Matrix Based Supervisor Design of Marine Traffic System

1
Matrix Based Supervisor Design of Marine Traffic
System

• D. Kezic, A. Gudelj, I. Vujovic

2

• Supervisory control, P/T and
• MRF1 Petri net 7
• Matrix approach of Supervisor design 7
• Case study marine canal traffic system 8

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Supervisory control, P/T and MRF1 Petri net
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Supervisory control
5
P/T Petri net definition
set of places
set of transitions
set P and T are disjointed
an input incidence matrix
,
an output output incidence matrix
weight function
initial marking
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P/T Petri net fundamental equation
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Structural properties of Petri net
P-invariant
Siphon responsible for deadlock
Trap
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MRF1 class of Petri net
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MRF1 class of Petri net
,
,
,
e)
.
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Matrix description of MRF1 type of Petri net
Input system matrices (rows-transitions
columns-places)
Output system matrices (rows-places
columns-transitions)
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Matrix Approach of Supervisor design
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Deadlock prevention supervisor step 1
Find all resource loops
via computing their covering P-invarijants.
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Deadlock prevention supervisor step 2
Find all circular waits
via computing their wait relation matrix, and
using string algebra.
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Deadlock prevention supervisor step 3
Find critical siphons and critical subsystems
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Deadlock prevention supervisor step 4 (first
level deadlock)
A CW C is in CB at any
if and only if critical siphon becomes empty
The critical siphon is empty if and only if
To avoid deadlock
by applying constraint
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Example
The system has a deadlock state reduce the set
of allowable states!
Apply constraint for deadlock free net
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Deadlock prevention supervisor step 5 (second
level deadlock)

• The system is regular if

• If

the system is irregular
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Deadlock prevention supervisor step 6 (second
level deadlock)
From RCCW it is possible to identify key resource
Ensure that key resource does not remain last
available resource.
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Case study Marine canal traffic system
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Marine canal traffic system
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Deadlock prevention supervisor step
1 (P-invariants)
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Deadlock prevention supervisor step 2 (2 CW, 1
CCW)
,
.
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Deadlock prevention supervisor step 3 (3
critical siphons)
,
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Deadlock prevention supervisor step 3 (3
critical subsystems)
,
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Deadlock prevention supervisor step 4 (first
level deadlock)
,
.
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Deadlock prevention supervisor step
5,6 (calculating CCW and RCCW)
To ensure the absence of second level deadlock
the supervisor has to take care of the
availability of key resource in the way that
canal K2 does not remain last available resource
in the system.
,
.
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Simulation
K1_A 1 h, B1A_A 0.5 h, K2_A 2 h, B2A_A
0.5 h, K3_A 1 h, K3_B 1 h, B2B_B 0.5 h,
K2_B 2 h, B1B_B 0.5 h K1_B1 h.
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Conclusion
The paper deals with calculating of the maximally
permissible deadlock prevention supervisor
First step is creating a suitable Petri net model
of traffic system using MRF1 type of Petri net
Second step is to find structural properties -
circular waits, critical traps, siphons, critical
subsystems, and key resource
Finally, the set of constraints must be defined
and calculation of control policy must be done
The supervisor calculation and realization are
simple
Analyzing the system of N-canals (more than 1 key
resources)?