMC and DLMC
 Over the same SCP
 Contributions
Conclusions
 References
Local Modular Supervisory Control of DES with Distinguisher – ETFA’11
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Preliminaries
 LMC
Supervision
System
Local
Plants
Plants
Specifications
Complexity
G1
D(L) = 2S*  2D*
E2
E1
G3
G2
 Distinguishers
Refine each original event s  S
Into a new nonempty set Ds≠
The refinements are driven by
information received from a
distinguisher model
D(L) = P-1(L) ∩ LD
G1loc
G
S1loc
S 2loc
loc
2
It identifies particular instances of
execution, facilitating the modeling
of specifications
Moving back:
Local Modular Supervisory Control of DES with Distinguisher – ETFA’11
4
Manufacturing Line
1
1
1
1
Subsystems Modeling
M1: G1
TU: G3
R: G4
M2: G2
Local Modular Supervisory Control of DES with Distinguisher – ETFA’11
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Specifications
 Controlling the buffers overflow and underflow:
 E1 :
 E2 :
 E3 :
 E4 :
avoids
avoids
avoids
avoids
overflow
overflow
overflow
overflow
and
and
and
and
underflow
underflow
underflow
underflow
of
of
of
of
the
the
the
the
Buffer
Buffer
Buffer
Buffer
1;
2;
3;
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
q1
q2
qd
:
:
:
:
without rework;
first rework;
second rework;
rejected parts.
Local Modular Supervisory Control of DES with Distinguisher – ETFA’11
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Specifications Modeling
B3
v
M1
y
B1
11
z
x
M2
w
r
E1 = Buffer 1
E5 =?
E2 = Buffer 2
1
2
B2
t
T
U
31
pd
d
Cd
qd
C0
q0
R
a
B4
41
E3 = Buffer 3
p0,
p1,
p2
C1 q1
C2
q2
E4 = Buffer 4
E6 =?
Local Modular Supervisory Control of DES with Distinguisher – ETFA’11
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Distinguishing
M1
B1
y
1
1
D = r0, r1
r
x
D z=
Dw=
z0
zz1
z2
w0
w
w1
w2
M2
r
M1:
TU:
B3
v
1
2
B2
t0, t1 t=D
t
T
U
dD a
=
a0
a
a 1
a2
B4
31
pd
Cd
qd
C0
q0
R
41
p0,
p1,
p2
C1 q1
C2
q2
R:
M2:
Local Modular Supervisory Control of DES with Distinguisher – ETFA’11
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Distinguished Specifications
B1
y
M1
11
D = r0, r1
r
x
E1 = Buffer 1
D z=
Dw=
z0
z1
z2
w0
w1
w2
M2
E2 = Buffer 2
B3
v
2
1
B2
t0, t1 =D
t
T
U
dDa
=
a0
a
a 1
a2
B4
31
pd
Cd
qd
C0
q0
R
4
1
E3 = Buffer 3
E5 =?
p0,
p1,
p2
C1 q1
C2
q2
E4 = Buffer 4
? = E6
Local Modular Supervisory Control of DES with Distinguisher – ETFA’11
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Distinguishers Modeling
M1
B1
y
11
D = r0, r1
r
x
D z=
Dw=
z0
z1
z2
w0
w1
w2
M2
B3
v
2
1
B2
t0, t1 =D
t
T
U
dDa
=
a0
a
a 1
a2
B4
31
pd
Cd
qd
C0
q0
R
4
1
p0,
p1,
p2
C1 q1
C2
q2
...
HD = Hz || Hw || Ht || Hr
Local Modular Supervisory Control of DES with Distinguisher – ETFA’11
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Distinguishers in LMC
 LMC
Complexity
E2
E1
G1
 DLMC
G3
G2
G1loc
Ed1 Ed2
loc
2
Ga1
HD
Ga3
Ga2
loc
1
loc
2
G
Gd
Gd
S 2loc
Sd1loc
Sd 2loc
Proposition:
S1loc
Global Problem
Global Problem
Local Modular Supervisory Control of DES with Distinguisher – ETFA’11
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Combined Synthesis
 LMC
Complexity
E6
E1
G1
 DLMC
G2
Ed1 Ed6
G3
Ga1
HD
Ga2 Ga3
G1loc
G6loc
loc
1
Gd
Gd 6loc
S1loc
S 6loc
Sd1loc
Sd 6loc
Original Global Solution
Refined Global Solution
Combined Global Solution
Local Modular Supervisory Control of DES with Distinguisher – ETFA’11
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Comparing LMC and DLMC results
LMC (i)
Gloc_i
Eioc_i
Kloc_i
Sloc_i
1
12
2
24
14
2
6
2
12
9
3
15
2
30
25
4
15
2
30
20
5
12
508
468
6
60
214
480
6720
32
DLMC (i)
Gdloc_i
Edioc_i
Kdloc_i
Sdloc_i
1
336
2
336
108
2
336
2
532
232
3
1680
2
3360
2880
4
1680
2
3360
2160
5
336
508
468
6
1680
2
4
6720
2880
Local Modular Supervisory Control of DES with Distinguisher – ETFA’11
‖iI Sloci
520
‖iI Sdloci
520
13
Combined Local Modular Results
LMC
(iI’’)
Gloc_i
Eioc_i
Kloc_i
Sloc_i
1
12
2
24
14
2
6
2
12
9
3
15
2
30
25
4
15
2
30
20
DLMC
(i I’)
Gdloc_i
Edioc_i
Kdloc_i
Sdloc_i
5
336
508
468
6
1680
2
4
6720
2880
Local Modular Supervisory Control of DES with Distinguisher – ETFA’11
loc

(
Sd
iI '
i )
loc
(
S
iI ''
i )
520
14
Conclusions and Prospects
 Conclusions:
Complex
Control Problem
Control Problems
Distinguishers
DLMC
Simple
Control Problems
LMC
Computational
Savings
DLMC
CLMC
Control Solution
Local Modular Supervisory Control of DES with Distinguisher – ETFA’11
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Acknowledgments
Thank you all!
I'm available for questions.
Local Modular Supervisory Control of DES with Distinguisher – ETFA’11
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