Aula 04 MP260

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Profa. Emília Villani

Lesson 4 – Automata and the Design of Supervisory

Systems

MP 260 – Modelling and Analysis of Discrete Event Dynamic Systems

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Purpose of the Lesson

Design supervisory systems for

DEDS using automata.

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✹ Control system that imposes the specified behaviour on the plant by enabling the occurrence of certain events:

✹ The supervisory system observe the occurrence of events on the plant and define the enabled events.

✹ Specification: set of restrictions that the system should obey (ex.: the robot can only pick up the part from the buffer if the destination is free).

Supervisory System1. Control of DEDS

Observed events

Plant

Supervisory system

Enabled events

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✹ The plant is modelled as an automaton G, with an alphabet Σ.

✹ The supervisory system is modelled as an automaton S defined over the same alphabet Σ.

✹ The behaviour of the controlled system is S/G:

Supervisory System and Automata1. Control of DEDS

Observed events

Plant

Supervisory system

Enabled events

Lg(S/G) = Lg(S||G)Lm(S/G) = Lm(S||G)

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✹ Controllable events - Σc:▪ Events of the plant that can be inhibited by the

control system.

✹ Uncontrollable events - Σu:▪ Events of the plant that cannot be inhibited by

the control system.

✹ Properties: ▪ Σ = Σu∪ Σc▪ Σu ∩ Σc = ∅

Controllable and Uncontrollable Events

1. Control of DEDS

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Design of Supervisory Systems

1. Control of DEDS

Step 1 – Modelling the plant

Step 2 – Defining the specification

Step 3 – Synthesis of the supervisory system

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Step 1 – Modelling the Plant1. Control of DEDS

A. Identify the system components and build the automaton of each component.

B. Use synchronous composition to obtain the global model of the plant (uncontrolled plant).

C. Identify the controllable and uncontrollable events.

✹ Example: system composed of Machine 1 and Machine 2.

E1 F1

a

b

E2 F2

c

d

Machine 1

Machine 2

E1E2 F1E2

a

b

E1F2 F1F2

a

b

d c d cControllable events: a and c.Uncontrollable events: b and d.

Uncontrolled plant

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Step 2 – Defining the Specification1. Control of DEDS

A. Build an automaton for any restriction.B. Compose the restriction with the plant.C. Delete any non co-accessible states of the controlled plant.

✹ Example: The output from Machine 1 goes to Machine 2. The intermediate buffer has capacity 1.

A Bb

c

E1E2 F1E2a b E1E2

cA A B

E1F2Aa F1F2A

b E1F2Ba F1F2B

F1E2Bd

c

a

dd d

Restriction

Controlled plant

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Controllability 1. Control of DEDS

✹ Consider the following plant and specification:

▪ What happens when the system is in state 1B?▪ Can the controller forbid the occurrence of the second event b?

A Bb

c

Restriction:

a b d0A 1A 2B 0B a 1B c 3A

eControlled plant:

0 1a

2

3

b

ce

dPlant:

NO!

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✹ Condition for controllability:

EΣu ∩ Lg(G) ⊆ E

▪ E – Language of the controlled plant resulting from Step 2.

▪ EΣu – Strings from the controlled plant followed by uncontrolled events.

▪ EΣu ∩ Lg(G) – Subset of EΣu that can actually happen in the plant.

▪ EΣu ∩ Lg(G) ⊆ E – All the possible uncontrolled events of EΣu must be in E. The supervisory system cannot inhibit the occurrence of uncontrolled events.

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✹ Sometimes the solution is not possible...

a b d0A 1A 2B 0B a 1B c 3A

e

✹ Solution:▪ Eliminate from the controlled plant transitions of controlled

events that lead to dangerous states.

0A Resulting trim automaton !!!


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Step 3 – Synthesis of the Supervisory System

1. Control of DEDS

A. Identify dangerous states and delete controllable transitions that lead to dangerous states.

B. Determine the trim automaton.

✹ Example: system of Machine 1 and 2.

F1E2B

E1E2 F1E2a b E1E2

cA A B

E1F2Aa F1F2A

b E1F2Ba F1F2B

d

c

a

dd d

E1E2 F1E2a b E1E2

cA A B

E1F2A

a F1F2A

b E1F2B

dd d

F1E2B

F1F2B

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Software IDES2. Introduction to IDES

✹ Download from: https://qshare.queensu.ca/Users01/rudie/www/software.html

✹ Unzip and double clip on IDES3.jar.States: click on ‘Create nodes and edge’ and on drawing área.

Events: write name in the 'Add new event' box and click on 'Add‘.

Transitions: click on the starting node and then on the ending node.

Initial and/or marked states: select the state and click on the right button of the mouse, click on 'initial' and/or 'marked‘.

Add events to transitions: select the transition and click on the right button of the mouse, select 'Label with events‘ and assign events to edge

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✹ Step 1 – Modelling the plant▪ Create the automata of Machine 1 and Machine 2.

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✹ Step 1 – Modelling the plant▪ Compose the automaton of the plant: menu ‘operations’, ‘DES

operations’.▪ Use ‘sync’ operation.

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✹ Step 2 – Defining the specification▪ Compose the automaton of the plant: menu ‘operations’, ‘DES

operations’.▪ Use ‘sync’ operation.

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✹ Step 3 – Synthesis of the supervisory system▪ Use ‘supcon’ operation with ‘Plant’ as the plant model and

‘Controlled_plant’ as the specification.

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Production System3. Exercises

✹ Design the supervisory system

Components and Events

Valve_1:Events: open1, close1



Uncontrollable:close1, close2, close3

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✹ Step 1 – Modelling the plant

Valve_1

Valve_2

Valve_3

Valve_1+Valve_2+Valve_3


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✹ Step 2 – Defining the specification

Restriction_1

Restriction_2

Restriction_3

Controlled_plant


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✹ Step 3 – Synthesis of the supervisory system

Supervisory_system


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Manufacturing System3. Exercises

Buffer(max 1 part)

Machine(max 1 part)

Robot(max 1 part)

Exit

a – Part arrives at Buffer,b – Robot picks up part from Buffer, c – Robot delivers part to Machined – Robot picks up part from Machinee – Robot delivers part to Exit.

Uncontrollable events:

a, c , d, e


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Transportation system

Machine 1 Machine 2Exit

AGV

a

Automated Guided Vehicle

b c d e

a – Part enters Machine 1b – AGV picks up part at Machine 1c – AGV delivers part to Machine 2

d – AGV picks up part at Machine 2e – AGV delivers part to exitUncontrollable events: a, c, e

3. Exercises


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Quality Assurance

✹ Camera detects good and faulty parts at P1. The good ones go to the Machine, faulty ones are rejected.

Track

Reject

P1 P2

Robot

Machine

Part

Camera

a – Part arrives at P1b – Track rotates from P1 to P2c – Robot picks up part at P2d – Robot rejects the part

e – Robot delivers the part to the machinef – Machines delivers the partg – Camera detects faulty parth – Camera detects good partUncontrollable events: g, h, f

3. Exercises


Aula 04 MP260

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