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DESIGN AND IMPLEMENTATION OF INTELLIGENT
CONTROLLERS FOR A CONTINUOUS STIRRED TANK
REACTOR SYSTEM
D.SIVA NAGARAJU
M-tech – control system
Sivadevarala.d3@gamil.com.
Departmemt of Electical and Electronic Engg
Gudlavalleru engg college,gudlavalleru,
Krishna dist,A.P.
G.RAMESH
Asst.professor
Departmemt of Electical and Electronic Engg
Gudllavaleru engg college,gudlavalleru.
Krishna dist,A.P.
ABSTRACT
All the industrial process applications
require solutions of a specific chemical
strength of the chemicals or fluids considered
for analysis. Continuous Stirred Tank Reactor
(CSTR) is one of the common reactors in
chemical process and all industrial process
requires a solution of specific chemical
strength of chemicals considered for analysis.
Such specific concentrations are achieved by
mixing a full strength solution with water in
the desired proportions. In this paper design a
controller for controlling the concentration of
one chemical with the help of other has been
analyzed. This paper features the influence of
different controllers like PI, PID, Fuzzy logic
controller and Genetic algorithm (GA) upon
the process model. Model design and
simulation are done in MATLAB SIMULINK.
The concentration control is found better
controlled with the addition of Genetic
algorithm (GA) instead of fuzzy logic and
conventional PID controllers. The
improvement of the process has been
observed.
KEY WORDS: Genetic algorithm(GA)
Fuzzy Logic (FL), conventional PID Control,
Chemical Concentration, CSTR.
1. INTRODUCTION
The Continuous Stirred Tank Reactor
system (CSTR) is a complex nonlinear system.
Due to its strong nonlinear behaviour, the
problem of identification and control of CSTR
is always a challenging task for control
systems engineer[1]. Chemical reactors often
have significant heat effects, so it is important
to be able to add or remove heat from them. In
a CSTR (continuously stirred tank reactor) the
heat is add or removed by virtue of the
temperature difference between a jacked fluid
and the reactor fluid. Often, the heat transfer
fluid is pumped through agitation nozzle that
circulates the fluid through the jacket at a high
velocity. The reactant conversion in a
chemical reactor is a function of a residence
time or its inverse, the space velocity. For a
CSTR, the product concentration can be
controlled by manipulating the feed flow rate,
which change the residence time for a constant
chemical reactor.
In the conventional PID controller, the
proportional, integral and derivative actions on
error are placed in the forward path. The
proportional or derivative action on the error
cause an abrupt change in the controller output
when the set point change is introduced. This
one is the addressed drawbacks of
conventional PID controller [4]. This
proportional and derivative kick can be
avoided by I-PD controller where the
proportional and derivative terms are given in
the feedback path to avoid the set point kick.
In this paper parameters of I-PD controller an
abstract algebra and linear algebra and the
structure of a Fuzzy system, which comprised
of an implication between actions and
conclusion as antecedents and consequents.
Abstract algebra incorporates systems or
models dealing with groups, fields and rings.
Linear algebra incorporates system models
dealing with vector spaces, state vector and
transition matrices.
Proceedings of International Conference On Current Innovations In Engineering And Technology
International Association Of Engineering & Technology For Skill Development
ISBN : 978 - 1502851550
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116
The primary benefit of fuzzy system
theory is to approximate system behaviour
where numerical functions or analytical
functions do not exist. Hence, Fuzzy systems
have high potential to understand the very
systems that are devoid of analytical
formulations in a complex System. Complex
systems can be new systems that have not
been tested, they can involve with the human
conditions such as biological or medical
systems. The ultimate goal of the fuzzy logic
is to form the theoretical foundation for
reasoning about the imprecise reasoning, such
reasoning is known as approximate reasoning.
Genetic Algorithm (GA) was first
introduced by Holland [7] and popularized by
Goldberg [8]. It is one of the modern heuristic
algorithms based on a principle of Charles
Darwinian theory of evolution to natural
biology. The GA technique can generate a
high quality solution within shorter calculation
time and stable convergence characteristics.
GA method is an excellent method for solving
the optimal PID controller parameters.
Therefore, this study develops the GA-PID
controller to search optimal PID parameters.
In this paper, CSTR has been used to
mix ethylene oxide with water to make
ethylene glycol. Here the purpose is to control
the concentration of ethylene glycol with the
help of concentration of ethylene oxide. But
undershoot, overshoot and inverse response
come in the considered system while
performing in a conventional way. But after
implementation of PID controller to the
process, removing of those shoots can be seen
but still the design requirement is not
achieved. So finally auto tuning method of
PID controller is implemented in order to
achieve the design requirement [3].
2.Continuous Stirred Tank Reactor (CSTR)
Modeling :
In this paper, CSTR has been
considered in which concentration of two
chemicals is controlled for better results, the
chemical ‘X‘ and ‘Y‘ and the byproduct is ‘Z‘.
Ethylene oxide (X) is reacted with water (Y)
in a continuously stirred tank reactor (CSTR)
to form ethylene glycol (Z) .Assume that the
CSTR is manipulated at a constant
temperature and that the water is in large
excess.
Fig. 1. A CSTR Control System.
The stoichiometric equation is
X+Y= Z…………………(1)
The reactant conversion in a chemical
reactor is a function of residence time or its
inverse, the space velocity. For anisothermal
CSTR, the product concentration can be
controlled by manipulated the feed flow rate,
which change the residence time (for a
constant volume reactor). It is convenient to
work in molar units when writing components
balances, particularly if chemical reaction is
involved. Let CX and CZ represent the molar
concentration of X and Z (mol/volume).
dVC
dt
= F CX − FC + V … … (2)
dVC
dt
= −FC + V … … … (3)
Proceedings of International Conference On Current Innovations In Engineering And Technology
International Association Of Engineering & Technology For Skill Development
ISBN : 978 - 1502851550
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Where rX and rZ represent rate of
generation of species X and Z per unit volume,
and CXi represents the inlet concentration of
species X. If the concentration of the water
change than the reaction rate is second order
with respect to the concentration of Ethylene
oxide.
r = −K C − K C … …… (4)
Where k1, k2 & k3 are the reaction
rate constants and the minus sign indicate that
X is consumed in the reaction. Each mole X
reacts with a mole of Y and produces one
mole of Z, so the rate of generation of Z is
r = K C − K C … … … … … … (5)
Expanding the left hand side of equation (1)
= V + C ……………(6)
Combining eq (1) & (5)
dC
dt
=
F
V
	 C − C − K C − K C .. (7)
Similarly,
dC
dt
= −
F
V
C + K C − K C …	(8)
3. PROBLEM FORMULATION
The linear space model or case study
of CSTR is given by
.
x = Ax + Bu …………… (9)
y = Cx + Du …………….. (10)
Where the states, inputs and output are
in deviation variable form.
The first input (dilution rate) is
manipulated and the second(feed
concentration of A) is a disturbance input.
Linearization of the two modeling equations
(from equation (6) & (7)) at steady state
solution to find the following state space
matrices is done:
For the particular reaction under
consideration, the rate constants are k1=5/6
/min k2 =5/3 /min k3=1/6 mol/litre.min Based
on the steady state operating point of CXs = 3
gmol/liter, CZs = 1.117 gmol/liter and Fs/V
= 0.5714 min-1. The state model is
Proceedings of International Conference On Current Innovations In Engineering And Technology
International Association Of Engineering & Technology For Skill Development
ISBN : 978 - 1502851550
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118
The manipulated input output process
transfer function
G(s)= C(sI –A)-1 B
is calculated with the help of Matlab.
G (S) =
−1.117S + 3.1472
S + 4.6429S + 5.3821
… (10)
It is desired to produce 100 million
pounds per day of ethylene glycol. The feed
stream concentration is 1.0 lbmol/ft3 and an
80% conversion of ethylene
oxide has been to be determined reasonable.
Since 80% of ethylene oxide is converted to
ethylene glycol, the ethylene glycol
concentration is 0.8 lbmol /ft3. In this process
it is seen that the process has inverse response
with delay time as well as overshoot while
tunning in conventional PI,PID and fuzzy
logic controllers are used. To overcome this
problem and to obtain the desired response For
that, soft computing based optimization
method is used.
4. Controller design
Industrial PID controllers usually
available as a form and to perform well with
the industrial process problems,the PID
controllers structures requires modifications.
The structures are given below
( ) = 1 +
1
+ … … (11)
the controller parameters are calculated. The
desired parameters for the PID controller are
the proportional gain (KP), integral gain (KI)
and the differential gain (KD). Firstly, find
and solve for the characteristic equation of the
process which is given by
+ (4.6429 – 1.117kc) s + (5.3821 + 3.1472
kc ) = 0………. (12)
Where kc is the critical (ultimate) gain.
The value of kc can be calculated by the Routh
Hurwitz criterion and the other parameters can
be calculated by the Ziegler Nichols tuning
method.
Fig 2:Block diagram of conventional PID
controller
A basic PID controller directly
operates on the error signal and this may
produce a large overshoot in the process
response due to the proportional and derivative
kick. The process is unstable and to overcome
the effect of proportional and derivative kick,
a modified PID structure known as I-PD is
considered. In I- PD structure, the integral
term responds based on the error and the P+D
terms works based on the measured process
output. In conventional PID controller (Fig. 3),
the changes in set point cause an impulse
signal or sudden change in the controller
output as well as in output response [2]. This
spike in the controller output is called
Proceedings of International Conference On Current Innovations In Engineering And Technology
International Association Of Engineering & Technology For Skill Development
ISBN : 978 - 1502851550
www.iaetsd.in
119
proportional or derivative kick. The controller
output is given to the final control elements
like control valve, motor or electronic circuit
in which the spikes create serious problem.
But in I-PD controller (Fig. 4) , the
proportional and derivative terms are acting
only to the change in process variable not on
the error as these terms are given in the
feedback path. This structure may eliminate
the proportional and derivative kick during
any set point change [5]. Minimizing the ISE
criterion generates the controller parameters.
The values of the controller parameters are
continuously adjusted, until the ISE of the
closed loop system is minimum [7].
Figure 3. Tuning of I-PD controllers
4.1 Ziegler-Nichols Tuning Method
ZN tuning rule was the first such effort
to provide a practical approach to tune a PID
controller. According to the rule, a PID
controller is tuned by firstly setting it to the P-
only mode but adjusting the gain to make the
control system in continuous oscillation. The
corresponding gain is referred to as the
ultimate gain uK and the oscillation period is
termed as the ultimate period uP . The key
step of the ZN tuning approach is to determine
the ultimate gain and period. Then, the PID
controller parameters are determined from uK
and uP using the ZN tuning Table I.
controller
P 0.5 - -
pi 0.45 0.83 -
pid 0.6 0.5 0.125
Table 1. Commonly used Ziegler-Nichols
rule.
By putting the proportional gain (KP),
integral gain (KI) and the differential gain
(KD) values in the simulink PID controller,
the response for the step input is obtained. We
see that the output have overshoot little
inverted response and also its settling time and
rise time is little bit more. That is not the
desired response. Now for the better control,
the Fuzzy logic controller is used.
4.2 Fuzzy logic controller
When we connect a Fuzzy logic
controller, then we require a multiplexer to
give input to the controller.The inputs to the
controller are error (difference of the set point
and output) and feedback output (output as the
feedback). Now construct the membership
function for the inputs and the output taking
triangular memberships.
In this paper, the input is unit step
input. In this process, the 80% of the ethylene
oxide converted in to the ethylene glycol
(output is 80% of the input). Thus the range
for the output is [0 – 0.8]. The second input is
error and its range is [0 – 0.2]. Using these
values, make fuzzy rules in the fuzzy rule base
editor and observe the response that there is no
inverted response, no overshoot, no
undershoot, rise time and settling time are
reduced.
4.3. GENETIC ALGORITHM
The GA is a global optimization and
search technique based on the principles of
genetics and natural selection. GA differs
significantly from most classical optimization
techniques in many aspects. First of all, unlike
classical methods, GA are not gradient based,
i.e. they do not require the objective functions
to be continuous, neither do they need
information about the derivatives of the
objective functions, therefore they can handle
problems with discrete solution spaces.
Second, the search mechanism is stochastic in
nature, which makes them capable of
searching the entire solution space with more
Proceedings of International Conference On Current Innovations In Engineering And Technology
International Association Of Engineering & Technology For Skill Development
ISBN : 978 - 1502851550
www.iaetsd.in
120
likelihood of finding the global optima. Third,
GA are able to solve problems with non-
convex solution space, where classical
procedures usually fails. All these differences
make GA superior over classic methods in
some real world applications, particularly for
some very complex engineering problems, for
example: complex truss-beam design,
component’s design, and structure design.
GAs features can be explained for solving
complex control system engineering problems
Controller design
System Identification
Fault Diagnosis
System Analysis
Robotics
Further control related combination
problem
In GA, the individuals (solutions) in a
population are represented by chromosomes;
each of them is associated to a fitness value.
According to the principle of survival of the
fittest, the population reproduces, crossovers,
mutates and produces a new generation that is
fitter than the old generation. Those processes
are done again and again until the fittest
chromosome is found and the best result of the
problem is got. Figure.3 shows GA process
flowchart having key blocks as initial
population, fitness evaluation, and
optimization
.
Fig.4 Genetic algorithm process flowchart
Simple GA has three basic operators:
Selection
Crossover
Mutation
A GA starts iteration with an initial
population. Each member in this population is
evaluated and assigned a fitness value. Strings
with higher fitness values have more
opportunities to be selected for reproduction in
next step.
Reproduction makes the clones of good
chromosomes but does not create new one
because of this crossover operator is applied.
Crossover operator produces new individuals
which have some part of both the parents
genetic material. The crossover probability
indicates how often crossover is performed.
Using reproduction and crossover on their own
will generate a large amount of different
strings. However there are two main problems
with this:
Depending on the initial population chosen,
there may not be enough diversity in the initial
strings to ensure the GA searches the entire
problem space.
The GA may converge on sub-optimum
strings due to a bad choice of initial population
These problems overcome by the
introduction of a mutation operator into the
GA. Mutation are the occasional random
alteration of a value of a string position. The
probability of mutation is normally low
because a high mutation rate would destroy fit
strings and degenerate the GA into a random
search.
4. SIMULATION, TESTING AND
RESULTS
The process is represented by the transfer
function given in fig. 5, and fig. 6 depicts the
output of the process.
Proceedings of International Conference On Current Innovations In Engineering And Technology
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Fig. 5: Process model
Fig. 6: Time response of uncontrolled
process
When there is no control to the
process, there is some time delay and inverted
response and also the response is settled below
the desired magnitude.
The process with P controller is shown
in the fig.7 and fig.8 depicts the output of the
process.
Fig. 7: Process model with P controller
Fig. 8: Time response with P controller
By using P controller there is not much
effect to the output response as compared to
uncontrolled process.
As can be seen from fig. 8, there is
almost the same response as that of
uncontrolled and P controller model.
The process with PID controller is
shown in the fig. 9 and fig. 10 depicts the
output of the process.
The tuning of controller parameters is
done by Zeigler & Nichols method.
Here KP= 1.2, KI =5.73, KD= 0.78
Fig. 9: Process model with PID controller
Proceedings of International Conference On Current Innovations In Engineering And Technology
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Fig. 10: Time response with PID controller
As can be observed from the fig. 8,
Rise time ( tr) = 1.5sec
Overshoot= 78%
Settling time ( ts) = 23sec
Fig.11: Time response with i-pd controller
There is almost negligible time delay
and inverted response.So Fuzzy controller is
used to reduce the rise time, settling Time,
overshoot and also try to remove the time
delay and inverted response
Fig. 12: Process model with fuzzy logic
controller.
The output response is shown below.
Fig. 13: Time response with fuzzy
controller
As can be seen from fig. 10,
Rise time ( tr) = 3 sec Settling time ( ts) = 4
sec
Overshoot= 0% Undershoot= 0%
There is no any time delay and also no
any inverted response. All the limitations are
reduced as compared to the PID controller.
In fig.14, membership values of input
1 called ―errorǁ having three ranges low,
medium and high is shown.
Fig. 14: Fuzzy membership sets of input ‘1’
(error)
In fig. 15, the membership values of
input 2 called ―change in error having the
three ranges low, medium and high.
Proceedings of International Conference On Current Innovations In Engineering And Technology
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Fig. 15: Fuzzy membership sets of
input ‘2’ (change in error)
In fig. 16, membership values of
―outputǁ having the same ranges low,
medium and high.
Fig. 16: Fuzzy membership sets of output
(output)
In fig. 17, fuzzy if-then rules using mamdani
fuzzy model are shown.
Fig. 17: Fuzzy If – then rules
Fig. 18 depicts the mesh analysis of the two
inputs (error and change in error) and output.
Fig. 18: mesh analysis of both the inputs
and outputs
Fig. 19 depicts the surface view of the
two inputs (error and change in error) and
output.
Fig.19: surface analysis of both
inputs and outputs
To overcome the problems occurs in
fuzzy logic controller we are using the soft
computing technique. By using the Gentic
algorithm we can reduce the rise time, settling
time is shown in the fig 20.
Proceedings of International Conference On Current Innovations In Engineering And Technology
International Association Of Engineering & Technology For Skill Development
ISBN : 978 - 1502851550
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124
Fig. 20 : time response for Genetic
algorithm
Parameters/
type
Peak
overshoot
(%)
Rise
time
(Sec)
Delay
time
(Sec)
Sett
time
(Sec)
PID 78% 1.95 1.2 28
I-PD 75% 2.1 1.6 17
Fuzzy logic
controller
0 3 1.3 4
Genetic
algorithm
0 2 1.3 2.5
Table.2:comparision results of pid,i-pd
Fuzzy logic and genetic algorithm
5. CONCLUSION
When there is no control to the
process, it generates an inverse response
together with an overshoot and considerable
delay time. But when the PID controller and
fuzzy logic controllers is implemented to the
process, the problems of inverse response and
delay time are controlled in the ongoing
process and are removed considerably but then
it was showing instability in terms of rise time,
overshoot and settling time. To overcome this
instability in rise time, overshoot & in settling
time a soft computing technique Genetic
algorithm used and the results are shown in the
above figs.so the Rise time and settling time
and overshoots are also reduced. By
comparison with ZN, fuzzy and genetic
algorithm, it shows that this method can
improve the dynamic performance of the
system in a better way by the selection of an
appropriate objective function.
6. REFERENCES
[1] Schmidt, Lanny D. (1998). The
Engineering of Chemical Reactions. New
York: Oxford University Press. ISBN 0-19-
510588-5
[2] Yung C. Shin, Chengying Xu ―Intelligent
Systems: Modeling, Optimization, and
Controlǁ CRC Press 2009.
[3] Fried land B., ―Advanced Control System
Designǁ, Prentice Hall, New Jersey, 1996.
[4] Jaya, N. , Sivakumar, D. and
Anandanatarajan, R. (2007)— Implementation
of fuzzy gain scheduling of PID controllers for
a two capacity interacting nonlinear process,
paper presented at TIMA, January
[5] K.J. Astrom, & T. Hagglund, ―The future
of PID control Control Engineering
Practice”, pp.1163 -1175. 2001.
[6] Rajani K. Mudi, Chanchal Dey, & Tsu –
Tian Lee, “An improved auto – tuning scheme
for PI controllersǁ, Journal of science Direct
ISA Transactions, 47: 45 – 52, 2008.
[7] Luis E. Zarate, Peterson Resende, & M.
Benjamin,” A Fuzzy Logic and Variable
Structure Base Controller forCSTR Controlǁ.
Annual conference of IEEE, 2001.
[8] Xiao-Feng Li, Jian Sun, Hui-Yan Wu,
Wei-Dong Zong, “Application of the fuzzy
PID to the Power Plantǁ, IEEE
2007.
[9] Yun Li,Kiam Heong Ang and Gregory
C.Y.Chong,―PID Control System Analysis
and Design – Problems, Remedies, and Future
Directionsǁ. IEEE control system magazine,
February 2006 pp. 32-41,2006
[10] Dimiter Driankov, Hans Hellendoorn,
Michael Reinfrank, Fuzzy control
Proceedings of International Conference On Current Innovations In Engineering And Technology
International Association Of Engineering & Technology For Skill Development
ISBN : 978 - 1502851550
www.iaetsd.in
125

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Iaetsd design and implementation of intelligent

  • 1. DESIGN AND IMPLEMENTATION OF INTELLIGENT CONTROLLERS FOR A CONTINUOUS STIRRED TANK REACTOR SYSTEM D.SIVA NAGARAJU M-tech – control system Sivadevarala.d3@gamil.com. Departmemt of Electical and Electronic Engg Gudlavalleru engg college,gudlavalleru, Krishna dist,A.P. G.RAMESH Asst.professor Departmemt of Electical and Electronic Engg Gudllavaleru engg college,gudlavalleru. Krishna dist,A.P. ABSTRACT All the industrial process applications require solutions of a specific chemical strength of the chemicals or fluids considered for analysis. Continuous Stirred Tank Reactor (CSTR) is one of the common reactors in chemical process and all industrial process requires a solution of specific chemical strength of chemicals considered for analysis. Such specific concentrations are achieved by mixing a full strength solution with water in the desired proportions. In this paper design a controller for controlling the concentration of one chemical with the help of other has been analyzed. This paper features the influence of different controllers like PI, PID, Fuzzy logic controller and Genetic algorithm (GA) upon the process model. Model design and simulation are done in MATLAB SIMULINK. The concentration control is found better controlled with the addition of Genetic algorithm (GA) instead of fuzzy logic and conventional PID controllers. The improvement of the process has been observed. KEY WORDS: Genetic algorithm(GA) Fuzzy Logic (FL), conventional PID Control, Chemical Concentration, CSTR. 1. INTRODUCTION The Continuous Stirred Tank Reactor system (CSTR) is a complex nonlinear system. Due to its strong nonlinear behaviour, the problem of identification and control of CSTR is always a challenging task for control systems engineer[1]. Chemical reactors often have significant heat effects, so it is important to be able to add or remove heat from them. In a CSTR (continuously stirred tank reactor) the heat is add or removed by virtue of the temperature difference between a jacked fluid and the reactor fluid. Often, the heat transfer fluid is pumped through agitation nozzle that circulates the fluid through the jacket at a high velocity. The reactant conversion in a chemical reactor is a function of a residence time or its inverse, the space velocity. For a CSTR, the product concentration can be controlled by manipulating the feed flow rate, which change the residence time for a constant chemical reactor. In the conventional PID controller, the proportional, integral and derivative actions on error are placed in the forward path. The proportional or derivative action on the error cause an abrupt change in the controller output when the set point change is introduced. This one is the addressed drawbacks of conventional PID controller [4]. This proportional and derivative kick can be avoided by I-PD controller where the proportional and derivative terms are given in the feedback path to avoid the set point kick. In this paper parameters of I-PD controller an abstract algebra and linear algebra and the structure of a Fuzzy system, which comprised of an implication between actions and conclusion as antecedents and consequents. Abstract algebra incorporates systems or models dealing with groups, fields and rings. Linear algebra incorporates system models dealing with vector spaces, state vector and transition matrices. Proceedings of International Conference On Current Innovations In Engineering And Technology International Association Of Engineering & Technology For Skill Development ISBN : 978 - 1502851550 www.iaetsd.in 116
  • 2. The primary benefit of fuzzy system theory is to approximate system behaviour where numerical functions or analytical functions do not exist. Hence, Fuzzy systems have high potential to understand the very systems that are devoid of analytical formulations in a complex System. Complex systems can be new systems that have not been tested, they can involve with the human conditions such as biological or medical systems. The ultimate goal of the fuzzy logic is to form the theoretical foundation for reasoning about the imprecise reasoning, such reasoning is known as approximate reasoning. Genetic Algorithm (GA) was first introduced by Holland [7] and popularized by Goldberg [8]. It is one of the modern heuristic algorithms based on a principle of Charles Darwinian theory of evolution to natural biology. The GA technique can generate a high quality solution within shorter calculation time and stable convergence characteristics. GA method is an excellent method for solving the optimal PID controller parameters. Therefore, this study develops the GA-PID controller to search optimal PID parameters. In this paper, CSTR has been used to mix ethylene oxide with water to make ethylene glycol. Here the purpose is to control the concentration of ethylene glycol with the help of concentration of ethylene oxide. But undershoot, overshoot and inverse response come in the considered system while performing in a conventional way. But after implementation of PID controller to the process, removing of those shoots can be seen but still the design requirement is not achieved. So finally auto tuning method of PID controller is implemented in order to achieve the design requirement [3]. 2.Continuous Stirred Tank Reactor (CSTR) Modeling : In this paper, CSTR has been considered in which concentration of two chemicals is controlled for better results, the chemical ‘X‘ and ‘Y‘ and the byproduct is ‘Z‘. Ethylene oxide (X) is reacted with water (Y) in a continuously stirred tank reactor (CSTR) to form ethylene glycol (Z) .Assume that the CSTR is manipulated at a constant temperature and that the water is in large excess. Fig. 1. A CSTR Control System. The stoichiometric equation is X+Y= Z…………………(1) The reactant conversion in a chemical reactor is a function of residence time or its inverse, the space velocity. For anisothermal CSTR, the product concentration can be controlled by manipulated the feed flow rate, which change the residence time (for a constant volume reactor). It is convenient to work in molar units when writing components balances, particularly if chemical reaction is involved. Let CX and CZ represent the molar concentration of X and Z (mol/volume). dVC dt = F CX − FC + V … … (2) dVC dt = −FC + V … … … (3) Proceedings of International Conference On Current Innovations In Engineering And Technology International Association Of Engineering & Technology For Skill Development ISBN : 978 - 1502851550 www.iaetsd.in 117
  • 3. Where rX and rZ represent rate of generation of species X and Z per unit volume, and CXi represents the inlet concentration of species X. If the concentration of the water change than the reaction rate is second order with respect to the concentration of Ethylene oxide. r = −K C − K C … …… (4) Where k1, k2 & k3 are the reaction rate constants and the minus sign indicate that X is consumed in the reaction. Each mole X reacts with a mole of Y and produces one mole of Z, so the rate of generation of Z is r = K C − K C … … … … … … (5) Expanding the left hand side of equation (1) = V + C ……………(6) Combining eq (1) & (5) dC dt = F V C − C − K C − K C .. (7) Similarly, dC dt = − F V C + K C − K C … (8) 3. PROBLEM FORMULATION The linear space model or case study of CSTR is given by . x = Ax + Bu …………… (9) y = Cx + Du …………….. (10) Where the states, inputs and output are in deviation variable form. The first input (dilution rate) is manipulated and the second(feed concentration of A) is a disturbance input. Linearization of the two modeling equations (from equation (6) & (7)) at steady state solution to find the following state space matrices is done: For the particular reaction under consideration, the rate constants are k1=5/6 /min k2 =5/3 /min k3=1/6 mol/litre.min Based on the steady state operating point of CXs = 3 gmol/liter, CZs = 1.117 gmol/liter and Fs/V = 0.5714 min-1. The state model is Proceedings of International Conference On Current Innovations In Engineering And Technology International Association Of Engineering & Technology For Skill Development ISBN : 978 - 1502851550 www.iaetsd.in 118
  • 4. The manipulated input output process transfer function G(s)= C(sI –A)-1 B is calculated with the help of Matlab. G (S) = −1.117S + 3.1472 S + 4.6429S + 5.3821 … (10) It is desired to produce 100 million pounds per day of ethylene glycol. The feed stream concentration is 1.0 lbmol/ft3 and an 80% conversion of ethylene oxide has been to be determined reasonable. Since 80% of ethylene oxide is converted to ethylene glycol, the ethylene glycol concentration is 0.8 lbmol /ft3. In this process it is seen that the process has inverse response with delay time as well as overshoot while tunning in conventional PI,PID and fuzzy logic controllers are used. To overcome this problem and to obtain the desired response For that, soft computing based optimization method is used. 4. Controller design Industrial PID controllers usually available as a form and to perform well with the industrial process problems,the PID controllers structures requires modifications. The structures are given below ( ) = 1 + 1 + … … (11) the controller parameters are calculated. The desired parameters for the PID controller are the proportional gain (KP), integral gain (KI) and the differential gain (KD). Firstly, find and solve for the characteristic equation of the process which is given by + (4.6429 – 1.117kc) s + (5.3821 + 3.1472 kc ) = 0………. (12) Where kc is the critical (ultimate) gain. The value of kc can be calculated by the Routh Hurwitz criterion and the other parameters can be calculated by the Ziegler Nichols tuning method. Fig 2:Block diagram of conventional PID controller A basic PID controller directly operates on the error signal and this may produce a large overshoot in the process response due to the proportional and derivative kick. The process is unstable and to overcome the effect of proportional and derivative kick, a modified PID structure known as I-PD is considered. In I- PD structure, the integral term responds based on the error and the P+D terms works based on the measured process output. In conventional PID controller (Fig. 3), the changes in set point cause an impulse signal or sudden change in the controller output as well as in output response [2]. This spike in the controller output is called Proceedings of International Conference On Current Innovations In Engineering And Technology International Association Of Engineering & Technology For Skill Development ISBN : 978 - 1502851550 www.iaetsd.in 119
  • 5. proportional or derivative kick. The controller output is given to the final control elements like control valve, motor or electronic circuit in which the spikes create serious problem. But in I-PD controller (Fig. 4) , the proportional and derivative terms are acting only to the change in process variable not on the error as these terms are given in the feedback path. This structure may eliminate the proportional and derivative kick during any set point change [5]. Minimizing the ISE criterion generates the controller parameters. The values of the controller parameters are continuously adjusted, until the ISE of the closed loop system is minimum [7]. Figure 3. Tuning of I-PD controllers 4.1 Ziegler-Nichols Tuning Method ZN tuning rule was the first such effort to provide a practical approach to tune a PID controller. According to the rule, a PID controller is tuned by firstly setting it to the P- only mode but adjusting the gain to make the control system in continuous oscillation. The corresponding gain is referred to as the ultimate gain uK and the oscillation period is termed as the ultimate period uP . The key step of the ZN tuning approach is to determine the ultimate gain and period. Then, the PID controller parameters are determined from uK and uP using the ZN tuning Table I. controller P 0.5 - - pi 0.45 0.83 - pid 0.6 0.5 0.125 Table 1. Commonly used Ziegler-Nichols rule. By putting the proportional gain (KP), integral gain (KI) and the differential gain (KD) values in the simulink PID controller, the response for the step input is obtained. We see that the output have overshoot little inverted response and also its settling time and rise time is little bit more. That is not the desired response. Now for the better control, the Fuzzy logic controller is used. 4.2 Fuzzy logic controller When we connect a Fuzzy logic controller, then we require a multiplexer to give input to the controller.The inputs to the controller are error (difference of the set point and output) and feedback output (output as the feedback). Now construct the membership function for the inputs and the output taking triangular memberships. In this paper, the input is unit step input. In this process, the 80% of the ethylene oxide converted in to the ethylene glycol (output is 80% of the input). Thus the range for the output is [0 – 0.8]. The second input is error and its range is [0 – 0.2]. Using these values, make fuzzy rules in the fuzzy rule base editor and observe the response that there is no inverted response, no overshoot, no undershoot, rise time and settling time are reduced. 4.3. GENETIC ALGORITHM The GA is a global optimization and search technique based on the principles of genetics and natural selection. GA differs significantly from most classical optimization techniques in many aspects. First of all, unlike classical methods, GA are not gradient based, i.e. they do not require the objective functions to be continuous, neither do they need information about the derivatives of the objective functions, therefore they can handle problems with discrete solution spaces. Second, the search mechanism is stochastic in nature, which makes them capable of searching the entire solution space with more Proceedings of International Conference On Current Innovations In Engineering And Technology International Association Of Engineering & Technology For Skill Development ISBN : 978 - 1502851550 www.iaetsd.in 120
  • 6. likelihood of finding the global optima. Third, GA are able to solve problems with non- convex solution space, where classical procedures usually fails. All these differences make GA superior over classic methods in some real world applications, particularly for some very complex engineering problems, for example: complex truss-beam design, component’s design, and structure design. GAs features can be explained for solving complex control system engineering problems Controller design System Identification Fault Diagnosis System Analysis Robotics Further control related combination problem In GA, the individuals (solutions) in a population are represented by chromosomes; each of them is associated to a fitness value. According to the principle of survival of the fittest, the population reproduces, crossovers, mutates and produces a new generation that is fitter than the old generation. Those processes are done again and again until the fittest chromosome is found and the best result of the problem is got. Figure.3 shows GA process flowchart having key blocks as initial population, fitness evaluation, and optimization . Fig.4 Genetic algorithm process flowchart Simple GA has three basic operators: Selection Crossover Mutation A GA starts iteration with an initial population. Each member in this population is evaluated and assigned a fitness value. Strings with higher fitness values have more opportunities to be selected for reproduction in next step. Reproduction makes the clones of good chromosomes but does not create new one because of this crossover operator is applied. Crossover operator produces new individuals which have some part of both the parents genetic material. The crossover probability indicates how often crossover is performed. Using reproduction and crossover on their own will generate a large amount of different strings. However there are two main problems with this: Depending on the initial population chosen, there may not be enough diversity in the initial strings to ensure the GA searches the entire problem space. The GA may converge on sub-optimum strings due to a bad choice of initial population These problems overcome by the introduction of a mutation operator into the GA. Mutation are the occasional random alteration of a value of a string position. The probability of mutation is normally low because a high mutation rate would destroy fit strings and degenerate the GA into a random search. 4. SIMULATION, TESTING AND RESULTS The process is represented by the transfer function given in fig. 5, and fig. 6 depicts the output of the process. Proceedings of International Conference On Current Innovations In Engineering And Technology International Association Of Engineering & Technology For Skill Development ISBN : 978 - 1502851550 www.iaetsd.in 121
  • 7. Fig. 5: Process model Fig. 6: Time response of uncontrolled process When there is no control to the process, there is some time delay and inverted response and also the response is settled below the desired magnitude. The process with P controller is shown in the fig.7 and fig.8 depicts the output of the process. Fig. 7: Process model with P controller Fig. 8: Time response with P controller By using P controller there is not much effect to the output response as compared to uncontrolled process. As can be seen from fig. 8, there is almost the same response as that of uncontrolled and P controller model. The process with PID controller is shown in the fig. 9 and fig. 10 depicts the output of the process. The tuning of controller parameters is done by Zeigler & Nichols method. Here KP= 1.2, KI =5.73, KD= 0.78 Fig. 9: Process model with PID controller Proceedings of International Conference On Current Innovations In Engineering And Technology International Association Of Engineering & Technology For Skill Development ISBN : 978 - 1502851550 www.iaetsd.in 122
  • 8. Fig. 10: Time response with PID controller As can be observed from the fig. 8, Rise time ( tr) = 1.5sec Overshoot= 78% Settling time ( ts) = 23sec Fig.11: Time response with i-pd controller There is almost negligible time delay and inverted response.So Fuzzy controller is used to reduce the rise time, settling Time, overshoot and also try to remove the time delay and inverted response Fig. 12: Process model with fuzzy logic controller. The output response is shown below. Fig. 13: Time response with fuzzy controller As can be seen from fig. 10, Rise time ( tr) = 3 sec Settling time ( ts) = 4 sec Overshoot= 0% Undershoot= 0% There is no any time delay and also no any inverted response. All the limitations are reduced as compared to the PID controller. In fig.14, membership values of input 1 called ―errorǁ having three ranges low, medium and high is shown. Fig. 14: Fuzzy membership sets of input ‘1’ (error) In fig. 15, the membership values of input 2 called ―change in error having the three ranges low, medium and high. Proceedings of International Conference On Current Innovations In Engineering And Technology International Association Of Engineering & Technology For Skill Development ISBN : 978 - 1502851550 www.iaetsd.in 123
  • 9. Fig. 15: Fuzzy membership sets of input ‘2’ (change in error) In fig. 16, membership values of ―outputǁ having the same ranges low, medium and high. Fig. 16: Fuzzy membership sets of output (output) In fig. 17, fuzzy if-then rules using mamdani fuzzy model are shown. Fig. 17: Fuzzy If – then rules Fig. 18 depicts the mesh analysis of the two inputs (error and change in error) and output. Fig. 18: mesh analysis of both the inputs and outputs Fig. 19 depicts the surface view of the two inputs (error and change in error) and output. Fig.19: surface analysis of both inputs and outputs To overcome the problems occurs in fuzzy logic controller we are using the soft computing technique. By using the Gentic algorithm we can reduce the rise time, settling time is shown in the fig 20. Proceedings of International Conference On Current Innovations In Engineering And Technology International Association Of Engineering & Technology For Skill Development ISBN : 978 - 1502851550 www.iaetsd.in 124
  • 10. Fig. 20 : time response for Genetic algorithm Parameters/ type Peak overshoot (%) Rise time (Sec) Delay time (Sec) Sett time (Sec) PID 78% 1.95 1.2 28 I-PD 75% 2.1 1.6 17 Fuzzy logic controller 0 3 1.3 4 Genetic algorithm 0 2 1.3 2.5 Table.2:comparision results of pid,i-pd Fuzzy logic and genetic algorithm 5. CONCLUSION When there is no control to the process, it generates an inverse response together with an overshoot and considerable delay time. But when the PID controller and fuzzy logic controllers is implemented to the process, the problems of inverse response and delay time are controlled in the ongoing process and are removed considerably but then it was showing instability in terms of rise time, overshoot and settling time. To overcome this instability in rise time, overshoot & in settling time a soft computing technique Genetic algorithm used and the results are shown in the above figs.so the Rise time and settling time and overshoots are also reduced. By comparison with ZN, fuzzy and genetic algorithm, it shows that this method can improve the dynamic performance of the system in a better way by the selection of an appropriate objective function. 6. REFERENCES [1] Schmidt, Lanny D. (1998). The Engineering of Chemical Reactions. New York: Oxford University Press. ISBN 0-19- 510588-5 [2] Yung C. Shin, Chengying Xu ―Intelligent Systems: Modeling, Optimization, and Controlǁ CRC Press 2009. [3] Fried land B., ―Advanced Control System Designǁ, Prentice Hall, New Jersey, 1996. [4] Jaya, N. , Sivakumar, D. and Anandanatarajan, R. (2007)— Implementation of fuzzy gain scheduling of PID controllers for a two capacity interacting nonlinear process, paper presented at TIMA, January [5] K.J. Astrom, & T. Hagglund, ―The future of PID control Control Engineering Practice”, pp.1163 -1175. 2001. [6] Rajani K. Mudi, Chanchal Dey, & Tsu – Tian Lee, “An improved auto – tuning scheme for PI controllersǁ, Journal of science Direct ISA Transactions, 47: 45 – 52, 2008. [7] Luis E. Zarate, Peterson Resende, & M. Benjamin,” A Fuzzy Logic and Variable Structure Base Controller forCSTR Controlǁ. Annual conference of IEEE, 2001. [8] Xiao-Feng Li, Jian Sun, Hui-Yan Wu, Wei-Dong Zong, “Application of the fuzzy PID to the Power Plantǁ, IEEE 2007. [9] Yun Li,Kiam Heong Ang and Gregory C.Y.Chong,―PID Control System Analysis and Design – Problems, Remedies, and Future Directionsǁ. IEEE control system magazine, February 2006 pp. 32-41,2006 [10] Dimiter Driankov, Hans Hellendoorn, Michael Reinfrank, Fuzzy control Proceedings of International Conference On Current Innovations In Engineering And Technology International Association Of Engineering & Technology For Skill Development ISBN : 978 - 1502851550 www.iaetsd.in 125