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CHAPTER 5

REAL TIME APPLICATIONS

5.1 OVERVIEW

In Chapter 4, the proposed methodology to achieve FDI and FTC along with

numerical and simulation results were presented. For this purpose, benchmark

systems under various case studies were analysed. In this Chapter, the applications

of the proposed methodology on real time systems are discussed and presented. The

real time systems considered in this research work are the Sulphur Recovery Unit

(SRU) in petroleum refinery, Sewage Treatment Plant (STP) in waste water

treatment system and Bottle Filling Plant (BFP). In SRU unit, two main systems

namely, Main Clause Recovery Converter (MCRC) and Vaporized Liquefied

Petroleum Gas (LPG) header systems are modeled and analysed. Based on the

analysis done, the applications of the proposed methodology to achieve FDI are

discussed. Likewise, operations of STP and BFP are modeled, and analyzed in Petri

net environment. A MATLAB based GUI toolbox is then developed to estimate the

typical faults occurring in a STP. Finally, the conditions for achieving FDI along

with FTC in BFP are derived analytically and presented.

5.2 PROPOSED FDI IN SULPHUR RECOVERY UNIT (SRU)

In this section, methods adopted for modeling, analysis and FDI of the systems

in a typical SRU unit of a petroleum refinery are discussed. For this purpose, real

time data collection for a SRU in Chennai Petroleum Corporation Ltd (CPCL) is

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done and based on the data, available techniques as discussed previously are

applied.

5.2.1 Introduction to SRU

The Chemical Process considered here is the SRU of Refinery process of Chennai

Petroleum Corporation Ltd., Chennai. The SRU forms an important and essential

unit in Refining process where extraction and removal of Sulphur from the products

of refining are carried out to improve the purity and efficiency of the products. SRU

comprises several sub-units working together to achieve the purest form of the

products, thereby reducing the content of elemental sulphur. Since the SRU

developed in CPCL works on the principle of Main Clause Recovery concept

(MCRC), the MCRC sequence working is considered here for study. The detailed

description of MCRC unit will be covered in a later section separately.

Refining Process Industry comprises various components of boilers, heat

exchangers, cooling towers, etc. and the flow of the fuel/gas is done through a series

of pumps and valves, controlled through control units placed at various locations in

the Industry. The control units take appropriate control actions through the help of

numerous sensors for controlling flow, level, pressure, temperature, etc. System

normally monitored through automatic/Manual means is subjected to frequent

malfunction and has to be rectified so as to improve the efficiency avoiding frequent

breakdowns. Moreover, the faults or malfunctions that frequently occur in the

system are either due to Valve failures or sensor failures. Since valves and sensors

are an integrated part of every sub-unit of the process, it becomes quite difficult to

identify and detect the faults arising due to these failures. Hence, it is utmost

necessary to develop algorithms to achieve effective fault diagnosis to detect valve

and senor failures.

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In Literature, as discussed in section 1.5 of Chapter 1, there have been numerous

schemes and designs developed, and made available to achieve fault diagnosis.

Here, the concept of Petri nets is used to model the systems as DEDSs, rather than

continuous systems for the sake of simplicity. The faults occurring in valves are

classified as Transition faults and the ones occurring in sensors are classified as

Place faults in a Petri net environment. The normal condition of an event is

considered to be observable, and is thus modeled. Once the fault has occurred, the

corresponding event is termed as unobservable, and thus, the system is again

modeled based on the unobservabilty nature. By comparing the new system with the

original system, the faults occurred in the system are identified analytically.

5.2.2 Process description

The process design of SRU is based on the Main Clause Recovery Concept

(MCRC) technology, which is licensed by M/s. DELTA HUDSON

ENGINEERING LIMITED. It is a combination of the Clause process and the

extension of the Clause reaction up to the temperature at which the product sulphur

starts condensing on the catalyst itself. Extension of Clause reaction upto sulphur

dew point enhances sulphur recoveries beyond 99%. As sulphur condensation on

the catalyst leads to its activity reduction, regeneration of such portion of the

catalyst bed is required. Overview of the total SRU plant is shown in Figure 5.1.

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Figure 5.1 Overview of SRU plant

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5.2.2.1 Clause section

Each Train of SRU consists of a thermal reactor and four catalytic converters. The

first catalytic converter is a conventional clause converter, while the last three are

MCRC converters that alternate between a sub-dew point mode, and a regeneration

mode. With such a four-converter MCRC configuration, sulphur recovery higher

than 99 % is achievable. The salient feature of the MCRC process is that

regeneration takes place on line.

The acid gas from Amine Regeneration Unit (ARU), Hydrogen Sulphide (H2S)-

rich gas from the 1st stage Sour Water Stripping Unit (SWS) and Ammonia (NH3)-

rich gas from the 2nd stage SWS Unit is fed to the SRU to convert H2S contained in

the feed gas to elemental sulphur. The acid gas is preheated to 89°C using Low

Pressure (LP) Steam. The preheated acid gas is fed into the Main Combustion

Chamber (MCC) furnace in each train, which is already heated to 1100°C, with fuel

gas or vaporized Liquefied Petroleum Gas (LPG). Air flow to MCRC is adjusted to

get H2S to SO2 ratio as 2:1. The major part of heat generated in the furnace is

recovered by producing Main Pressure (MP) steam in the Waste Heat Boiler

(WHB). The vapours leaving WHB is further cooled to 191°C in sulphur

condenser-1 to remove elemental sulphur from the gas mixture producing LP steam.

The gas from condenser is reheated in a line burner using a slip stream of ARU gas

from Knock Out (KO) Drum as fuel. The preheated vapours from the line burner at

273°C further flows to the 1

st clause converter, where additional conversion to

sulphur takes place. The reaction gases from the converter are cooled in a reheat gas

exchanger, and sulphur condenser 2. The produced sulphur condenses and flow to

sulphur pit via sulphur lock. Overview of the MCRC converter is shown in Figure

5.2.

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5.2.2.2 Main clause recovery section

In the MCRC section as observed in Figure 5.2, there are three catalytic stages

along with respective sulphur condensers. Operating conditions in two of the three

MCRC reactors are aimed in such a way that the adsorption of produced sulphur

takes place on the part of the catalyst present in the reactor. Such adsorption of

sulphur of the catalyst is achieved by maintaining temperature in the corresponding

reactors lower than the sulphur dew point. Removal of sulphur from product gases

of Clause reaction by way of adsorption on catalyst is to increase sulphur

conversion by moving Clause reaction in the forward direction. Additionally lower

reaction temperature also helps thermodynamic equilibrium to shift towards higher

sulphur equilibrium concentrations. Thus, overall higher sulphur conversions are

easily achieved by reducing the operating temperature in the catalytic reactors.

However, deposition of sulphur on active site of catalyst prohibits its further

activity. To regenerate the activity of such catalyst sites, sulphur present on such

site needs to be desorbed. Desorption of sulphur is carried out by operating the

reactors at a temperature higher than the sulphur vaporization temperature. The

need of operating sulphur loaded catalyst at higher temperature is met by operating

one of the three MCRC reactors at any given time under regeneration mode. Each

MCRC reactor operates in a sequence under the following operating modes: (1)

Regeneration mode, (2) Sub-dew point mode-1, and (3) Sub-dew point mode-2.

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Figure 5.2 Overview of MCRC Section

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As mentioned before, MCRC section includes the three sub-dew point sulphur

converters. These converters alternate between a sub-dew point mode of operation

and a regeneration mode. For the purpose of discussion, the converter operating in

the regeneration mode is said to be in the sulphur converter II position, and the

converters operating in the sub-dew point mode are said to be in No. III and No. IV

positions.

The reheated gas from the Clause section enters the No. II position sulphur

converter and regenerates the catalyst bed by vaporizing sulphur which was

previously adsorbed onto the catalyst when this converter occupied the No. III and

IV positions. Clause conversion continues in this converter even while it is

regenerating. The exit gas is cooled to remove elemental sulphur and flows directly

(without reheat) to the No. III position where sulphur condenser is operating in a

sub-dew point mode. The gas mixture from converter flows to the condenser and

the balance gas from condenser directly flow to No. IV position sulphur converter,

where additional sulphur is produced and adsorbed onto the catalyst.

The adsorbed sulphur onto the catalyst is removed from the same converter in the

next cycle. Approximately every 24 hours, one of the three MCRC converters is

changed from sub-dew point mode to regeneration mode, and another one is

changed from regeneration mode to sub-dew point mode. The cycle time may be

changed depending on the loading of sulphur onto the catalyst bed during the actual

operation.

MCRC section is equipped with three converters and three sulphur condensers.

Process gas from Clause section at a temperature of 277°C enters into the MCRC

converter-II and regenerates the catalyst at high temperature by vaporizing sulphur

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from the catalyst pores, where sulphur was already adsorbed when the converter

was in a sub-dew point mode. Catalyst is regenerated and simultaneously Clause

reaction further proceeds to produce elemental sulphur in the regeneration mode

reactor. The process gas from MCRC Converter II flows directly to sulphur

condenser-III at a temperature of 296°C. The condensed elemental sulphur is

separated in the outlet channel of the sulphur condenser-II, and flows to sulphur pit

via sulphur lock. The balance gas exiting from sulphur condenser III at a

temperature of 143°C flows to sub-dew point converter-III. The Clause reaction

conversion to sulphur occurs at sub-dew point condition where produced sulphur is

adsorbed onto a catalyst pore structure. The leaving process gas from sub-dew

converter III flows to sulphur condenser-IV where Sulphur is condensed and flows

to sulphur pit via sulphur lock. The balance process gas at a temperature of 124°C

leaving sulphur condenser IV flows to converter-IV without re-heating. The clause

reaction continues at a sub-dew point mode to produce sulphur. The process gas

from converter-IV flows directly to condenser-V, from where condensed sulphur is

taken out to sulphur pits via sulphur seal pit. Tail gas from condenser-V flows

directly to a tail gas incinerator, and to the stack. A tail gas coalesce is not necessary

since demister in the outlet channels of the condensers are adequately designed to

separate any sulphur mist. Furthermore, adsorption of sulphur at a sub-dew point

converter catalyst depresses mist formation.

When the catalyst is on a sub-dew point, sulphur converter-III reaches a certain

weight percentage loaded with sulphur, and the converters interchange positions

with converter-II automatically by means of switching valves. The valves operate

on a time cycle control system. Interchange of position of converters-II and III

means the process gas from clause section enters first into converter-III, which is

put in regeneration mode, and the balance gas from converter-III after cooling in

condenser-IV enters into converter-II at a sub-dew point mode. The gas from

converter-II after cooling flows to converter-IV which is still at a sub-dew point

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mode. Similarly, in the next cycle, converter-IV will be in the regeneration mode

and the other two converters will be put at a sub-dew point mode by switching

valves. Hence, at any time one converter is in regeneration mode and two converters

are in sub-dew point mode.

The switch over cycle of MCRC converters is explained as follows. Due to low

temperature reaction in the sub-dew point converters, and in order to condense as

much sulphur vapour as possible, the last three condensers operate at a low

temperature. This low temperature is obtained by generating steam at a lower

pressure (1.1 kg/cm2) than in the preceding condensers. The steam is condensed in a

steam condenser from which the condensed steam is drained back into the shell side

of the sulphur condensers. The vaporised steam from the condensers is sent to

fin-fan coolers, which consists of two fans, one is fixed drive, and the other is

variable one. The variable drive controlled by a temperature controller placed at the

outlet adjusts the speed of the fan motor. The following are the reactions taking

place in Clause and MCRC Catalytic converters:

The equilibrium clause reaction, Equation (5.1), which is exothermic at the

converters temperatures - is led to an almost total completion over an activated

alumina catalytic bed:

2H2S + SO2 3/x Sx + 2 H2O, (5.1)

where x is mainly 6 or 8 at the operating temperature of the converter.

The above reaction, given by (5.1), takes place on all four catalytic beds. The

hydrolysis of most of COS and CS2 produced in the reaction furnace is also

accomplished in the lower part of the 15th

catalytic bed according to the reactions:

COS + H2O H2S + CO2, (5.2)

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CS2 + 2 H2O 2 H2S + CO2. (5.3)

The above mentioned endothermic reactions, Equation (5.2) and Equation (5.3),

take place due to high temperature achieved in the catalytic bed despite no

dedicated catalyst being foreseen.

The following sulphur equilibrium reactions take place continuously in vapour

phase during the combustion, the catalytic conversion and the cooling phases,

depending upon the operating temperatures:

3S2 S6, (5.4)

4S2 S8. (5.5)

Condensation of the vapour sulphur produced in thermal and catalytic conversion

steps is achieved in the waste heat boiler and sulphur condensers according to the

following reaction:

S8 (vap) 8 S1 (liq). (5.6)

Sulphur degassing is achieved in the sulphur pit; the following chemical reaction

of poly-sulphides dissociation also takes place:

H2Sx H2S + S (x-1). (5.7)

H2S absorbed in liquid sulphur is stripped and sent to the incinerator via a steam

ejector.

5.2.2.3 Thermal incinerator

In the thermal incinerator, the combustible components in the process gas from the

last condenser of MCRC section and vent gas from sulphur pit are thermally

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oxidized at high temperature. Thermal Incinerator is common for two-train sulphur

recovery. There are two tail gas streams from two trains and one vent gas stream

from sulphur pit; those are oxidized in incinerator.

The thermal incinerator converts almost all H2S and NH3 in the tail gas so that H2S

in stack gases has concentration lower than 10 Parts Per Million (PPM) in volume.

The exit gas temperature must be kept at 750°C. The proper ratio of air to fuel is

controlled by the ratio-controller. The oxygen content of flue gases is controlled by

the oxygen analyzer. Excess air operation is essential for complete incineration of

process gases. Oxygen content of stack gases is set at 2 % vol. The flue gases are

vented to atmosphere through the vent stack. Shutdown of thermal incinerator due

to any reason will activate the shutdown of SRU.

5.2.2.4 Sulphur storage

Sulphur produced is routed to Run/Down (R/D) line through specially designed

sulphur lock, and collected in the sulphur pit. Sulphur pit is provided with degassing

facility and LP steam heating coil to keep sulphur in molten condition. Sulphur

pump pumps the product sulphur to pelletization unit, where molten sulphur is

pelletized, and stored in silos through bucket conveyor. Sulphur yard is also

provided to produce lump sulphur by pumping molten sulphur to yard by cooling

with cooling water.

5.2.2.5 Initial firing

For start-up of Main and Line Burners, and as a supplementary fuel for line

burners, in case of low H2S content of acid gas, vaporized LPG is used. The

overview of the LPG header unit is shown in Figure 5.3.

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Liquid LPG from Battery Limits is received in a LPG vaporiser drum and is

vaporized by means of LP steam flowing into the internal coil of the drum. The

level in vaporizer drum is controlled by a level controller acting on a LPG inlet line

valve and its pressure is controlled by a pressure controller, acting on a control

valve on steam inlet to the internal coil. The vaporized LPG is sent to the vaporized

LPG Knock Out (KO) drum, where entrained liquids are separated and from where

it is distributed to main burners and to line burners of both the trains.

Figure 5.3 Overview of LPG Header Unit

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5.2.3 Process modeling and analysis

As discussed in Chapter 2, here, process modeling is done using Petri nets

considering the whole process as DEDSs. Thus, the model comprises discrete

places and discrete transitions connected by normal arrows.

The presence of a token in a place denotes the condition for starting an operation

or event, firing of a transition denotes the start of the event, and movement of the

token from one place to another represents condition after the operation or event is

completed. Based on these conditions, the modeling of the systems is done.

Figure 5.4 and Figure 5.5 represent the equivalent systems for valve sequence

operations of Main Clause Recovery Concept (MCRC) and vaporized LPG train

modeled using Petri nets.

Dark circles in Figure 5.4 and Figure 5.5 represent the actual valves that are

present in the unit. White circles represent the conditions for the valve, i.e., whether

it is open or closed. Thus, the presence of a token in the respective white circles

shows that the corresponding valves are to be kept open for sequential operation.

The explanation for each place and transitions used for modeling in Figure 5.4 are

mentioned in Table 5.1, and for Figure 5.5, in Table 5.2.

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Figure 5.4 Petri net model of MCRC valve sequence 1

Figure 5.5 Petri net model of vaporized LPG header train

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The inlet valves are represented as IN1, IN2 and IN3, the outlet valves

represented as OUT1, OUT2 and OUT3, and intermediate valves are represented as

IM1, IM2, and IM3, for the simplicity of understanding.

Once successful modeling of the system is completed, the algorithms for FDI are

developed, and the corresponding faults (valve failure, sensor failure etc.) can be

detected and identified.

Table 5.1 Description of places/transitions and conditions for model shown in

Figure 5.4 P/T Description P/T Condition

Yes-Token present

No- Token absent

ON-Firing enabled

OFF-Firing disabled

Cycle

1

Cycle

2

Cycle

3

P1 Process Flow gas Yes Yes Yes

T1 Valve 1 ON ON ON ON

P2, P4, P6 Flow gas ready No No No

P3, P5, P7 Mode I, II, III No No No

T2, T3, T4 Inlet valve

1, 2, 3

ON OFF OFF

T8, T9, T10 Intermediate valve

1, 2, 3

ON ON OFF

T5, T6, T7 Outlet valve

1, 2,3

OFF OFF ON

P9, P10, P11 Inlet Valve 1, 2, 3

condition

Yes No No

P12, P13, P14 Outlet valve 1, 2, 3

condition

No No Yes

P15, P16, P17 Intermediate valve

1, 2, 3 condition

Yes Yes No

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Table 5.2 Description of places/transitions and conditions for model shown in

Figure 5.5 S. No P/T Description

1. P1 KO drum output

2. P2, P3 Valve 1 condition and operation

3. P4, P10 Valve 2 condition and operation

4. P5, P11 Valve 4 condition and operation

5. P6, P7 Pressure switch and Reaction furnace condition

6. P8, P9 Alternate Valve 1 line condition and operation

7. P12 Furnace operation

8. P13, P14 Flare output for alternate line

9. P15, P16 Flare output for main line

10. P17, P18 Flow transmitter output and condition

11. P19, P20 Condition for flare operation and main and alternate

lines

12. P21, P22 Conditions for valve 1 in alternate line

13. P23, P24 Condition for valve 3 in flare output of main and

alternate lines

14. T1-T6 Main line valves

15. T7-T10 Alternate line valves

16. T11, T15 Flare output valves of main line

17 T14, T12 Flare output valves of alternate line

18. T13 Condition for Flow Transmitter

19. T16 Condition for valve 1 in alternate line

5.2.4 Proposed FDI

As mentioned in the earlier section, Petri nets are a powerful tool for system

description. Nevertheless, they can be an useful tool for process monitoring also.

The problem of process monitoring in any Process plant can be stated as follows:

Measurement signals come from the system at a constant scanning rate. When

processing these data, a computer based system should decide on-line in real-time,

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if an error has occurred or not. To perform this, the computer program needs to

know the “total” process description.

Suppose it is possible to map the structure of the total process using a Petri net, the

transport of physical conservation quantity can be represented by firing of tokens. If

the conservation quantity takes only few discrete values, and if the measured signals

are not noisy, then by comparison, and using the property of reachability, errors can

be identified. This is carried out by finding the initial marking, and comparing it

with the new marking vectors developed after firing of tokens. Any change in the

sequence will result in an error in the corresponding element of the marking vector,

which gives indication of the faulty nature of the process. From the erroneous data

obtained, the corresponding faults can be easily diagnosed.

Even when the signals received from the system are noisy, the property of

observability can be considered as the criterion for diagnosis where suitable

threshold limit has to be satisfied. If the error measured as mentioned above is

higher than the limit, it means that a fault has occurred. Then suitable diagnosis is

done to classify the faults.

Normally in Petri nets, presence of place faults are similar to sensor faults and the

presence of transition faults are equivalent to valve failure. Based on these

conditions, the fault monitoring algorithm for identifying faults in a MCRC model

shown in Figure 5.4 is given as follows:

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Step (i): With respect to the modeled control structure, the initial token content per

place is found by determining the initial marking vector denoted by

Mi(0).

Step (ii): After determining Mi(0), the actual number of tokens arising in the

running of the process is found out, which is denoted by Mi(k).

Step (iii): The difference between the marking vectors are calculated i.e. Mi(k)-

Mi(0).

Step (iv): If the difference is zero, then the system is considered as fault free.

Step (v): If not, the corresponding place fault has occurred, and an algorithm is

developed to identify the faulty place in the structure modeled earlier.

Figure 5.6 and Figure5.7 show the development of the system for fault diagnosis

modeled in a MATLAB environment.

Figure 5.6 View of original model of MCRC valve sequence 1

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Figure 5.7 View of fault model of MCRC valve sequence 1

The presence of a place fault is diagnosed by considering and checking the

reachability of markings. For diagnosing the transition faults, evaluation of

performance measures are considered, which will be discussed in Chapter 6. The

algorithm developed in MATLAB environment is shown in Figure 5.8. Likewise,

Figure 5.9 and Figure 5.10 show the views of the simulation results obtained for a

faulty and a non-faulty process.

As observed in Figure 5.8, using the commands available in NETLAB toolbox

[81] in a MATLAB environment, the values of pre-incidence, post-incidence, and

incidence matrices are determined similar to the method discussed in section 3.2.2

in Chapter 3.

Faulty

place P10

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Figure 5.8 View of algorithm developed for FDI in MATLAB

Once the matrices are known, the values of place markings can be found out from

(2.4) as described in section 2.2.1 in Chapter 2. Now, for any fault occurring in the

model (especially place faults), the value of place marking obtained when fault

occurs will not be the same as obtained for a non-faulty condition.

Thus, the non-presence of a null value in the difference between the place marking

vectors shows that the corresponding place is under fault. As discussed in this case,

the presence of a fault in place P10 is determined and the simulated results are

shown in Figure 5.9.

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Figure 5.9 View of Simulation result developed in MATLAB for a faulty

process

Figure 5.10 View of Simulation result developed in MATLAB for a non-faulty

process

The modeled

system is faulty

and faulty place

is P10

The modeled

system is fault free

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For the purpose of simulating the processes modeled using Petri nets as shown in

Figure 5.11, SIRPHYCO software [82] is utilized. The simulation window shows

time taken for firing of each valve to operate in the MCRC sequence. Moreover, the

graphs also depict the sequence of operation, i.e., initially P3 is marked followed by

P5, P7 and finally outputted through P8. Similar graphs can be obtained by

considering the other valve sequences of the MCRC.

Figure 5.11 Results for MCRC valve sequence 1

Figure 5.12 Results for MCRC valve sequence 2

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The marking evolution of the places considering valve sequences 2 and 3 are

simulated and shown in Figure 5.12 and Figure 5.13, respectively.

Figure 5.13 Results for MCRC valve sequence 3

5.3 PROPOSED ESTIMATION BASED FDI IN SEWAGE TREATMENT

PLANT

The second real-time application considered here is a sewage water treatment plant

which is analogous to a three tank benchmark system [83]. Sewage treatment, or

domestic waste-water treatment, is the process of removing contaminants from

waste-water and household sewage, both runoff (effluents) and domestic. It includes

physical, chemical, and biological processes to remove physical, chemical and

biological contaminants. Its objective is to produce a waste stream (or treated

effluent) and a solid waste or sludge suitable amount for discharge or reuse back

into the environment. This material is often inadvertently contaminated with many

toxic organic and inorganic compounds.

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Here, the objective is to develop model-based analysis for a typical STP plant and

to achieve estimation based FDI.

5.3.1 Process description

STP plant [84] as shown in Figure 5.14 comprises three major processes which

follow:

Primary Treatment,

Secondary Treatment, and

Tertiary Treatment.

Primary Treatment:- In the primary sedimentation stage, sewage flows through

large tanks, commonly called "primary clarifiers", or "primary sedimentation tanks"

[84]. The tanks are large enough that sludge can settle and floating material, such as

grease and oils can rise to the surface and be skimmed off. The main purpose of

primary sedimentation stage is to produce both a generally homogeneous liquid,

capable of being treated biologically and a sludge that can be separately treated or

processed.

Secondary Treatment: - The rotating disks support the growth of bacteria and

micro-organisms present in the sewage, which breakdown and stabilize organic

pollutants. To be successful, micro-organisms need both oxygen to live and food to

grow. Oxygen is obtained from the atmosphere as the disks rotate. As micro-

organisms grow, they build up on the media until they are sloughed off due to shear

forces provided by the rotating discs in the sewage. The spinning mesh wheel

develops a bio-film coating of microorganisms that feed on the suspended wastes in

the aquarium water and are also exposed to the atmosphere as the wheel rotates.

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This is especially good at removing waste urea and ammonia urinated into the

aquarium water by fish and other species [84].

Tertiary Treatment: - The purpose of tertiary treatment is to provide a final

treatment stage to raise the effluent quality before it is discharged to the receiving

environment (sea, river, lake, ground, etc.). More than one tertiary treatment process

may be used at any treatment plant. If disinfection is practiced, it is always the final

process. It is also called "effluent polishing" [84].

Figure 5.14 Overview of a STP Plant [84]

The STP plant shown in Figure 5.14 is analogous to a three tank system as shown

in Figure 5.15. Hence, based on this consideration, modeling and analysis for the

STP plant is done by considering the plant as a three tank system. The details of the

three tank system are as follows:

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The water to be treated is given to tank 1 through pump 1.

The fluid from tank 1 after sedimentation is passed over to tank 2 through

valve 1 with constant out flow.

After secondary treatment in tank 2, the treated water flows to tank 3.

In tank 3, “effluent polishing” takes place by the addition of disinfectant

through pump 2.

Figure 5.15 Equivalent three tank system model for the STP plant shown in

Figure 5.14

The other details with respect to the process parameters are as follows:

Tank 1 - Maximum level is 15 cm.

Tank 2 - Maximum level is 15 cm.

Tank 3 - Maximum level is 25 cm.

The considered tank is cylindrical in shape.

Valves used are on-off valve.

Level and flow sensors are used to sense their corresponding parameters.

Pump 1 has a flow rate of 3 cm3/sec.

Pump 2 has a flow rate of 2 cm3/sec.

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Valve 1 and Valve 2 have an outflow rate of 4 cm3/sec and 5 cm

3/sec,

respectively.

Note: A raise of 1 unit in level is seen if the volume filled is 1 cm3.

In tank 2 there is a delay given for the stirrer action.

5.3.2 Process modeling and analysis

The Petri net model consists of a hybrid net structure which has five discrete

places and three continuous places as shown in Figure 5.16. The three continuous

places signify the three tank system, and the four continuous transitions with

maximal speed signify valves and pumps. The discrete place signifies the logic with

which the system should work. The movement of token in discrete places resembles

the flow of logic in the system. The first place is analogous to pump 1, and the next

is valve 1 open and valve 2 closed. The third place is valve 2 open and valve 1

closed. The fourth one is a delay, and the last one signifies the second pump. A

token in each of the places means that the corresponding condition comes true.

Figure 5.16 Petri net model of the system shown in Figure 5.15

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The details of the corresponding places and their logic are shown in Table 5.3.

Table 5.3 Details of corresponding places for the model as shown in Figure 5.16

PLACE LOGIC

P1 Pump 1 ON

P3 Valve 1 open ,Valve 2 close

P4 Valve 1 close , Valve 2 open

P7 Pump 2 ON

P8 Delay

P2 Tank 1

P5 Tank 2

P6 Tank 3

As observed in Figure 5.16, the equivalent of pump 1 initially ON is shown by the

presence of a token in place, P1. The level in tank 1 increases in accordance with the

maximal speed of transition, T1. When the level in tank 1 reaches 15 cm, transition,

T3, fires, and token from place, P4, moves to place, P3, which means valve 1 is open

thus fluid flows from tank 1 to tank 2 where there is a delay given for the purpose

of secondary treatment. The same procedure is repeated in valve 2, thus fluid moves

to tank 3. Now pump 2 is activated and the disinfectant is allowed to flow through

the tank to reach a height of 25 cm.

Figure 5.17 shows the response of the tanks with respect to time, i.e., the response

of the places. The response of tank 1 and tank 2 are shown with respect to the

response obtained for place, P2, and place, P5. Similarly, the response of tank 3 is

obtained by considering the response of place, P6.

121

(a)

(b)

(c)

Figure 5.17 Responses of (a) tank 1, (b) tank 2 and (c) tank 3 obtained with respect

to places P2, P5 and P6

122

5.3.3 Proposed estimation based FDI

The proposed fault diagnosis algorithm uses the status signal of the devices from

the Programmable Logic Control (PLC) unit at start-up to estimate the output and

predict the fault. This is otherwise called as observer technique as discussed in

section 2.4 in Chapter 2. The observer does estimation and prediction on how the

output might turn out in case of an error.

The proposed methodology is adopted in developing a GUI toolbox in MATLAB

for performing FDI in a three tank system. Figure 5.18 shows the display of the

front panel for the three tank model developed and analysis done for the purpose of

fault diagnosis.

Figure 5.18 Overview of front panel for three tank system

123

There are mainly three panels at the front end.

Algorithm Panel

Graphical Panel

Others Panel

Algorithm Panel:- The first one deals with the algorithm part. This panel contains

two push buttons that are linked to two key algorithms. The first push button in the

panel is the index button. This button has the link to all coding, where all the

schemes, i.e., estimation, evolution, error marking, and fault diagnosis algorithm are

combined into a single program that has directional links to all the other programs.

The second push button in the panel is the one that contains link to the continuous

evolution part. This module can be executed by the push of this button.

Graphical Panel: - This panel mainly deals with the analysis graphs and evolution of

marking of each place. There are six push buttons in this panel. The first one shows

the evolution of a particular place in accordance with time, when the system is

normal. Second button is linked to the original marking of a faulty system (if it

contains any fault). The third one is the evolution of a fault obtained from the error

matrix (the difference between marking evolution of the estimate and the faulty

system). The fifth and sixth are 3 dimensional plots that are used to identify faults

easily. They provide us better perspective of the faults obtained.

Others Panel: - This panel can be easily comprehended. The index button in the

algorithm panel guides us through all the required steps to find out the fault, but this

panel provides us access to all specific algorithms, i.e., all specific modules like

discrete evolution, estimation, etc., and it gives us option to look at all the variables

at once so that we can view the results again for the purpose of documentation, etc.

124

The details of the algorithms applied in the developed GUI toolbox for achieving

FDI are as follows:

Estimation: -The main purpose of estimation is to estimate the evolution of the

marking using the observer technique. The main purpose of the estimator algorithm

is to develop an observer, observer reachabilty graph, and obtain a change in the

system with respect to the observer. The algorithm for the same is as follows:

Algorithm 1-Discrete evolution

Discrete evolution- Discrete evolution is a module developed to obtain the working

of a proper system without a fault. As quoted earlier, Petri net has a strong

mathematical background. Through the addition of old marking with the incidence

matrix column of the particular transition fired (known by the word), the new

marking of the model can be obtained. The initial conditions assumed are as

follows:

Net structure is known,

Transition firing is observable,

Initial marking is not known, and

Word is known.

The algorithm is as follows:

Step 1: Initial estimate Me = 0 , let word W = W0.

Step 2: Wait until transition, t, fires.

Step 3: Update previous estimate: M 'e = max{Me, pre(:, t)}.

Step 4: New estimate: Me = M 'e + c(:, t).

Step 5: W = transition fired Wt ; goto Step 2 until word is complete.

Algorithm 2- Continuous evolution

Continuous evolution- Continuous evolution is the module developed in order to

obtain the evolution of the continuous places. The initial conditions assumed are as

follows:

125

Initial marking of the fault-free system is known,

Word is known, and

Pre, Post, Incidence matrix is known.

The algorithm is as follows:

Step 1: Input the initial matrix M0.

Step 2: Input the transition, t, to be fired.

Step 3: The new marking, M = M0 + C (:, t).

Step 4: Repeat the procedure till the word is complete.

Algorithm 3 –Proposed FDI

Proposed FDI- The concept of FDI as explained before utilizes the estimated value

from the observer to develop the observability graph. This graph contains a variable

called observability error, which is the difference between the original marking and

the estimated marking. This error changes in the case of an occurrence of a fault. In

this way, the place where the fault has occurred is determined. The initial conditions

assumed are as follows:

Net structure is known,

Initial marking is known, and

Transition speed is known.

The algorithm is as follows:

Step 1: Input initial marking, transition speed, Mc, v.

Step 2: Add the speed to the marking M 'c = Mc + v.

Step 3: Repeat the procedure till desired height (marking) is obtained.

Step 4: Repeat the procedure for all continuous places.

Algorithm 4-Estimation

The initial conditions assumed are as follows:

Net structure is known,

Initial marking of the faulty system is known, and

The word is known.

126

The algorithm is as follows:

Step 1: Input the initial marking Mf, word W.

Step 2: The column of incidence matrix corresponding to particular transition

fired is added to the initial marking M 'f = Mf + C (:, t).

Step 3: The observability graph is developed by generating the estimation

error.

Step 4: The fault is narrowed down by generating the residue of estimate

error.

Figure 5.22 and Figure 5.23 show various graphs obtained for the purpose of

analysis. Here, three 3-dimentional plots have been plotted which are useful for the

purpose of visualizing a fault. For good understanding of various conditions of a

fault, and to analyze the performance of the algorithm, the input to the sequence is

given as [ 456321 ]. This is the sequence in which transitions fire. Once

this sequence of firing is given as the input, the system generates the estimated

marking matrix as shown in Figure 5.19.

Figure 5.19 Window showing the estimate matrix for sequence 1

Estimation is done as explained in Chapter 4. Once the estimated matrix is

found, the next procedure is to give initial marking of the proper model, i.e., the

fault-free system and the details of the marking given in Table 5.4.

127

Table 5.4 Details of marking for fault free system

Place Marking Meaning

P1 1 Pump 1 ON

P3 0 Valve 1 open ,Valve 2 close ( no app)

P4 1 Valve 1 close , Valve 2 open

P7 0 Pump 2 Off

P8 0 Delay off

Thus, the marking to be given is [ 00101 ]. When this input is given, the

module in itself develops the discrete evolution, i.e., the marking matrix of the

fault-free system, and then the error matrix is also developed as shown in Figure

5.20.

Figure 5.20 Window showing the discrete evolution of error matrix and marking

for sequence 1

Now, after these two matrices are developed, the input of the fault system is given

(The faults in this case are assumed for the purpose of simulation). Let a fault in

pump 1 be assumed, and the supply and status signal from the pump becomes 0

instead of 1, i.e., marking is [ 00100 ]. Then, the fault occurred is shown in

Figure 5.22. The details of the original marking and error marking in real time are

shown in Figure 5.21.

128

Figure 5.21 Window showing original marking and error marking in real time

The first row of the residue matrix as shown in Figure 5.21 shows a constant value

which means an error has occurred in this system as that place is said to be

deadlocked. When this input is given to the system, a fault place is located, and the

corresponding analysis graph, and place of fault is found with minimum

information about the system. The results obtained from simulation of the fault are

shown in Figure 5.22 and Figure 5.23.

Figure 5.22 Details of faults occurring with respect to time

129

Figure 5.23 3-D plot of the fault

The constant value of marking in the 3-D plot shown in Figure 5.23 shows a

typical fault. Here, it is to be noted that multiple faults can also be detected at the

same time. The details of marking to be given for detecting typical place faults are

shown in Table 5.5.

Table 5.5 Details of input sequence marking for detecting typical place faults

MARKING FAULT

[ 00100 ] 1st place (P1)

[ 00111 ] 3rd

place (P3)

[ 00001 ] 4th

place (P4)

[ 01101 ] 7th

place (P7)

[ 10101 ] 8th

place(P8)

130

5.4 PROPOSED ESTIMATION BASED FDI AND FTC IN BOTTLE

FILLING PLANT (BFP)

The third real-time application considered for study in this research work is the

Bottle Filling Plant (BFP). The main purpose to consider BFP for study in this

research is because of the fact that any BFP resembles Hybrid Dynamic Systems

(HDSs) [85]. As discussed in Chapter 2, a hybrid system is one that exhibits both

continuous and discrete dynamic behavior, i.e., a system that can

both flow (described by a differential equation) and jump (described by a difference

equation or control graph). Often, the term "hybrid dynamic system" is used, to

distinguish over hybrid systems, such as those that combine neural nets and fuzzy

logic, or electrical and mechanical drivelines. A hybrid system has the benefit of

encompassing a larger class of systems within its structure, allowing more

flexibility in modeling dynamic phenomena.

In general, the state of a hybrid system is defined by the values of the continuous

variables and a discrete control mode. The state changes either continuously

according to a flow condition, or discretely according to a control graph.

Continuous flow is permitted as long as the so-called invariants hold, while discrete

transitions can occur as soon as the given jump conditions are satisfied. Discrete

transition may be associated with events. HDSs thus can be used to emulate the

functioning of a plant more effectively. Hence, for the above reasons, modeling and

analysis of a BFP using Hybrid Petri nets is obtained to achieve FDI and FTC.

5.4.1 Process description

BFP [86] considered here as shown in Figure 5.24, includes both continuous

processes and discrete processes.

131

Discrete Processes:- The discrete processes are those which involve a jump

of control from one part to another of a system. A bottle-filling system consists of

various discrete processes, the systematic movement of bottles one by one, the

detection of sensor, Opening and closing of valves for filling, Counting of bottles,

collection and packaging of bottles.

Continuous Processes:- The continuous process is the filling of the bottle

from the reservoir. Although the flow of liquid from the reservoir to the bottle is not

continuous, it is considered to be so through “Fluidification”. Through

fluidification, the modeling of the bottle-filling system as a hybrid Petri net model

becomes easier.

Due to these reasons, the bottle-filling systems are considered to be HDSs. The

various parts of BFP which have been taken into consideration are: (1) Switch,

(2) Conveyor system, (3) IR sensor, and (4) Reservoir tanks.

Conveyor system:- A conveyor system is a common piece of mechanical

handling equipment that moves materials from one location to another. Conveyors

are especially useful in applications involving the transportation of heavy or bulky

materials. Conveyor systems allow quick and efficient transportation for a wide

variety of materials, which make them very popular in material

handling and packaging industries. Many kinds of conveyer systems are available,

and are used according to the various needs of different industries. Here, a normal

conveyor system is considered to transport the bottles in the packaging industry.

The conveyor system is controlled through a conveyor motor, and the control of the

motor helps moving the conveyor belt. Bottles are placed over the conveyor at

regular intervals and according to bottle-filling, the conveyor automatically moves

to bring the next bottle into position once a bottle gets filled.

132

IR Sensor: - Infra Red (IR) sensors are generally used for object detection

and not for distance measurement. The basic idea is to send infra red light through

IR-LEDs, which is then reflected by any object in front of the sensor. In the system

shown in Figure 5.24, IR sensor is considered to sense the presence of a bottle in the

conveyor system before bottle-filling takes place.

Reservoir Tanks: - The reservoir tanks are used to give a constant supply of

liquid to the filling system. There are reservoir systems with level monitoring and

automatic refilling. The reservoir system considered here fills itself automatically

when the amount of liquid drained through it becomes large.

Figure 5.24 Overview of a Bottle Filling Process plant [86]

133

5.4.2 Modeling and analysis of process

Here, in this research work, two different prototypes of BFP have been modeled

and analysed. The first one is a multiple BFP, and the second one is ratio filling

BFP. The details of modeling and analysis of both are explained separately in the

following subsections.

5.4.2.1 Modeling and analysis of multiple BFP

The Petri net model for multiple BFP consists of a hybrid net structure which has

five discrete places and three continuous places as shown in Figure 5.25. The three

continuous places signify the reservoir and filling nozzles, and the two continuous

transitions with maximal speed signify the valves. The discrete places signify the

logic with which the system should work. The movement of token in the discrete

places resembles the flow of logic in the system. The First place is analogous to the

main switch of the bottle-filling system. The conveyor motor is denoted by a

discrete place, P2. The motor has bottles present on the top of it, and rotates with the

capacity load. The third place is analogous to the Infra Red (IR) sensor; the IR

sensor is used to find whether the bottle is in position or not. The sixth and seventh

places form a loop for continuous bottle-filling. Places, P16, P17 act as bottle count

and the place, P14, act as a packing unit, where every two bottles are packed

together. A token in each of the places means that the corresponding condition

becomes true.

The equivalent Petri net model is shown in Figure 5.25. The model considered here

is a multiple bottle filling process, where, 30 litre capacity bottles and 40 litre

capacity bottles are filled simultaneously in two different parallel set-ups. For a

transition to fire, there should be a token in every connecting place.

134

Figure 5.25 Equivalent Hybrid Petri net model developed for the process shown in Figure 5.24

135

The algorithm is explained as follows:

Main switch is ON, i.e., there is presence of a token, and the conveyor motor

starts to run and the bottles present on top of them appear at the filling position

in both the parallel modules.

Bottle is detected when IR sensor senses the presence of a bottle and then

subsequently, the conveyor motor stops.

Filling system is initiated and the valves of the 30 litre as well as 40 litre

capacities are opened, which means liquid flows from the reservoir to the

bottles.

Delay is provided for the operation of bottle-filling completely.

Bottle count is updated for both the systems as soon as the 30 litre and 40 litre

bottles are filled.

When bottle gets filled, it arrives at the collection unit, where two bottles are

filled, and finally appear at the packaging unit, i.e., when two tokens are

collected in the place, then bottles are sent to a carton for packaging.

By the time 40 litre bottle is filled twice, the 30 litre bottle will be filled

approximately 3 times, and hence the reservoir is refilled as soon as the two

tokens are present in the bottle collection place.

136

Table 5.6 shows corresponding places and their logic with respect to the developed

model.

Table 5.6 Places and transitions with their corresponding logic

Figure 5.26 shows the response of bottle-filling with respect to time, i.e., the

response of the places, P4 and P5. The graphs as shown in Figure 5.26 indicate the

bottle-filling as well as the bottle counts that are tracked every instant of time.

Place/Transition Logic details

P1, P11 The system is switched “ON”

P2, P10 The conveyor motor starts to run

P3, P9 The IR sensor senses the bottle

P6, P7, P12, P13 Bottle filling start; valve open; delay

P16, P17 Bottle counter

P14 Bottle collection and packing

P15 Reservoir Tank refill

P5 Reservoir Tank

P4 30 litre capacity bottle filling

P5 40 litre capacity bottle filling

T5 Valve for 30 litre bottle filling

T7 Valve for 40 litre bottle filling

T15 Packing unit activation

T16 Refill for reservoir

137

Figure 5.26 Response of bottle filling Places

5.4.2.2 Modeling and analysis of ratio based BFP

Apart from the previous model as discussed in section 5.4.2.1, a ratio based BFP is

designed, modeled and analyzed through Hybrid Petri net structure and explained in

detail in this section. Here, the Petri net model consists of four continuous places

and nine discrete places as shown in Figure 5.27.

Place, P1, indicates the “start/stop” switch. Place, P2, indicates the conveyor motor,

Place, P3, is analogous to an IR sensor; Places, P5 and P6 form a loop for continuous

bottle-filling. This controls the opening and closing of valves, and thus controls the

ratio of the liquid that gets filled in the bottle. The Continuous places, P4 and P9 are

analogous to the reservoir of different liquids that need to be mixed in a ratio.

Places P8 and P10 are the filling places that gets filled according to the ratio

designed. A token in each of the places means that the corresponding condition is

138

true. The continuous transitions fired at a maximal speed signify the valves of the

filling system.

Both systems are modeled through Constant Continuous Petri Net (CCPN) which

fire at a constant maximal speed throughout the process. In the ratio BFP designing

of the speed for firing of continuous transitions is of utmost importance as it decides

the ratio of liquid to be mixed. In the considered model, the maximal speed is set in

such a way that a ratio of 1:2 is obtained, i.e., for one unit of one liquid, two units of

another liquid should be mixed together. The Petri net model of the ratio based BFP

is shown in Figure 5.27. Table 5.7 shows corresponding places and transitions and

logic they signify.

Table 5.7 Places and transitions with their corresponding logic for model

shown in Figure 5.27

Place/ Transition Logic details

P1 The system is switched “ON”

P2 The conveyor motor starts to run

P3 The IR sensor senses the bottle

P5, P6 Bottle filling start; valve open; delay

P7, P11 Mixing of liquids

P12 Bottle filling

P13 Bottle is collected and sent to

packaging

P4,P9 Reservoir Tanks of two different

liquids

P8 Liquid A

P10 Liquid B

T6,T8 Ratio adjustment

T10 Mixing of two liquids inside bottle

T11 Packing unit activated

139

Figure 5.27 Petri net model of the ratio-based BFP

140

The algorithm is explained as follows:

Main switch is ON, i.e., there is the presence of a token and the conveyor motor

starts to run, and the bottles present on top of them appear at the filling position.

Bottle detected when IR sensor senses the presence of a bottle, and then the

conveyor motor stops.

Filling system is initiated and the valves of Liquid A and Liquid B are opened,

which means the liquids A and B flow from the reservoir to the filling places

according to the firing rates of the continuous transitions, which determine the

ratio of the liquid mixture.

Delay is given for the purpose of maintaining proper ratio during the mixing of

two liquids.

Once the required ratio is obtained, i.e., for one part of liquid A, two parts of

liquid B are to be added. The bottle is sent to a collecting unit.

In that unit, when two tokens are collected in a place, the bottles are sent to a

carton for packaging.

Figure 5.28 shows the response of liquid A filling with respect to time, i.e., the

response of the place, P8.

Figure 5.28 Response of bottle filling at place, P8

141

The response of the filling at place, P10, is shown in Figure 5.29. Here, place, P10,

refers to the filling of liquid B.

Figure 5.29 Response of bottle filling at place, P10

Figure 5.30 shows another graph that displays the number of bottles filled with

respect to time. The distinct peak at a particular time instant refers to the fact that a

bottle is being filled at that time instant.

Figure 5.30 Number of bottles filled with respect to time at place P12

142

5.4.2.3 Proposed FDI and FTC

The proposed FDI and FTC block diagram as shown in Figure 5.31 comprise

fault diagnosis, fault tolerance and fault isolation. As detailed earlier once faults are

identified, they are checked if the faults are tolerant. If they are tolerant, then the

system runs normally. When the fault is intolerable, then the redundant path is

chosen and the process carries on without the system being halted. This is called

fault Isolation. The various components of the block diagram are as follows:

Optimized system model:- The optimized system model refers to the model that

is designed mathematically as well as through Petri nets according to the

requirements fulfilling the ideal conditions.

Diagnoser model:- The diagnoser model is one that is designed keeping in mind

the various probable faults that might occur in the system due to many factors

such as prolonged running, friction, level violation, etc.

Fault diagnosis: - Once the ideal model and the faulty models are designed, the

next process is comparison of the ideal model with the faulty model and finding

out reason for faults to have occurred. The various faults are taken care by

applying the fault tolerance algorithm procedures.

Fault tolerance:- Fault tolerance is one of the important steps as it checks the

extent of the fault, and prevents the system from stalling due to minor faults and

through the algorithm, a threshold is set for the faults and minor faults that do

not cross the threshold do not affect the smooth functioning of the system. Only

when the fault crosses the threshold, further steps are taken.

143

Figure 5.31 Block diagram of Fault Diagnosis and Identification (FDI) and Fault Tolerant Control (FTC)

144

The developed fault tolerance algorithm to achieve this condition is shown in

Figure 5.32.

Figure 5.32 Algorithm to achieve Fault Tolerant Control (FTC)

The condition to be satisfied for fault tolerance of BFP is given as L. q ≤ b,

where L represents the nc × n integer matrix, b represents the nc × 1 integer vector,

nc is the number of constraints and q is the marking vector of the Petri net. Based on

Check if

ideal marking –

obtained marking =0

System is in

IDEAL

working

condition

System is Faulty

Check whether the fault in the system is

within the tolerant limit.

If

L. q ≤ b

L. q ≤ b

L

represen

ts nc × n

integer

matrix,

b

represen

ts nc × 1

integer

vector,

nc is the

Fault is

within the

tolerable

limit

Faults have exceeded the tolerant limit,

and hence isolate the faulty part of the

system.

Obtain the ideal condition matrix and

current condition incidence matrix of the

system and check for error

Yes

No

Yes

No

END

145

the condition above, the ideal condition for constraint matrix L and the marking

vector q are estimated and given as

100

001

140

60

30

≤

40

30. It can be observed

here that if this condition is satisfied, the system is within the tolerable limit and the

system runs normally. (The tolerable limit is that the product (L.q) should be within

30 litre and 40 litre, respectively, and if it exceeds the value, then the bottle

overflows, and the filling process is isolated).

Once fault tolerant algorithm is developed, and the tolerance level of the fault is

checked according to the degree of tolerance, the system decides whether to tolerate

the fault or isolate it from the main process for repair.

If the fault is not within tolerance limits, fault isolation is carried out. This

process involves designing a redundant path for the process to take in case of a

conflict in the system. The design of the redundant path has been done using a

software called HPSIM [87], and this allows the faulty part to be isolated from the

main system, and the rest of the process carries out as normal. The main advantage

is that even though there is fault, the system does not come to a halt, but it continues

working. The design of the redundant path is shown by considering an example as

shown in Figure 5.33.

146

Figure 5.33 Example of fault isolation using HPSIM

As observed in Figure 5.33, there is a redundant path that is present for each

flow of control so that if any of which fails, then an alternative path is taken and the

system does not halt.

In this part of the research work, C programming has been used as a front end

interface to identify the current status of the system. A program has been developed

which compares the ideal condition markings and the obtained markings of the

bottle-filling system. This program compares these two markings of the system and

it identifies the working condition of the system, and indicates the user whether the

bottle is filled correctly, or any fault is detected in the system. The erroneous system

response is the vital analyzing tool from which the occurrence of a fault is detected.

The faults that could possibly occur are either due to overflow of the bottle due to

the conveyor not moving (Place fault), errors due to the improper functioning of the

147

IR sensor, and fault occurrence due to the improper filling valve operation

(transition fault). The graphs in Figure 5.34 show the response of faulty system.

Figure 5.34 Response of a faulty system

From Figure 5.34, it can be observed that:

Bottle overflow occurs as the marking cross 30, and it should be maintained

within the threshold, i.e., 30 markings (litres).

It is clear that when there is a fault in the system, the bottle fills up haphazardly.

148

Apart from graphical analysis, in this part of the research work, mathematical

analysis is also done and results are presented. As discussed earlier, the ideal

marking for the BFP process considered is given as 3016030

PPP 854

, where capacity

of bottle - A is 30 units, capacity of bottle-B is 40 units, P4 is the place analogous to

bottle-filling in bottle – A and P5 is analogous to bottle-filling in bottle – B.

Now, the condition for bottle overflow is given as

Faulty marking

3016032

PPP 854

,

For partial bottle-fiiling, the normal and faulty markings are given by

Normal marking

4013410

PPP 854

,

Faulty marking

3613410

PPP 854

.

Similarly, for bottle missing, the values of normal marking and faulty markings are

given as follows:

Normal marking

000000100100

PPPPPPPPPPPP 151413121110976321

Faulty marking

Marking P4 indicates bottle

overflow

Marking P8 indicates partial filling

of bottle B

149

000000100000

PPPPPPPPPPPP 151413121110976321

Marking P3 represents missing of bottle

Hence, in this Chapter, a detailed description of the major contributions made in

this research work with respect to achieve FDI and FTC in real-time systems is

presented. In Chapter 6, the details of evaluation of performance measures for

model checking and analysis are discussed.