Stb of Condensate system

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Stability Analysis of
Condensate System
Presented by
Mitali Soni
Rishikesh Bagwe

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Acknowledgements
We would like to thank Mr. C. Saha (SME (I)) and Mr. Nilesh Bobade (SO/D), our
mentor who guided us throughout the project through his extensive knowledge of the
systems and valuable inputs wherever required. We would also like to thank Mr.
Saumitra Trivedi, ATO, Nuclear Training Center (NTC) and other members of the NTC
at TAPS 3&4 for helping and motivating us throughout the project.
We would also like to thank BITS Pilani for giving us the opportunity to attain this
exposure to industry atmosphere and functioning. Lastly we would like to thank our
Instructors In-charge, Mr. Shamuel Tharu and Mr. Pawan Poddar, as well as our
Practice School batch-mates who have been supportive and encouraging throughout
the duration of the project.

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Preface
The following project is based on the study of Programmable Logic Controllers (PLC)
and their networking at NPCIL’s Tarapur Atomic Power Station, Units 3&4 (TAPS 3&4).
It also gives information about the current profile of the nuclear energy organization,
Nuclear Corporation of India Limited (NPCIL) and its policies of managing the 20
nuclear reactors in the country. It also explains the process of conversion of nuclear
energy into electricity. There are some other benefits of nuclear energy shown in this
report.
The second part of the report emphasizes on the stability analysis of Condensate
system using MATLAB- Simulink.
This report is made in the partial fulfilment of the course Practice School -1(PS 1) of
BITS Pilani on July 9, 2014. The data in the report was gathered from various sources,
the prominent being the manuals available at TAPS 3&4 and the orientation session at
TAPS 3&4. Our mentor at TAPS 3&4, Mr. Nilesh Bobade (SO/D) guided us throughout
the project.

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Introduction
The Secondary Cycle 24
Condensate System 25
Deaerator 26
Feedwater System 27
MATLAB
Simulink 28
Simulink Real Time 29
Stability Analysis of Process Control Loops
Control System Terminology 30
Closed Loop System 32
Table of Contents
Page No.
6
Company Profile: NPCIL
Introduction to Nuclear Energy
Working Principle of a Nuclear Reactor
Types of Nuclear Reactors
Pressurised Water Reactor
Boiling Water Reactor
Pressurised Heavy Water Reactor
7
Details of NPCIL plants in India 12
Need for Nuclear Energy in India 14
India’s Three Stage Nuclear Program
Stage 1 - Pressurised Heavy Water Reactors
Stage 2 - Fast Breeder Reactors
Stage 3 - Thorium Based Reactors
15
Advantages and Disadvantages of Nuclear Energy
Advantages
Disadvantages
18
General Description of TAPS 3&4 21
The Power Plant Cycle and Main Systems Involved 22

5
Checking the Stability of Condensate System
Transfer Functions 32
PI controller 34
Saturator 36
E/A converter 36
Control Valve Positioner 37
Control Valve 39
Resistance of a Pipe 41
Pressure drop across Low pressure Heaters 43
Gain of Control Valve 46
Transfer function of level control process 48
Transfer function of Deaerator Storage Tank 49
References 50

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Company Profile: NPCIL
Nuclear Power Industry has developed manifold since its inception in India. Studies in
nuclear science in a systematic basis began in India during the late forties with the
establishment of Tata Institute of Fundamental research (TIFR) at Mumbai. Exploitation
of Nuclear energy for generation of electricity has supplied the country with nearly more
of electricity so far.
Keeping in mind the increasing need of industry and global competitive challenges,
Nuclear Power Corporation India Limited (NPCIL) with it’s headquarter at Vikram
Sarabhai Bhavan, Mumbai was started. NPCIL is a Public Sector Enterprise under the
Department of Atomic Energy (DAE), Government of India. It was incorporated on
September 17, 1987 as a Public Limited Company under the Companies Act 1956, with
the objective of operating the atomic power stations and implementing the atomic power
projects for the generation of electricity, in pursuance of the schemes and programmes
of Government of India under the Atomic Energy. The formation of NPCIL was
necessitated to give it operational flexibility and raise financial resources from the
capital market to finance the setting up of the projects.
Bhabha Atomic Research Center (BARC) at Mumbai is a premier institute aiming to
provide quality manpower for NPCIL’s nuclear power projects all over the country for
last 35 years. BARC encompasses fields like agriculture, medicine, computer,
electronics, R & D and other areas which are directly relevant to the development of the
nuclear resources of the country in a very efficient way.
The fundamental of the electricity generation at atomic power station is the generation
of heat by bombarding neutrons on the isotope of U-235. The heat, which is thus being
generated, is used to heat up the water to convert it into steam which is used to rotate
turbines, which further runs the turbo generator, and thus generates electricity. It is
estimate to have Nuclear Power Capacity of 20000 MW to make the country self-
sufficient in electricity production. Considering that Nuclear Power is a safe and
environmentally clean source of power generation and that India has vast thorium
reserves, NPCIL is going to play a leading role in future to meet energy demands of the
country.
With a total capacity of 1400 MW, Tarapur is the largest nuclear power station in India.
The facility is operated by the Nuclear Power Corporation of India Limited (NPCIL). It
was initially constructed with two boiling water reactor (BWR) units of 210 MWe. More
recently, an additional two pressurised heavy water reactor (PHWR) units of 540 MW
each were added

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Introduction to Nuclear Energy
Working Principle of a Nuclear Reactor
Nuclear Reactor is a source of heat, which is produced by self-sustained and controlled
chain reaction within the reactor core. The geometrical boundaries within which the
nuclear fuel, moderator, coolant and control rods are arranged to facilitate production
and control of the nuclear reaction to provide heat energy at desired rate is called the
reactor core.
The natural uranium is used as a fuel in our Pressured Heavy Water Reactors.
Uranium has a natural property to emanate radio-active particles. This element has 3
isotopes i.e. U-238, U-235 and U-234. Only the isotope U-235 which is around 0.7% in
the natural uranium is important for energy production. When thermal neutron strikes
the atom of U-235, fission of U-235 atom takes place breaking it up into two or more
fragments. During this process enormous heat energy is generated along with
production of two to three fast moving neutrons.
These fast moving neutrons are slowed down in the presence of moderator (heavy
water) and its probability to cause further fission with uranium atom increases. This
process continues and self-sustained chain reaction is maintained. This provides the
constant heat energy source. The energy produced in this process is proportional to the
neutron density in the reactor core. Thus the reactor power is regulated by controlling
the absorption of the excess neutrons in the core.
The heat produced in the reactor is used to generate light water steam at high pressure,
which drives the turbo-generator to produce electrical energy.
Types of Nuclear Reactors
Pressurised Water Reactor (PWR)
This is the most common type, with over 230 in use for power generation and several
hundred more employed for naval propulsion. The design of PWRs originated as a
submarine power plant. PWRs use ordinary water as both coolant and moderator. The
design is distinguished by having a primary cooling circuit which flows through the core
of the reactor under very high pressure, and a secondary circuit in which steam is
generated to drive the turbine. In Russia these are known as VVER types - water-
moderated and -cooled.
A PWR has fuel assemblies of 200-300 rods each, arranged vertically in the core, and a
large reactor would have about 150-250 fuel assemblies with 80-100 tonnes of uranium.

8
Water in the reactor core reaches about 325°C, hence it must be kept under about 150
times atmospheric pressure to prevent it boiling. Pressure is maintained by steam in a
pressuriser (see diagram). In the primary cooling circuit the water is also the moderator,
and if any of it turned to steam the fission reaction would slow down. This negative
feedback effect is one of the safety features of the type. The secondary shutdown
system involves adding boron to the primary circuit.
A Typical Pressurized Water Reactor (PWR)
(Source: http://www.world-nuclear.org/)
The secondary circuit is under less pressure and the water here boils in the heat
exchangers which are thus steam generators. The steam drives the turbine to produce
electricity, and is then condensed and returned to the heat exchangers in contact with
the primary circuit.
Boiling Water Reactor (BWR)
This design has many similarities to the PWR, except that there is only a single circuit in
which the water is at lower pressure (about 75 times atmospheric pressure) so that it
boils in the core at about 285°C. The reactor is designed to operate with 12-15% of the

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water in the top part of the core as steam, and hence with less moderating effect and
thus efficiency there. BWR units can operate in load-following mode more readily then
PWRs.
The steam passes through drier plates (steam separators) above the core and then
directly to the turbines, which are thus part of the reactor circuit. Since the water around
the core of a reactor is always contaminated with traces of radionuclides, it means that
the turbine must be shielded and radiological protection provided during maintenance.
The cost of this tends to balance the savings due to the simpler design. Most of the
radioactivity in the water is very short-lived*, so the turbine hall can be entered soon
after the reactor is shut down.
A BWR fuel assembly comprises 90-100 fuel rods, and there are up to 750 assemblies
in a reactor core, holding up to 140 tonnes of uranium. The secondary control system
involves restricting water flow through the core so that more steam in the top part
reduces moderation.
A Typical Boiling Water Reactor (BWR)

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Pressurised Heavy Water Reactor (PHWR)
The PHWR reactor design has been developed since the 1950s in Canada as the
CANDU, and more recently also in India. PHWRs generally use natural uranium (0.7%
U-235) oxide as fuel, hence needs a more efficient moderator, in this case heavy water
(D2O).** The PHWR produces more energy per kg of mined uranium than other
designs.
The moderator is in a large tank called a calandria, penetrated by several hundred
horizontal pressure tubes which form channels for the fuel, cooled by a flow of heavy
water under high pressure in the primary cooling circuit, reaching 290°C. As in the
PWR, the primary coolant generates steam in a secondary circuit to drive the turbines.
The pressure tube design means that the reactor can be refuelled progressively without
shutting down, by isolating individual pressure tubes from the cooling circuit.
A Typical Pressurized Heavy Water Reactor (PHWR)
A CANDU fuel assembly consists of a bundle of 37 half metre long fuel rods (ceramic
fuel pellets in zircaloy tubes) plus a support structure, with 12 bundles lying end to end
in a fuel channel. Control rods penetrate the calandria vertically, and a secondary

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shutdown system involves adding gadolinium to the moderator. The heavy water
moderator circulating through the body of the calandria vessel also yields some heat
(though this circuit is not shown on the diagram above).
Newer PHWR designs such as the Advanced CANDU Reactor (ACR) have light water
cooling and slightly-enriched fuel.
CANDU reactors can readily be run on recycled uranium from reprocessing LWR used
fuel, or a blend of this and depleted uranium left over from enrichment plants. About
4000 MWe of PWR can then fuel 1000 MWe of CANDU capacity, with addition of
depleted uranium. Thorium may also be used in fuel.
(** with the CANDU system, the moderator is enriched (i.e. water) rather than the fuel, -
a cost trade-off.)

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Details of NPCIL plants in India
At present 20 reactors are operating with an installed capacity of 4,780 MWe (including
RAPS-1 of 100 MWe owned by the Government) supplying quality electricity to
consumers in a cost effective manner.
Plant Unit and Location Type Capacity in MW
Existing
TAPS
Tarapur, Boisar,
Maharashtra
1BWR
2BWR
160
160
RAPS
Rawatbhata, Rajasthan
1 PHWR
2 PHWR
3 PHWR
4 PHWR
5 PHWR
6 PHWR
100
200
220
220
220
220
MAPS
Kalpakkam, Tamil Nadu
1 PHWR
2 PHWR
220
220
KGS
Kaiga, Karnataka
1 PHWR
2 PHWR
3 PHWR
4 PHWR
220
220
220
220
NAPS
Narora, Uttar Pradesh
1 PHWR
2 PHWR
220
220
KAPS
Kakrapar, Gujarat
1 PHWR
2 PHWR
220
220
Under Construction
Kudankulam, Tamil Nadu 1 LWR
2 LWR
1000
1000
Kakrapar, Gujarat 3 PHWR
4 PHWR
700
700
RAPS
Rawatbhata, Rajasthan
7 PHWR
8 PHWR
700
700

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Need for Nuclear Energy in India
Electricity is a basic input which is closely related to the economic development of a
country. In spite of the impressive strides in increasing overall installed capacity in the
country, we are still facing shortages. In a world that is increasingly demanding more
energy, resources are getting stressed and strained. Countries and governments today
have to make careful choices to generate growth
that is as much about wealth as it is about well-
being of its citizens.
Options available for commercial electricity
generation are hydro, thermal, nuclear and
renewables. In the energy planning of the country,
a judicious mix of the different types of energy
sources is an important aspect. Diversified energy
resource-base is essential to meet electricity
requirements and to ensure long-term energy
security.
Nuclear energy is a clean and sustainable source of energy. It has the potential and
capability to contribute significantly to India’s quest for long-term energy security. The
conventional fossil fuels are fast depleting in supply. Moreover, with driving global
concerns all over the world about climate change and deployment of environment
friendly power generation technologies, nuclear power has clear advantages to meet
the dual challenge of managing consumption as well as developing low-carbon
energies. India has abundant reserves of Thorium that have the potential to be utilised
to generate nuclear power – an option that is clean, sustainable and economically
viable.

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India’s Three Stage Nuclear Program
India has been following a three-stage nuclear power programme, which aims at the
development of
1. Pressurized Heavy Water Reactors, (PHWR) based on natural uranium.
2. Fast breeder reactors utilizing plutonium-uranium fuel cycle, and
3. Breeder Reactors for utilization of thorium.
The ultimate focus of the programme is on enabling the thorium reserves of India to be
utilised in meeting the country's energy requirements. Thorium is particularly attractive
for India, as it has only around 1–2% of the global uranium reserves, but one of the
largest shares of global thorium reserves at about 25% of the world's known thorium
reserves.
THE THREE-STAGE PROGRAMME

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(Source: www.conceptualphysicstoday.com )
Stage 1 – Pressurized Heavy Water Reactors
In the first stage of the programme, natural uranium fuelled pressurised heavy water
reactors (PHWR) produce electricity while generating plutonium-239 as by-product.
PHWRs was a natural choice for implementing the first stage because it had the most
efficient reactor design in terms of uranium utilisation, and the existing Indian
infrastructure in the 1960s allowed for quick adoption of the PHWR technology. India
correctly calculated that it would be easier to create heavy water production facilities
(required for PHWRs) than uranium enrichment facilities (required for LWRs).
Natural uranium contains only 0.7% of the fissile isotope uranium-235. Most of the
remaining 99.3% is uranium-238 which is not fissile but can be converted in a reactor to
the fissile isotope plutonium-239. Heavy water is used as moderator and coolant.
Indian uranium reserves are capable of generating a total power capacity of 420 GWe-
years, but in order to ensure that existing plants get a lifetime supply of uranium, it
becomes necessary to limit the number of PHWRs fuelled exclusively by indigenous
uranium reserves. US analysts calculate this limit as being slightly over 13 GW in
capacity. Several other sources estimate that the known reserves of natural uranium in
the country permit only about 10 GW of capacity to be built through indigenously fuelled
PHWRs. The three-stage programme explicitly incorporates this limit as the upper cut
off of the first stage, beyond which PHWRs are not planned to be built.
Stage 2 – Fast Breeder Reactors
In the second stage, fast breeder reactors (FBRs) would use a mixed oxide (MOX) fuel
made from plutonium-239, recovered by reprocessing spent fuel from the first stage,
and natural uranium. In FBRs, plutonium-239 undergoes fission to produce energy,
while the uranium-238 present in the mixed oxide fuel transmutes to additional
plutonium-239. Thus, the Stage II FBRs are designed to "breed" more fuel than they
consume. Once the inventory of plutonium-239 is built up thorium can be introduced as
a blanket material in the reactor and transmuted to uranium-233 for use in the third
stage.
The surplus plutonium bred in each fast reactor can be used to set up more such
reactors, and thus grow the Indian civil nuclear power capacity till the point where the
third stage reactors using thorium as fuel can be brought online, which is forecasted as
being possible once 50 GW of nuclear power capacity has been achieved.

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The uranium in the first stage PHWRs that yield 29 EJ of energy in the once-through
fuel cycle, can be made to yield between 65 and 128 times more energy through
multiple cycles in fast breeder reactor
Stage 3 – Thorium Based Reactors
Stage III Reactor or an Advanced Nuclear Power System involves a self-sustaining
series of Thorium-232 and Uranuim-233 fuelled reactors. This would be a thermal
breeder reactor, which in principle can be refuelled – after its initial fuel charge – using
only naturally occurring thorium. According to the three-stage programme, Indian
nuclear energy could grow to about 10 GW through PHWRs fuelled by domestic
uranium, and the growth above that would have to come from FBRs till about 50GW ,
The third stage is to be deployed only after this capacity has been achieved.

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Advantages and Disadvantages of Nuclear Energy
Advantages
1 .Amount of Fuel Needed
With little fuel large amounts of energy are obtained. This saves on raw materials but
also in transport, handling extraction nuclear fuel. The cost of fuel is 20% of the cost of
energy generated.
2. Production of electric energy is continuous.
A nuclear power plant is generating electricity for almost 90% of the hours of the year.
This reduces the price volatility that exist in other fuels such as petrol. The fact that is
also conducive to continuous electrical planning as no such dependency in natural
aspects.
3. An alternative to fossil fuels
Thus, need not consume as much of carbon fuels like oil, so therefore the problem of
global warming, which is believed to have reduced one more important influence on
climate change on the planet. By reducing the consumption of fossil fuels we also
improve the quality of the air we breathe with all that this implies in the decline of
disease and quality of life. Interestingly, nuclear power plants these days carry a zero
carbon footprint policy!
4. Cheap electricity
The cost of uranium which is used as a fuel in generating electricity is quite low. Also,
set up costs of nuclear power plants is relatively high while running cost is low. The
average life of nuclear reactor range from 4.-60 years depending upon its usage. These
factors when combined make the cost of producing electricity very low. Even if the cost
of uranium rises, the increase in cost of electricity will be much lower.
5. Low Fuel Cost
The main reason behind the low fuel cost is that it requires little amount of uranium to
produce energy. When a nuclear reaction happens, it releases million times more
energy as compared to traditional sources of energy
6. Nuclear power plants don't require a lot of space
They have to be built on the coast, but do not need a large plot like a wind farm

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Disadvantages
1. Efficiency
The use of nuclear energy for conversion into mechanical energy is very low.
2. Security in their use remains the responsibility of individuals.
Although there are many automated safety systems at nuclear power plants, people can
make wrong or irresponsible decisions. A series of bad decisions led the worst nuclear
accident in Chernobyl. Once an accident has occurred, the way how it is managed is
also dependent on the decisions made by people who are in office.
3. Use that can be given to nuclear power in the defence industry.
Interestingly, nuclear debuted in front of the world as two bombs dropped on Japan at
end World War II.
1. Generation of nuclear waste
The difficulty to manage the waste and it takes many years to lose its radioactivity and
danger.
5. Nuclear reactors, once constructed, have an expiration date.
After this date must be dismantled, so that in the main countries producing nuclear
energy to maintain constant the number of operating reactors should be built about 80
new nuclear reactors the next ten years. The investment for the construction of a
nuclear plant is very high and must be recovered in no time, so this raises the cost of
electricity generated. In other words, the energy generated is cheap compared to the
cost of fuel, but having to repay the construction of the nuclear plants significantly more
expensive.
6. Nuclear power plants are targets for terrorist organizations
7. Generation of external dependence.
Shortly countries have uranium mines and not all countries have nuclear technology, so
both have to be hired abroad
8. Current nuclear reactors work by fission nuclear reactions.
These chain reactions occur so that if the control systems should fail every time more
and more reactions would occur to cause a radioactive explosion that would be virtually
impossible to contain

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General Description of TAPS-3&4
Tarapur Atomic Power Station (T.A.P.S.) is located in Tarapur, Maharashtra (India). It
was initially constructed with two boiling water reactor (BWR) units of 210 MWe each
initially by Bechtel and GE under the 1963 123 Agreement between India, the United
States, and the International Atomic Energy Agency. The capacity of units 1 and 2 was
reduced to 160 MWe later on due to technical difficulties. Units 1 and 2 were brought
online for commercial operation on October 28, 1969. These were the first of their kind
in Asia. More recently, an additional two pressurised heavy water reactor (PHWR) units
of 540 MW each were constructed by L &T and Gammon India, seven months ahead of
schedule and well within the original cost estimates. Unit 3 was brought online for
commercial operation on August 18, 2006, and Unit 4 on September 12, 2005.
With a total capacity of 1400 MW, Tarapur is the largest nuclear power station in India.
The facility is operated by the Nuclear Power Corporation of India Limited (NPCIL)
Tarapur nuclear plant has received the highest safety awards given to any electricity
producing plants in India.
Source: www.thehindubusinessline.com

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The Power Plant Cycle and Main Systems Involved
The conversion to electrical energy takes place indirectly, as in conventional thermal
power plants. The heat is produced by fission in a nuclear reactor (a light water reactor).
Directly or indirectly, water vapour (steam) is produced. The pressurized steam is then
usually fed to a multi-stage steam turbine. After the steam turbine has expanded and
partially condensed the steam, the remaining vapour is condensed in a condenser. The
condenser is a heat exchanger which is connected to a secondary side such as a river
or a cooling tower. The water is then pumped back into the nuclear reactor and the
cycle begins again.
Nuclear Power Plant Cycle
(Source: www.ems.psu.edu )
(The power plant cycle showing the reactor vessel, control rods, reactor, steam generator, pumps,
generator, turbine, and condenser and cooling tower.)

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Introduction
The Secondary Cycle
In nuclear power plant the heat generated by nuclear fission of uranium is used to heat
the DM (de-mineralized) water. The cycle of DM light water in which it gets heated and
the steam formed turns the turbine and again gets condensed, is called as the
secondary cycle. This cycle is common to most types power plants (like Thermal, geo-
thermal, diesel power plants).
The system on the right side in the above image is the secondary cycle. The high
pressure steam generated is first passed through a high pressure (HP) turbine, the
exhausted steam is then reheated in a moisture separator heater and send to two low
pressure (LP) turbine. The low enthalpy exhausted steam is then condensed to water in
a hot well with the help of sea-water and is fed into a steam generator(SG). In SG, the
water is converted to steam and again passed through the HP turbine. This cycle goes
on and the same water is circulated till the plant is active.
The Condensate system and Feed water system are two major systems on the
secondary cycle.

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Condensate System
The part of the secondary cycle from the hot well to the deaerator storage tank is called
the condensate system. The condensed water in the hot well is extracted by 3
Condensate Pumps and sent ahead at an increased pressure of 21 kg/cm2
. This water
is passed into Gland Steam Condenser (GSC) where the remaining steam is
condensed. The pure liquid DM water at 400
C is sent through a series of Low Pressure
Heaters (LPH) in a set of 2 lines. Here at TAPS 3&4 there are 3 LPH in each line. These
heaters increase the temperature of water in steps i.e. LPH1 heats the water from 40C
to 62C, LPH2 heats the water from 62C to 104C and LPH3 from 104C to 125C. This
heated water is then sent to a deaerator tank where air and other non-condensable
gases which are trapped are removed and this deaerated water is stored in deaerator
storage tank. There are control valves on both the lines to control the flow and
consequently increase the water level in deaerator storage tank.

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Deaerator
Deaerator is Spray cum tray type. The function of deaerator heater is to remove oxygen,
dissolved non-condensable gases and to heat boiler feed water. It works in 2 stages.
In the 1st
stage it consists of a pressure vessel in which water and steam are mixed in a
controlled manner.
This steam has many sources:
A. Flash Steam from SGBD (Steam Generator Blown Down)
B. Extraction Steam from MSRs (Moisture Separator Reheater)
C. Drain Steam from HP (High pressure) heaters.
When this occurs, water temperature rises, and all non-condensable dissolved gases
are liberated and removed and the effluent water may be considered free from non-
condensable gases.
In the second stage, the heated water 1st
stage is passed in between the surfaces of
trays. There are many trays inside the deaerator. Due to this even small traces of gases
in the condensate is removed.

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Feed water system
The part of the secondary cycle from feed-water suction pump (booster pumps) to
steam generator is called the feed water system. The condensed water from deaerator
storage tank is extracted by 3 booster pumps and passed to 3 boiler feed pumps (BFP)
which increases its pressure. This pressurized water is split into 2 streams and then
heated in High Pressure (HP) Feed water heaters (one on each line). Finally the high
pressure, high temperature water is fed into the Steam Generator (SG).
Between the Condenser and Feedwater Pump, the water is called condensate; between
the Feedwater Pump and the Steam Generator the water is called Feedwater.

26
MATLAB
MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and
fourth-generation programming language. Developed by MathWorks, MATLAB allows
matrix manipulations, plotting of functions and data, implementation of algorithms,
creation of user interfaces, and interfacing with programs written in other languages,
including C, C++, Java, and Fortran.The language, tools, and built-in math functions
enable you to explore multiple approaches and reach a solution faster than with
spreadsheets or traditional programming languages, such as C/C++ or Java.
MATLAB can be used for a range of applications, including signal processing and
communications, image and video processing, control systems, test and measurement,
computational finance, and computational biology.Although MATLAB is intended
primarily for numerical computing, an optional toolbox uses the MuPAD symbolic
engine, allowing access to symbolic computing capabilities. An additional package,
Simulink, adds graphical multi-domain simulation and Model-Based Design for dynamic
and embedded systems.
In 2004, MATLAB had around one million users across industry and academia.
MATLAB users come from various backgrounds of engineering, science, and
economics. MATLAB is widely used in academic and research institutions as well as
industrial enterprises.
Simulink
Simulink, developed by MathWorks, is a data flow graphical programming language tool
for modeling, simulating and analyzing multidomain dynamic systems. Its primary
interface is a graphical block diagramming tool and a customizable set of block libraries.
Simulink is a block diagram environment which supports simulation, automatic code
generation, and continuous test and verification of embedded systems.
Simulink provides a graphical editor, customizable block libraries, and solvers for
modeling and simulating dynamic systems. It is integrated with MATLAB, enabling one
to incorporate MATLAB algorithms into models and export simulation results to
MATLAB for further analysis.
Capabilities:
 Building the Model — Model hierarchical subsystems with predefined library
blocks.

27
 Simulating the Model — Simulate the dynamic behavior of your system and view
results as the simulation runs.
 Analyzing Simulation Results — View simulation results and debug the
simulation.
 Managing Projects — Easily manage files, components, and large amounts of
data for your project.
 Connecting to Hardware — Connect your model to hardware for real-time testing
and embedded system deployment.
Applications:
 Model-Based Design
 Control Systems
 Digital Signal Processing
 Communications Systems
 Image and Video Processing
 Embedded Systems
 Mechatronics
Simulink Real Time
Simulink Real-Time is a platform to create real-time applications from Simulink models
and run them on dedicated target computer hardware connected to a physical system. It
supports real-time simulation and testing, including rapid control prototyping, DSP and
vision system prototyping, and hardware-in-the-loop (HIL) simulation.
Simulink Real-Time can extend Simulink models with driver blocks, automatically
generate real-time applications, define instrumentation, and perform interactive or
automated runs on a dedicated target computer equipped with a real-time kernel,
multicore CPU, I/O and protocol interfaces, and FPGAs.
Simulink Real-Time and Speedgoat target computer hardware are expressly designed
to work together to create real-time systems for desktop, lab, and field environments.
Simulink Real-Time can also be used with custom target computer and I/O hardware.
Capabilities:
 Setting Up the Real-Time Simulation and Testing Environment
 Selecting the Target Computer Hardware
 Creating and Controlling a Real-Time Application
 Instrumenting a Real-Time Application
 Defining Concurrent Execution for a Real-Time Application

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 Creating a Standalone Real-Time Application
 Using Reconfigurable FPGA I/O Modules
Stability Analysis of Process Control Loops
Control System Terminology
For understanding the stability criteria and stability analysis of process control loops,
following terminology may be used. Thus they have been briefly given in the beginning
for better understanding of the system.
Bode Diagram
A plot of log amplitude ratio and angle values on a log frequency base for a transfer
function.
Corner Frequency
In the Bode diagram, the frequency where the product wT is unity, is called as the
Corner Frequency.
Damping
Progressive reduction in the amplitude of a cycling system. Critically damped describes
a system which is damped just enough to prevent overshoot following an abrupt
stimulus.
Dead Band (Dead Zone)
The change through which the input to an instrument can be varied without initiating
instrument response.
Dead Time
Time that elapses between application of input signal to the system and the system
starts to respond.
Derivative Time
The time interval by which the effect of proportional action is advanced.
Frequency Response Analysis
A system of dynamic analysis which consists of applying sinusoidal changes to the input
and recording both input and output on the same time using an oscillograph.
Gain
The ration of change in output to input which caused it.

29
Gain Margin
It is the factor by which the gain of a system can be increased to drive it to the verge of
instability. It can also be defined as the reciprocal of the gain at which phase angle
becomes -180 in the bode plot.
Gain Crossover Frequency
The frequency at which amplitude ratio is unity is called gain crossover frequency.
Hysteresis
The maximum difference in output, at any measured value within the specified range,
when the value is approached first increasing and then with decreasing measurement.
Maximum Overshoot
Largest deviation of the output over the step input during the transient cycle.
Phase Crossover Frequency
The frequency at which the phase angle is -180 is called the phase crossover
frequency.
Phase Margin
The amount of additional phase lag which can be increased to drive it to the verge of
instability.
Time Constant
The product of resistance and capacitance T=RC which becomes the time required for
the first order system to reach 63.2% of a total change when forced by a step input.
Time constant defines the speed of response of a system. In higher order systems there
is a time constant for each of the first order components.
Transportation Lag
A delay caused by the time required for the material to travel from one point to another.
E.g. water flowing at the rate 10feet/sec requires 10 sec to travel 100feet and if this
100feet exists between manipulation and measurement, it would constitute a 10sec lag.
Open Loop System
Open-loop system, also referred to as non-feedback system, is a type of continuous
control system in which the output has no influence or effect on the control action of the
input signal. In other words, in an open-loop control system the output is neither
measured nor ―fed back‖ for comparison with the input. Therefore, an open-loop system
is expected to faithfully follow its input command or set point regardless of the final

30
result.
Closed Loop System
A Closed-loop Control System, also known as a feedback control system is a control
system which uses the concept of an open loop system as its forward path but has one
or more feedback loops (hence its name) or paths between its output and its input. The
reference to ―feedback‖, simply means that some portion of the output is returned ―back‖
to the input to form part of the systems excitation.
Transfer Function
A Transfer Function is the ratio of the output of a system to the input of a system, in the
Laplace domain considering its initial conditions and equilibrium point to be zero. If we
have an input function of X(s), and an output function Y(s), we define the transfer
function H(s) to be:

31
Checking the stability of the Condensate System in Matlab-Simulink
Transfer Functions
Transfer Function of a Controller
Assuming no reset and derivative action, the transfer function of the P-Controller with
Time constant τc and dead time τd can be written as
𝐺𝑐 =
𝐾𝑝
1+sτ 𝑐
e-td*s
Assuming no reset action, the transfer function of PD Controller can be written as
Gc= Bagwe Eqn
Where Td is the derivative time in seconds.
As the gain of the controller is unity and being a digital controller it has a cycle time of
175 msec which can be treated as a pure dead time.In the design of DPHS-PCS, the
output rate of rise is in ramp fashion. Hence when any step change is expected in the
output, the final value is achieved through a ramp function. The slope of the ramp is
adjustable. For TAPS 3 & 4 purpose this rate has been selected as 5% of Span per sec.
Thus it takes 20sec to reach the final value. Therefore the time constant can be taken
as
τc =
20
5
= 4 sec
Hence, proportional controller transfer function can be written as
𝐺𝑐 =
𝐾𝑝 𝑒−0.175𝑠
4𝑠 + 1

32
1. PI without dead time
𝑇𝐹 =
66.4𝑠 + 1.66
40𝑠
MATLAB Code:
>>num=[66.4 1.66]
>>den=[40 0]
>>sys=tf(num,den)
sys =
66.4 s + 1.66
-------------
40 s
>>bode(sys)
>>margin(sys)
>> [Gm, Pm, Wgm, Wpm]=margin(sys)

33
2. PI with Dead time
𝑇𝐹 =
−5.81𝑠2
+ 66.25𝑠 + 1.66
3.5𝑠2 + 40𝑠
MATLAB Code:
>>num=[-5.81 66.25 1.66]
>>den=[3.5 40 0]
>>sys=tf(num,den)
sys =
-5.81 s^2 + 66.25 s + 1.66
--------------------------
3.5 s^2 + 40 s
>>bode(sys)
>>margin(sys)
>> [Gm, Pm, Wgm, Wpm]=margin(sys)

34
Results:
Gm = 0.6024
Pm = Inf
Wgm= Inf
Wpm = NaN
3. Gain (Saturator)
Converts 1-100 output of PI Controller to 4-20mA current output
𝐺1 =
20 − 4
100 − 0
= 0.16
𝑇𝐹1 =
−0.9296𝑠2
+ 10.6𝑠 + 0.2656
3.5𝑠2 + 40𝑠

35
Results:
Gm= 3.7651
Pm = 105.3324
Wgm= Inf
Wpm = 0.0069
4. E/A Converter
E/A converter receive current output from the (4-20A) from PI controller and sends pneumatic
signal (3-15psi) to the control valve positioner. Its transfer function can be computed in terms of psi
per mA input signal from the controller.
Hence for feed valve E/A converter, the gain can be computed as
𝐺𝑎𝑖𝑛 = 𝐴1 =
15 − 3
20 − 4
= 0.75 𝑝𝑠𝑖/𝑚𝐴
Time constant τ2 of the E/A converter (as obtained from them manufacturer’s data sheet) is
computed as follows:
As per specification the corner frequency (fc) for E/A converter is 2Hz.
At the corner frequency, the product of corner frequency and time constant is unity.
ωc * τ2= 1
Where,
ωc is corner frequency of E/A converter and
τ2 is a time constant of E/A converter
ωc=2πfc
ωc=2π*2
ωc=4π
We have, ωc * τ2= 1
Substituting ωc=4π in the above equation, we get,
τ2 =
1
4𝜋
𝑠𝑒𝑐
τ2 = 0.078 seconds
Hence, transfer function of E/A converter of feed control valves is,
𝑇𝑓 =
0.75
0.078𝑠 + 1

36
Results:
Pm =Gm=Inf
Combined Transfer Function:
𝑇𝐹2 =
−0.6972𝑠2
+ 7.95𝑠 + 0.1992
0.273𝑠3 + 6.62𝑠2 + 40𝑠

37
Results:
Gm = 9.4890
Pm = 101.4157
Wgm = 20.5641
Wpm = 0.0051
Control Valve Positioner
A position controller (servomechanism) that is mechanically connected to a moving part
of a control valve or its actuator and that automatically adjusts its output to the actuator
to maintain a desired position in proportion to the input signal.
The positioner converts the pressure applied on the valves actuator(3 – 15 psi) into the
percent opening of closing member of the control valve.
𝐺𝑎𝑖𝑛 = 𝐴3 =
100 − 0
15 − 3
= 8.33%
To fully open i.e. from 0 to 100% it has 20 sec, so the time constant of the positioned is
20/4 = 5 sec.
So the transfer function of the positioner becomes ;
Tf =
8.333
5𝑠+1

38
Results:
Gm = Inf
Pm = 96.8969
Wgm = NaN
Wpm =1.6535
Combined transfer function:
𝑇𝐹3 =
−5.807𝑠2
+ 66.223𝑠 + 1.659
1.365𝑠4 + 33.37𝑠3 + 206.62𝑠2 + 40𝑠
Results:
Gm= 23.9750
Pm = 117.6771
Wgm = 6.9841
Wpm = 0.2664
Transfer function of a Control Valve
Control Valve
Process plants consist of hundreds, or even thousands, of control loops all networked
together to produce a product to be offered for sale. Each of these control loops is

39
designed to keep some important process variable such as pressure, flow, level,
temperature, etc. within a required operating range to ensure the quality of the end
product. Each of these loops receives and internally creates disturbances that
detrimentally affect the process variable, and interaction from other loops in the network
provides disturbances that influence the process variable. To reduce the effect of these
load disturbances, sensors and transmitters collect information about the process
variable and its relationship to some desired set point. A controller then processes this
information and decides what must be done to get the process variable back to where it
should be after a load disturbance occurs. When all the measuring, comparing, and
calculating are done, some type of final control element must implement the strategy
selected by the controller. The most common final control element in the process control
industries is the control valve. The control valve manipulates a flowing fluid, such as
gas, steam, water, or chemical compounds, to compensate for the load disturbance and
keep the regulated process variable as close as possible to the desired set point.
For a control valve :
Cv = 𝑄𝑐𝑣 ×
√𝑆𝐺
√∆𝑃𝑐𝑣
Where,
Cv = Flow coefficient
Qcv = flow through the valve
∆PCV = Pressure drop across the valve
SG = specific gravity
Since we have water SG= 0.992 and √(0.992) = 0.9959
Cv = 𝑄𝑐𝑣 ×
0.9959
√∆𝑃𝑐𝑣
The inherent characteristics links the Cv with the % opening of the valve. From this we
can link % opening with flow from above equation.

40
The inherent characteristics of the control from the manual.

41
Calculation of Pressure Drop across Control Valve
For calculating pressure drop across the control valve we should first calculate its
upstream pressure and downstream pressure. And for this we should calculate the
pressure drops across each pipes and low pressure heaters in the condensate system.
Resistance of a pipe of flow
The connecting pipes in the condensate system offer resistance due to which there is a
pressure drop across them. The pressure depends on the resistance and flow; and the
resistance depends on pipe geometric and fluid characteristics.
∆P = R × w2
Where,
∆P = pressure drop across the pipe
R = Resistance of the pipe
w = velocity of flow
R = λ ×
𝐿
𝐷
×
ρ
2
Where,
λ = pipe friction coefficient
L = length of pipe
D = diameter of pipe
ρ = density of fluid

42
Reynolds number(Re) plays a role in determining the pipe friction coefficient
Re =
64
λ
If Re < 2320, then it’s a laminar flow
Re > 2320, then it’s a turbulent flow
λ =
64
𝑅𝑒
; but Re =
𝑤×𝐷
𝑣
; where v = kinematic viscosity.
∆Ppipe =
64×𝑣×𝐿×ρ
(𝐷^2)×2
× w
∆Ppipe =
81.536×𝑣×𝐿×ρ
𝐷4 ×2
× Q ; since w =
1.274
(𝐷^2)
× Q
Q = flow through the pipe.
Using the above formula, and calculating the actual lengths and diameters of
pipes from the field, we calculated the pressure drops across various pipes.

43
Calculation of Resistances of Low Pressure Heaters(LPH) : LPH1
Calculation of Frictional Head Loss through Tubes
for given flow rate, Q, pipe diam., D, pipe length, L, number of tubes, N,
pipe roughness, e, and fluid properties, r & m.
1. Determ. Frict. Factor, f, assuming completely turbulent flow { f = [1.14 + 2 log10(D/e)]-2
}
Inputs No. of tubes, N = 589.0
Pipe Diameter, D 18.05 mm Calculations
Pipe Roughness, e 0.15 mm Pipe Diameter, D 0.018 m
Pipe Length, L 9.677 m Friction Factor, f 0.03559
Pipe Flow Rate, Q 0.83333 m3
/s Cross-Sect. Area, A = 0.150716 m2
Fluid Density, r 988.039 kg/m3
Ave. Velocity, V 5.529 m/s
(tubeside fluid)
Fluid Viscosity, m 0.000547 N-s/m2
Reynolds number, Re 180,270
(tubeside fluid)
2. Check on whether the given flow is "completely turbulent flow"
(Calculate f with the transition region equation and see if it differs from the one calculated above.)
f = {-2*log10[((e/D)/3.7)+(2.51/(Re*(f1/2
))]}-2
Transistion Region Friction Factor, f: f = 0.0360
Repeat calc of f using new value of f: f = 0.0360
Repeat again if necessary: f = 0.0360
3. Calculate hL and DPf, using the final value for f calculated in step 2
(hL = f(L/D)(V2
/2g) and DPf = rghL)
Frictional Head Loss, hL30.08737 m
Frictional Pressure
Drop, DPf 291627 N/m2
Frictional Pressure
Drop, DPf 291.6 kN/m2
Pressure Drop 2.974593

44
LPH2
}
Pipe Diameter, D 15 mm Calculations
(tubeside fluid)
(tubeside fluid)
f = {-2*log10[((e/D)/3.7)+(2.51/(Re*(f1/2
))]}-2
(hL = f(L/D)(V2
Frictional Head Loss, hL 5.63838 m
Frictional Pressure
Frictional Pressure

45
LPH3
}
Pipe Diameter, D 18.05 mm Calculations
(tubeside fluid)
(tubeside fluid)
f = {-2*log10[((e/D)/3.7)+(2.51/(Re*(f1/2
))]}-2
(hL = f(L/D)(V2
Frictional Head Loss, hL 3.95874 m
Frictional Pressure
Frictional Pressure

46
Gain of a control valve
From the pressure drops calculated from the above equations we could calculate the total
pressure on the upstream and downstream of control valve.
The installed characteristics from the above calculations using ‘cftool’ command
in Matlab in its Curve Fitting Tool Box is.

47
We have to analyze the stability of the system at maximum change in slope (i.e. where
it is mostly likely to be unstable)
The maximum change in slope occurs at flow of 1000 m3/hr. So take the gain of the
control valve as 47.16.
Dead time = 100 msec
So the combined transfer function (with control valve )
TF =
12𝑠3−396.04𝑠2+3119.04𝑠+77.81
0.0682 𝑠5+3.033𝑠4+ 43.7𝑠3+ 208.62𝑠2+ 40𝑠

48
So bode plot of the system till control valve is
Transfer Function of a Level Control Process
Time constant τ =
𝑐
𝑎2
Where,
c=
𝑑𝑉
𝑑𝐿
; unit change in volume of liquid produced by unit change in level at normal
operating conditions.
a2=
𝜕𝑄
𝜕𝐿
; unit change in flow of liquid through the valve produced by unit change in tank
level keeping valve stroke constant.
Gain Kp =
𝑎1
𝑎2
;
Where,
a1=
𝜕𝑄
𝜕𝑋
; unit change in flow of liquid through the valve opening keeping tank level
constant.
TF =
𝐾𝑝
𝜏𝑠+1

49
Transfer function of Deaerator Storage Tank
Water from deaeartor is stored into the deaerator storage tank (DST). DST is a
horizontal cylindrical tank with semi ellipsoidal ends.
Dimensions: length=2783mm and height=3980mm and radius=1990mm and width of
ellipsoidal end=995mm
Volume as a function of height can be calculated for horizontal cylindrical tank with
ellipsoidal ends (2:1)
V=L (r2acos (1-h/r)-(r-h)(2rh-h2)1/2)+πah2(1-h/3r)
Where, r= radius of cylinder
V= volume occupied at height h
h = height from the bottom of tank
a = width of ellipsoidal length
Since the the tank is ellipsoidal, the change in height with respect to change in flow will
be different at each height. So we are calculating the gain function at the operating point
i. e. change in the level per unit change in volume.
Operating point: Volume corresponding to 2614mm is 240m3.

50
Refrences
Websites
 www.engineeringtoolbox.com
 www.wikipedia.com
 www.mathforum.org
 www.valvias.com
 www.mathworks.com
Literature
 Condensate System Design Manual
 Manufacturing manual of Condensate Extraction Pump(CEP)
 Manufacturing manual of Control Valve
 Flow sheets of Condensate System
 Stability Analysis Paper

Stb of Condensate system

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