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Dynamic Supervision in Mechatronic Systems Using Bond Graph Approach .

D. Benazzouz, Y. Touati & B. Ouled BouamamaSolid Mechanics & Systems Laboratory (LMSS)

University M’Hamed Bougara Boumerdes, Algeria

*Ecole Polytechnique Universitaire de Lille-France

dbenazzouz@umbb.dz

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Presentation

• Introduction• Structurelle Analysis• FDI Methods • Various Residu Generation Approaches• Study case• Modelisation & Simulation • Resultats et Comments• Conclusion

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Safety in critical or dangerous systems, such as the chemical factories, the nuclear centers, the thermal power stations or the air planes, any component failure can be extremely dangerous. As the case Tchernobyl (Skikda-Algeria), any partial failures or component failures or process malfunctions can be a desaster and increase operating factory expenses. There are many cause of these failures(operation – component or humain..)

Introduction

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Faulty Types

Controler Faulty: Caracterised by the difference between the real ouput controler value and its measure.

Actuator Faulty: Incoherency between command & output (pump

delivers an incohérent flow with respect to its hydraulic

characteristic).

Physical Process Faulty: Faulty due to structure modifications or

model parameters.

Sensor Faulty: Variation between the real and the measured value.

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Supervion: supervise the state of process in optimal functionning and gives assistance to operator in case of emergency to increase the realiability.

Supervion role : Fault Detection and Isolation (FDI)

Fault Tolerence Control (FTC)

Supervision

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FDI Methods with model

1-Identification: I/O of the system used to estimate various parameter values of the analytical model

2 -Observer: Estimate directly output system then compare it to measured output of sensors.

3- Analytical or Information redondancy: Rewriting state equations and measure (only known var. are considered)

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Various System Representations

Biparti Graph Representation

Ex: Electrical Engineering

1

2

3

4

5

6 1

7 2

c : 0

c : 0

c : 0

c : ( ) 0

c : 0

c :

c : 0

R

L

C

m C

e R L C

C

u Ri

diu L

dtdu

i Cdt

u F u

u u u u

diz

dtdu

zdt

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Using Matrix form which represents the set of var. Z and the set of constrains C: Tij =1 if Zj Є Cj

Otherwise Tij=0

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Structurel Analysis

Determines system property starting from existing constrains. This will help the designer to be able with respect to the functionning conditions to supervise and detect any faulty. To perform the structurel analysis on biparti graph, we use DM-decomposition

DM-Decomposition

Dulmage & Mendelsohn (1958) denoted DM-decomposition is the starting structurel analysis point. We can obtain it by appling using graph theory principal.

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Interchange colonn to raw of the incidence matrix to obtain the low triangular matrix.

S+: sub-system (observable & supervisable)S°: sub-system (observable not supervisable)S-: sub-system (not observable & not supervisable).

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Case of Simple system: graph biparti concept is easyBut, for Complex system: it usefull to apply Bond Graph analysis which is powerfull in multi-energy processesBG : oriented graph, showes dynamic var. (effort-flow) energy transfer between systems Se: effort source (voltage) & Sf: flux source (current), 3 passif elements (I, C & R), 2 junctions (0 et 1) & 2 transductors (TF (transformer) & GY (motor)) Sensors (De, Df)

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Structural Analysis on Bond Graph

The SCAP (Sequential causality application procedure) is as follows:

1 – Affect necessary causality to sources

2 – Put I & C in integral causality in preferential

3 – Affect the causality to R elements with respect to restriction junctions.

4 – In case of junction conflit, find I & C element causing conflit & put them in derivative causality. Restart 3.

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Observability from BG (2 canditions)

1- All the elements of storage must have a causal path towards at last 1 detector (reachability condition).

2- All the elements of storage can be put in preferential derivative causality (with detector causality inversion).

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Surveillability Condition

Suveillability canditions: 1. Sub-system is observable.2. A default j should be in the sub-system to be observable

All BG models have a correct causality, with causality inversion of storage and detector elements are over-determined systems.

In case of system causality conflit, we have a sub-determined system .

Conflit

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The observators

The methode by observator is based on residus analysis. (Residu or fault indicator expresses incoherency between avalable information & theoratical information given by the model.

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Fundamental Eq. of the observor

All linear systems are represented as follows:

( ) ( ) ( )

( ) ( )

x t Ax t Bu t

y t Cx t

Observor Eq. Are:

ˆ ˆ ˆ( ) ( ) ( ) ( ( ) ( ))

ˆ ˆ( ) ( )

x t Ax t Bu t K y t Cx t

y t Cx t

0(0)x x

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( )ˆ ˆ( ) ( )( )

ˆ ˆ( ) ( )

y tx t A KC x t B K

u t

y t Cx t

We can simplify the previous Eq. as follows:

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Generation of the RRAs

We can generate RRAs by using bi-party graph & coupled notation on the incidence matrix. This couple is then a causality which allow the construction the incidence matrix & calculate unknown variables from system constrains.

When unknown variables are all coupled, in case sup-system, the constrains which are not coupled are called RRAs

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ARRs Generation

An ARR is a constraint calculated from sub-system sup-determined & observable & expressed in terms

of known process variables. It has the following symbolic form:

( ) 0f k

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ARRs Generation by BG

ARRs generation by BG methodology is based on same principal as biparti graph, namely unknown variables elimination in the sub-system, sup-determined & observable.On BG model, the known variables K are those of detectors & sources and the unknown variables X are those of power links in C, I & R elements. The unknown variables elimination is systematic in BG model because of causal properties.

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ARRs Generations by Bond Graph

For ARRs generations, the supervised process BG model should be in preferential derived causality. Note that the integral causality is recommanded for simulation to avoid differential data processing illness. However, the derived causality is suited for RRAs to avoid the influence due to initiale values.

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Systematical ARRs generation algorithm from BG model is as follows: 1- Put the BG model in preferential derived causality (by inversing the detectors causality if possible).2- Write the equations of the obtained model: Behavior, junctions, measure, sources & command.3- For each junction equation 0 & 1 containing at least one detector, eliminate the unknown variables by following the causal path of BG.4- An ARR is obtained starting from each regulator by comparing the measured output with the predicted value given in its command algorithm

ARRs Generation by BG Algorithm

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Application

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Application

BG Model in derived causality:

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Application

Equations of the system are obtained from the BG model:

2 21 1 1 2

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1 1 1 2 2 2

1 1

1

1 1 1 0

Q QR C R CMSf

QQR C R C R C

Where Q1, Q2 reprent Volumes in tank 1 & 2, R1 & R2 are discharge inverse capacity through the 2 elctromagnetic valves:

1 11

2 22

,A est la surface dereservoir 1

,A est la surface dereservoir 2

gC

A

gC

A

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Simulation

Evolution of V1 & V2 as function on time (without default)

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ARRs Generation

Using ARRs generation rules starting from BG

11 1 1

( ): 0

d DeRRA MSf C Df

dt

23 1 2 2 2

2

1: . ( ) 0

dDeRRA Df C De Se sng De Se

dt R

4 1: ( ) 0RRA MSf f u

5 2 2: _ ( ) 0RRA u On OFF De

6 1 1: ( , ) 0cRRA u De H

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From the 6 ARRs, we can deduce the default signature matrix to determine the isolability & the detectability of default

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Simulation 2-ARRs

Let’s take examples to the behavior of RRAs in case of faulty

1- Residus response to leakage default on tank "C1"

ARR1ARR2

ARR3

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2- Residus response to leakage default on tank ’C2’

Simulation 2-ARRs

r2

r3

r1

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Simulation 2-ARRs

3 -Stopped (bouchage) default in tube between the 2 tanks

r1 r2

r3

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Conclusion

The advantages of this approach (structural) comparade to appraoch based on observer are: Simplicity of comprehentions of ARRs since they correspond to relations & variables which are fixed by the BG model, of the physical process, these relations are deduced directly from graphical representation, they can be generated in symbolic form & thus adapted to a data processing implementation.

The goal of BG representation is to use only one modeling tool, generation of ARRs, structural analysis & surveillability & sensors placement.