constrained ga based online pi controller parameter tuning
TRANSCRIPT
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:01 19
151701-9292-IJMME-IJENS © February 2015 IJENS I J E N S
Constrained GA Based Online PI Controller
Parameter Tuning for Stabilization of Water Level in
Spherical Tank System S.P.Selvaraj
1, A.Nirmalkumar
2
1Deparmemt of Electronics and Instrumentation Engineering, Bannari Amman Institute of Technology, sathyamanagalam,
Tamilnadu, India-638401.Ph: +91-4295 226227, Fax:+91-4295226666 [email protected] 2 Principal, Karpagam College of Engineering, Myleripalayam Village, Coimbatore, Tamilnadu, India- 641032.
Ph: +91-422 2619047, Fax: +91- 422 2619046, [email protected]
Abstract— Level Control of spherical tank is one of the
requirements in industries, where the storage of large volumes of
highly pressurized liquids takes place. The level control in
spherical tank is cumbersome due to variation of cross sectional
area with respect to its height. In the proposed work, PI
controller is used to control the level of spherical tank. Initially,
the Ziegler Nicholas step response method is used to geta first
order plus dead time mathematical model and single set of PI
parameter.Multiple models or multiple sets of PI controller
parameters are also obtained at different operating points using
Z-N and online CGA based tuning methods. By conducting
experimental study, the servo and regulatory responses of the
spherical tank process are obtained with the controller
parameters obtained through various tuning methods.The online
CGA based tuning method produce better output response with
minimum Integral Square Error (ISE) and Integral Absolute
Error (IAE) in real-time, with respect to set point and load
changes.
Index Term— Constrained GA, PI controller, Spherical Tank,
Online tuning, IAE and ISE.
I. INTRODUCTION
Liquid level control is one of the important schemes in many
products and process industries including manufacturing,
storage and service industries to get product accuracy, safety
and reduce energy consumption. Proportional-Integral-
Derivative (PID) controller is the most used continuous
controllers in the industry and universally accepted control
algorithm for industrial control due to its robust performance,
functional simplicity and operator friendly. The PID
controllers can be implemented tocontrol a variable at any
given operating point within an acceptable degree of accuracy,
which eliminates the need for continuous operator attention.
Basically the level process has fast output response, single
energy storage element (capacitive), considerable disturbance
and transportation lag. The use of proportional control may
require a large gain to minimize the steady state error and the
increase in gain will reduce the system stability. The PI action
offers both fast response and zero steady state error due to the
proportional and integral actions respectively. So, the
Proportional-Integral (PI) controller is commonly used to
control the level processes in industries.
The PI controller or PID controller performance is based on its
parameters controller gain (Kc), Integral/reset time (Ti) and
derivative time (Td). In industries, trial and error method is
used to assign the controller parameters and analyze the
response of the process. After analysis the parameters are
adjusted manually to improve the responses and this kind of
parameter selection is cumbersome even though the process
tank is linear. A tuning method is essential in order to select
suitable PI controller parametersfor the proposed level control
scheme, because small step change also introduce
considerable oscillations in the process due to variation in the
cross section of the tank.
Anandanatarajan R et al (2006) has tuned the controller
parameter at a nominal operating point using Ziegler-Nichols
Proportional Integral (ZNPI) controller method and response
of nonlinear systems has been obtained. A simulation study
has been conducted for the system using Non-Linear PI
(NLPI) controller and it produced less oscillatory response [1].
The NLPI controller is implemented only in simulation, in real
time the NLPI controller may behave differently due to
process dynamics. Nithya S et al (2008) has implementedan
Internal Model Control (IMC) and Skogestad’s IMC (SIMC)
for level control of spherical tank, at four different operating
points and it was concluded that the IMC and SIMC based
tuning exhibits minimum overshoot with faster settling time
when compared to ZN tuned controller for set point and load
changes [8]. The result shows that IMC controller also
exhibits considerable overshoot. This method requires a
mathematical model for each operating point and it is difficult
to get mathematical model for each operating point of a
spherical tank in real time.
Dhanalakshmi R and Vinodha R (2013), have compared the
performance of Multiple Model Adaptive based PI (MMAPI)
and Neural Network based Adaptive PI (NNAPI) controllers
for level control of the conical tank system. The authors
conclude that the NNAPI controller shows better performance
when compared with the MMAPI control strategy [4]. Since
conical and spherical tank behaves differently for various
operating points, the training of neural network for each
operating point of the tanks are highly time consuming in
practice. The parameters are obtained using simulation
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151701-9292-IJMME-IJENS © February 2015 IJENS I J E N S
technique and implementing them in real time may not give
robust performance.So, intelligent tuning algorithms are
essential to tune the parameters [2].
Genetic algorithms (GAs) are search algorithms based on the
mechanics of natural selection and natural genetics. GAs has
been applied to a wide range of optimization problemsto find
optimum solutions and the PI controller requires best possible
parameters to produce satisfactory response. Hence, they are
admirably suited to the controller parameter tuning.
Constraints are added in the GA during population
initialization and mutation process in order to reduce the
tuning period and keep the process variable in a specified
limit. After adding constraints, the algorithm is named as
Constrained Genetic Algorithm (CGA). Since CGA has better
intelligence than GA, it can be implemented when the process
is running and optimum parameters can be obtained.
The objective of the work is to maintain the water level in the
spherical tank system at various operating points using
LabVIEW software and CGA based tuningas a framework. In
section 2, the real time spherical tank system and the
development of mathematical models of the process are
analyzed. The traditional tuning method based results and
need for multiple models for controlling the level of spherical
tank system is discussed in section 3. The section 4, deals with
the development of CGA from GA. Section 5 and 6
investigates the implementation of CGA based online PI
controller parameter tuning for level control of a spherical
tank. The results obtained from real time process and
comparative studies are given in section 7. The section 8 gives
the conclusions based on the obtained results.
II. MATHEMATICAL MODEL FOR SPHERICAL TANK
SYSTEM
The spherical tank system exhibits non-linear behaviour due to
variation on its shape. The Fig. 1, shows the experimental
setup considered for modelling and analysis.The outline of the
system is shown in the Fig. 2.
A. Spherical Tank System
The real time system consists of one input (inflow) and one
output (level of the tank). The inflow is taken from a reservoir
tank through a centrifugal pump with 3-phase motor, which is
operated witha Variable Frequency Drive (VFD). The inlet
pipe has a Rotameter, Orifice with Differential Pressure
Transmitter (DPT) called as Flow Transmitter (FT), air-to-
open type pneumatic Control Valve (CV) and a hand valve to
monitor and regulate the flow rate. The orifice converts the
flow into differential pressure and FT converts differential
pressure into electrical signals (4 to 20 mA). The outlet has a
wheel type flow meter and air-to-open type pneumatic CV to
measure and regulate the outflow rate respectively. The tank
level is measured using a DPT, called as Level transmitter
(LT) and digital panel meters are used to monitor process and
control variables. The level in the tank is directly proportional
to the pressure created by liquid in it. LT measures the bottom
tank pressure with reference to the atmosphere and generates
an electrical signal (4 to 20mA).
The DPTs are energized with 24V DC source and Lower Rage
Value (LRV) & Upper Range Value (URV) are set using a
Highway Addressable Remote Transducer (HART)
communicator. The system is interfaced to the computer
through NI USB 6211 data acquisition card (NI DAQ) and it
can handle a maximum of 10 V. So, the DPT outputs (4 to 20
mA) are converted into 2 to 10V using a 500Ω resistances and
scaled up using LabVIEW. The control signal (0 to 10V) from
computer via NI DAQ is converted into 4 to 20 mA using a
voltage to current convertor and given to current to pressure
(E/P) convertor or VFD. The pneumatic line from the
compressor is connected with an air regulator to obtain a
constant pressure of 20 Pounds per Square Inch (PSI) and E/P
converters needs this constant pressure to generate a variable
pressure of 3 to 15 PSI with respect to electrical signal of 4 to
20 mA. The CVs are operated based on the pneumatic outputs
from E/Ps. The VFD can vary the pump speed proportional to
control signal (4 to 20 mA) and regulate the inflow rate.The
description of components used in the spherical tank system is
listedin Table I.
B. Process Modelling
The process modelling of spherical tank system is given by
mathematical mass-balance equation (1)
)1(-- --- πR3
4 = V=Ah =F-F 3
outin
From the equation (1), the transfer function can be
determined.
h.=R and R4 =A Where,(2) ---------Ah 3
1 AR
3
1 F-F 2
outin
Where, Fin = input flow rate, Fout= output flow rate, A= cross
sectional area, h = overall height of the tank, R = Radius of the
tank, r = Variable radius with respect to Actual level of
liquid.From theFig. 3, by applying side-angle-side similarity
theorem
)3(H
rh R
R
r
h
H
outin FF dt
dhA
dt
dV
R
h
dt
dhAF , hC
R
hF Where
V
in
V
out
By taking Laplace Transformation
R
H(s)AsH(s)(s)F
V
in Rearranging this equation
s1
K
sAR1
R
(s)F
H(s)
V
V
in
Where, RV = valve resistance,H= Actual level of liquid,
K=RV, τ=ARV, C= valve constant, RV= C
h
C. System identification
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The step response based open loop test is commonly adopted
procedure for system identification. The process reaction
curve is obtained by performing an open loop test on the real
time process and model parameters are identified from the
curve. LabVIEW platform is used to code the logic and the
process is allowed settle at 0 cm by assigning random gain to
the PI controller in closed loop and the LabVIEW Program
stores flow rate with the help of FT. Now the loop is made
open and flow rate is increased by P% from the stored value
using LabVIEW based soft switching, which isolates the
controller and the level starts increasing from 0 cm after a
considerable delay called delay time. Each 400 millisecond
the level is stored in a file for further analysis and it is allowed
to settle through self regulation. The flow increment P% is
selected therefore to make the level to reach more than half of
the tank (>21.5 cm) for obtaining single mathematical model
or only one set of PI parameters for the spherical tank system.
The open loop response is plotted and the values like
percentage change in level from 0 to 27.5 cm (Q%), delay
time (td), the time taken by the level to reach 28.3% (t1) and
63.2% (t2) are noted for getting mathematical model of the
spherical tank. Two-point method is used to estimate the time
constant (τ) of the system and delay time is taken directly
from the response curve. The process reaction curve obtained
in real time system for 0 to 27.5 cm range is shown in the Fig.
4.
τ = 1.5 (t2 - t1)
The First Order Process with Time Delay (FOPTD) model =
1τs
eK G(s)
s-t
Pd
Maximum flow =1500 lph, and 100 lph change in flow = P%
change in input.
Maximum level = 43 cm, 1% = 0.43 cm, 27.5 cm change=Q%
change in output
τ =1.5 (t2 - t1) =1290 seconds
Kp= 593.9P
Q
inputin Change %
outputin Change %
)6( 11290s
9.593e G(s)
-6s
The G(s) in equation (6) is the obtained mathematical model
for the entire operating range of spherical tank system
III. THE ZIEGLER-NICHOLS (Z-N) METHOD FOR PI
CONTROLLER PARAMETER TUNING
The Z-N open-loop tuning method uses three process
characteristics: process gain, delay time, and time constant,
obtained from process reaction curve to tune the PI
parameters. The controller gain (Kc) and Integral Time (Ti) are
calculated using the formula given by Ziegler-Nichols.
For PI control: Kc = 0.9 τ / (Kp* td);=20.171
Ti = 3.3 * td = 0.33 min
In this test the process reaction curve starts from 0 cm and
ends at 27.5 cm and the PI parameters tuned from this curve is
expected to providesatisfactoryvalue of the ISE and IAE when
set point or load changes are given to the process for the entire
operating range from 0 cm to 43 cm.
The above procedure is followed to find one more open loop
response and PI controller parameters for spherical tank
system, in which the initial level is maintained at 10 cm by
running the process in closed loop and assigning random gain
to PI controller. After level settled at 10 cm, the step change in
inflow of P1% is given in open loop. In this test the process
reaction curve starts from 10 cm and ends at 16.3 cm (say
level change is Q1%) which is shown in the Fig. 5. The PI
parameters tuned from this curve using the Z-N method is
expected to provide minimum ISE and IAE when set point or
load change is within the range of 10 to 16.3 cm.
Kp= 14.88.1
65.14
P1%
Q1%
)7(11065s
8.14e G(s)
-5.44s
Kc= 21.411, and Ti=0.299
The G(s) in equation (7) is the obtained mathematical model
for 10 cm to 16.3 cm range of spherical tank system From the
Fig. 5, it is found that, the response of the system is more
oscillatory for random PI parameters and it takes
approximately 500 seconds to settle from 0 cm to 10 cm in
closed loop. Now the tuned parameters are assigned to PI
controller and the level of the non-linear tank is controlled in
closed loop at various set points in real time when outlet valve
is opened 65%. During this test, the process variable, ISE and
IAE are noted at the interval of 400 milliseconds. The
responses of the system, the average value of the ISE and IAE
for 250 samples are compared to analyze the performance
controller settings obtained from two different open loop tests,
which is shown in the Fig. 6 and Table II.
The analysis shows that the model or PI controller parameters
obtained in the range 10 cm to 16.3 cm performs better for
positive and negative set point changes, than a single model or
only one set of PI controller parameters obtained from the
process reaction curve 0 to 27.5 cm range. It is concluded that
multiple models and set of PI parameters are essential to
improve the responses of level control process in a spherical
tank at various set points or load changes.
Three different methodical models and corresponding PI
controller parameters through 3 different open loop tests for
level control of spherical tank, one at lower range (10 to 16.3
cm) second at middle range (20 to 25.5 cm) and third, at a
higher range (35 to 38.9 cm) are obtained. These parameters
are expected to give better responses only for the specific
ranges. If 43 different models and 43 sets of PI parameters are
there, then, moderate responses for each 1 cm change in set
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points can be obtained. It is difficult to get 43 different open
loop tests in practice and the finest responses for entire
operating range are essential in industrial applications to
improve product quality, productivity and safety. So the
proposed method adopts an intelligent tuning method using
Constrained Genetic Algorithm to get the best response in the
spherical tank system.
IV. GENETIC ALGORITHMS
Genetic algorithms are random search and optimization
technique based on the descriptions of natural biological
evolution. GAs starts out with an initial “population” of
possible solutions (individuals) to a given problem (the
environment) where each individual is represented using some
form of encoding called as a “chromosome”. These
chromosomes are evaluated in some way for their fitness (i.e.
The extent to which the individuals they represent are suitable
to the environment). Using their fitness as a criterion, certain
chromosomes in the population are selected for reproduction
(survival of the fittest); the process of reproduction generally
consists of the introduction of stochastic modifying processes
such as mutation and crossover, and mechanisms by which
new chromosomes can be generated.
In the proposed work, Population = group of
chromosomes/solutions/individuals/parents, each chromosome
in the population is a combination of two genes, Proportional
Gain and Integral Time respectively.
Initial population: Each chromosome (solutions) in the
population is initialized through a random process.
Evaluation: The proportional gain (gene1) and integral time
(gene2) from the each chromosome are assigned to PI
controller and the system responses are obtained. Maximum
fitness is assigned to a chromosome, which yields better
system response.
A. Selection
Selection is the stage of a genetic algorithm in which fittest
individual chromosomes are chosen from a population for
breeding (crossover). Tournament Selection: Tournament
selection is similar to rank selection in terms of selection
pressure, but it is computationally more efficient and more
amenable to parallel implementation. In binary tournament
selection, two chromosomes are taken at random, and the
better chromosome is selected from the two by comparing the
fitness values of them. In proposed work, the two
chromosomes are selected for reproduction by executing the
above selection process twice and the already selected ones
were not replaced in the original population for the next
selection.
B. Crossover
Single point crossover - The crossover point is selected
between two genes and a number ‘n’ is generated through a
random process. When ‘n’ is odd, the parents’ genes from left
side of crossover points are swapped or ‘n’ is even, the
parents’ genes from right side of crossover points are swapped
to get two offspring.
Parent 1 = 12.185 | 0.289
Parent 2 = 15.301 | 0.309
When ‘n’ is an odd number
Child 1 = 15.301 0.289
Child 2 = 13.185 0.309
(Or)
‘n’ is even number
Child 1 = 13.185 0.309
Child 2 = 15.301 0.289
C.Mutation
Mutation is a genetic operator used to preserve genetic
diversity from parents to children. It alters one or more gene
values in a chromosome from its initial state. Delta: First a
gene of the child is chosen at random, and then that parameter
(gene) is perturbed by a fixed amount, set by a delta input
parameter. A gene is selected from two genes of the child
through a random process with 50% probability and the
selected gene is modified using delta value.
D. Constrained Genetic Algorithm (CGA)
It has all the operations of GA and constrains are assigned
during mutation and initialization of the population. The
sequence of operation of CGA is shown Fig. 7, in the form of
flow chart
1)Constrained Initialization: During initialization, after
generating each gene of the chromosome through a random
process, the genes are checked to satisfy the specified
constraints (lower and upper bound limits). If a gene is found
to be outside the boundary limit, then it is discarded and new
gene is generated randomly to satisfy the specified constraints,
which leads to maintain the process variable close to set point
when the CGA is operating.
2)Mutation: Delta parameter is used to modify the gene,
which is selected from the child through 50% probability.
After modification the lower and upper bounds are checked to
avoid deviation of the process variable from set point. If the
modified value is found to be, beyond the boundary limit, then
it is brought to within the limit by giving suitable
modification.
Let the lower and upper boundary limits of proportional gain
(gene1) and integral time (gene2) are 12 and 15and Integral
Time 0.2min and 0.32 min respectively.
Let the delta value gene1=0.2 and gene2 = 0.005.
Child = 13.185 0.309
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↓ ↓
x y
Let the Selected gain = x
Modified gain = x-0.2
If (Modified gain < 12)
then Modified gain =x+0.2
Child = 13.385 0.309
(OR)
Let the Selected gain = y
Modified gain = Ti-0.005
If(Modified gain < 0.2)
then Modified gain =Ti + 0.005
Child = 13.185 0.304
V. CGA BASED ONLINE PI CONTROLLER PARAMETER
TUNING
In online method, the PI controller parameters are
altereddynamically while the process is running and the
performance of the parameter is analyzed based on the real
time ISE. This method requires only one set of approximate PI
parameter values to set the constraints when the CGA is
operating, which can be obtained from Z-N open loop
response and it does not require mathematical model.
Initially the parameter obtained from the Z-N method is
assigned to the PI controller and required set point is given in
LabVIEW. The feedback from the spherical tank is taken and
connected to the controller through LT and NI DAQ. The
controller controls the inflow through VFD. When the process
variable reaches a nearby set point, CGA initiates operation.
The population is initialized through the constrained
initialization process. In the proposed work the constraints for
gene1 (Kc) is set from 8 to 16 and gene2 (Ti) is from 0.2 to
0.33. Since constraints are set, the real time response (process
variable) does not deviate much from set point and minimizes
the search space. One set of parameter from the populations is
assigned to PI controller and tested in real time and ISE is
monitored for each 400 milliseconds over a period of 30
seconds. The set of parameters (Chromosome) yields
minimum average ISE for 30 seconds is assigned with
maximum fitness and this chromosome influence more in the
next generation. When ISE exceeds 10, then the parameters
are discarded immediately, the fitness of that chromosome is
assigned to zero and next set of parameter of the population is
loaded. Since the chromosome with larger ISE is given
minimum fitness value, the chromosome will not have any
impact in the next generation. Once, all the chromosomes in
the population are tested, then selection, crossover,
constrained mutation operators are used to get new population
and the process is repeated 6 times to get optimum solution.
Population size: 6 (6 possible set of PI parameters)
Chromosome: 2 genes/ chromosome
Number of generations: 6
Crossover: single point crossover
Mutation: delta operator with constraints.
Since the real time process responses are compared for
performance analysis,the PI controller parameters obtained
through online CGA tuning gives satisfactory responses. The
intelligent is added in the process by comparing real time ISE,
helps to maintain the level very close to set point, even when
the PI parameters are changed during CGA operation. Based
on the requirements the stopping conditions, population size
and number of generations can be changed to get optimal
responses.
VI. REAL TIME IMPLEMENTATION OF LEVEL CONTROL
The PI controller parameters are tuned using 3 different
methods, Z-N with 0 to 27.5 cm range, Z-N with specific
range (Say 10 to 16.3cm), and CGA based online tuning. The
servo responses of the real time system are obtained through
experimental study, by assigning tuned parameters to the
controller for maintaining the level of the spherical tank at
various set points, 0 to 10 cm, 10 to 13 cm & 13 to 9 cm. The
set point changes at every 100 seconds are given through the
LabVIEW program. The real time process variable (level),
ISE and IAE are stored in a file (File extension: lvm) at every
400 milliseconds for further analysis.
The regulatory response is taken through experimental study,
by allowing the process variable to settle at a specified set
point with 20% disturbance (outlet valve is 20% open). Now
the outlet valve is opened to 100% for 15 seconds and then the
valve is set to the previous level of 20% open through soft
switching, then the process parameters are recorded for 100
seconds.
The servo and regulatory responses are obtained for all gain
tuning methods separately for giving uniform step and load
change and the results are consolidated for analysis. Similarly,
the PI controller parameter tuning and implementation of the
middle range (20 to 25.5cm) and upper range (35 to 38.9 cm)
of the spherical tank are done and results are stored in
different files for analysis.
VII. RESULTS AND COMPARATIVE ANALYSIS
The servo and regulatory responses of the four different tuning
methods are compared in terms of the performance indices
such as ISA and IAE. The real time ISE and IAE values are
taken from the resultant files; the average of value IAE and
ISE are calculated for 250 samples and tabulated for
comparison. The Table III, Shows the comparative results of
the lower range of set points (9 to 13 cm). The results of
middle (20 to 24 cm) and upper (34 to 38) set points are
compared in Table IV, and Table V respectively.
The servo and regulatory responses also compared by plotting
curves between the process variable and process time for the
four different tuning methods. The servo response plots for
lower, middle and upper range of set points are shown in Fig.
8, Fig. 9 and Fig. 10 respectively. Similarly, regulatory
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response plots are shown in Fig. 11, Fig. 12, and Fig. 13. The
CGA based online tuned parameters gives satisfactory
responses both in transient and steady state periods. The
response of a spherical tank system obtained at 21 cm during
the operation of CGA based online tuning at run time is shown
in the Fig. 14, and the process variable is oscillates only at
nearest set point boundary region.
VIII. CONCLUSION
The data obtained from the experimental results shows that the
proposed CGA based online tuning of PI controller parameter
yields better servo and regulatory response (minimum ISE and
IAE) over traditional and simulation based tuning techniques.
The conventional method requires 43 different sets of PI
parameters (say 1 set of parameters for 1 cm) or more to
control the level at various set points from 0 to 43 cm
forspherical tank having a diameter of 43 cm. It is difficult to
conduct 43 numbers of open loop tests in real time for a
spherical tank system to get 43 sets of PI parameters using Z-
N open loop tuning method. So the 4 different sets of Z-N
tuned parameters provideoscillatory responses for most of the
step and load changes.
Based on the performance indices analysis from Tables III, IV
and V (IAE and ISE), the proposed online CGA based tuning
method gives the optimized parameter values of the PI
controller with minimum average of IAE and ISE for various
set point and load changes when compared to conventional
tuning methods. In this method, the dynamic behaviour of the
real time system having good set point tracking capability
when compared to other tuning methods because, the PI
controller parameters are tuned at run time as per its
requirement. The proposed method can be adapted for level
control schemes for linear and non-linear tanks to improve
productivity, product quality and safety in industries. The
algorithm can be easily implemented through advanced
controllers used by industries like Programmable Logic
Controllers and Distributed Control Systems.
ACKNOWLEDGEMENT
I express my deep sense of gratitude and heartfelt thanks to
the management of the Bannari Amman Institute of
Technology for extending the required facilities in the college
campus. I wish to thank all the teaching and non-teaching staff
of the Department of Electronics and Instrumentation
Engineering for the help rendered by them at times of need. I
am thankful to All India Council for Technical
Education (AICTE) for funding my project. I have used the
fund to get field instruments and National Instruments Data
Acquisition Cards.
Title of the Project: Automation of Level Control of Non-
Linear Tanks (Spherical and Conical).
Fund Name: AICTE-Research Promotion Scheme.
Fund Value: INR 8, 20, 000.00; Duration 3 Years.
Reference Number: 20/AICTE/RIFD/RPS(POLICY-
III)70/2012-13 Date: February 15, 2013.
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Prof. S.P.Selvaraj obtained graduation in Electronics and Instrumentation
Engineering from Annamalai University and Post Graduation in Control
Systems from Bharathiyar University in 2001. Obtained
Research fund from AICTE in RPS scheme as a Co-PI and Published many International Journal & conference papers,
He has provided a major contribution to establish center of
excellence in Industrial Automation at Bannari Amman Institute of Technology, 2014. He has good industry contacts
to enhance teaching-learning and research activities. Research interests:
Evolutionary computation, Process Control and Automation, Control Systems.
Dr. A. Nirmal Kumar obtained graduation in Electrical
Engineering from Calicut University and Post Graduation from
Kerala University. Under Q.I.P. completed Ph.D from Bharathiyar University and has got several papers to his credit
published in International & National journals. Guided so far 5
Ph.D scholars and at present, has 10 Ph.D scholars doing research under him.
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:01 25
151701-9292-IJMME-IJENS © February 2015 IJENS I J E N S
He is the recipient of “Institution of Engineers” gold medal for the year 1989. He has about 37 Years of teaching experience.
TABLE I COMPONENT DESCRIPTION
S.No. Parts/Field instruments Description
1. Spherical Tank
Material :Stainless Steel, Diameter: 43 cm, (LRV= 436 mmH2O,
URV=866 mmH2O,
Volume : 42 liters
2. Pump and VFD
VFD: ABB-ACS350, 3Φ
4- 20 mA to 0 to 50 Hz.Pump: Grundfos-JP5 centrifugal
pump, 3Φ.
3. DPT for level
measurement(LT) 6200T Series, Range:0 to 6500 mmH2O, Output: 4 to
20mA+HART 4.
DPT for level
measurement (FT)
5. Control valves Linear, Air to open, Body:1”, Trim1/2”
6. Rotameter 150 to 1500 lph
7. E/P converter Input:4 - 20 mA, 20 psi
Output: 3 to 15 psi
8. NI USB 6211 DAQ Analog input: 8, Analog output: 2, Resolution: 16 bits, Sampling
rate: 250kS/s input & output voltage: -10V to +10V
TABLE II
COMPARISON OF PERFORMANCE INDICES
(Specified range PI parameters Vs Single set of PI parameter inthe entire operating range)
Gain Tuning
Methodology Gain
(Kc)
Integral
Time
(Min)
Average Error from real time system (250 samples)
Servo response (Initial set point = 10 cm)
Set Point Changes from
10 cm to 13cm
Set Point Changes from
13 cm to 9 cm
IAE ISE IAE ISE
Z-N (10-16.3
cm) 21.411 0.299 3.69 4.77 10.44 21.07
Z-N (0 to 27.5
cm range) 20.171 0.33 4.12 5.05 16.66 35.98
TABLE III
COMPARISON OF PERFORMANCE INDICES - LOWER RANGE OF SET POINTS
Gain Tuning
Methodology Gain
(Kc)
Integral
Time
(Min)
Average Error from real time system (250 samples)
Servo response (Initial set point = 10 cm) Regulatory response
Set Point Changes
from 10 cm to 13cm
Set Point Changes from
13 cm to 9 cm
SP =10 cm (Load
change for 15 Sec)
IAE ISE IAE ISE IAE ISE
Online CGA 13.918 0.254 2.99 4.37 6.97 15.26 6.05 5.55
Z-N (10-16.3
cm) 21.411 0.299 3.69 4.77 10.44 21.07 9.57 10.62
Z-N (0 to 27.5
cm range) 20.171 0.33 4.12 5.05 16.66 35.98 11.20 14.27
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TABLE IV COMPARISON OF PERFORMANCE INDICES – MIDDLE RANGE OF SET POINTS
TABLE V
COMPARISON OF PERFORMANCE INDICES - HIGHER RANGE OF SET POINTS
Gain Tuning
Methodology Gain
(Kc)
Integral
Time
(Min)
Average Error from real time system (250 samples)
Servo response (Initial set point = 35 cm) Regulatory response
Set Point Changes
from 35 CM to 38 CM
Set Point Changes from
38 CM to 34 CM
35 CM (Load change
for 15 Sec)
IAE ISE IAE ISE IAE ISE
Online CGA 8.866 0.314 3.60 4.70 6.61 13.07 8.92 20.24
Z-N (35 to
38.9 cm range) 8.999 0.302 4.15 5.19 6.84 13.78 8.25 21.06
Z-N (0 to 27.5
cm range) 20.171 0.33 4.71 6.46 8.74 18.58 8.11 16.04
Fig. 1. Spherical Tank Experimental Setup Fig. 2. Layout of Spherical Tank System
Gain Tuning
Methodology Gain
(Kc)
Integral
Time
(Min)
Average Error from real time system (250 samples)
Servo response (Initial set point = 21 cm) Regulatory response
Set Point Changes
from 21 CM to 24 CM
Set Point Changes from
24 CM to 20 CM
20 CM (Load change
for 15 sec)
IAE ISE IAE ISE IAE ISE
Online CGA 15.101 0.228 3.36 4.97 7.11 16.32 5.46 6.84
Z-N (20 to
25.5 cm range) 13.791 0.302 3.92 6.39 8.16 18.22 6.22 8.96
Z-N (0 to 27.5
cm range) 20.171 0.33 5.05 6.87 10.66 24.68 7.54 7.05
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Fig. 3. Outline of a Spherical Tank
Fig. 4. Open loop Response of Spherical Tank System for 0 to 27.5 cm
Fig. 5. Open loop Response of Spherical Tank System for 10 to 16.3 cm range
Fin
Fout O
R
r
h
H A
B
P
Q
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Fig. 6. Servo Response of Spherical Tank System
Fig. 8. Servo Response of Spherical Tank System for Lower Range of Set Points
Fig. 9. Servo Response of Spherical Tank System for Middle Range of Set Points
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Fig. 10. Servo Response of Spherical Tank System for Higher Range of Set Points
Fig. 11. Regulatory Response of Spherical Tank System for Lower Range of Set Point
Fig. 12. Regulatory Response of Spherical Tank System for Middle Range of Set Point
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Fig. 13. Regulatory Response of Spherical Tank System for a Higher Range of Set Point
Fig. 14. Response of Spherical Tank System when Set point = 21 cm during on-line CGA tuning process
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Fig. 7. Flow Chart for CGA
Yes
Generate Initial Population of solutions by satisfying the
given constraints
(Population => 6 Set of PI controller parameters;
1 set/solution = Kc Ti)
Evaluate fitness of each solution
(Maximum fitness is assigned to a parameter set, which
yields minimum average ISE in real time)
Selection of individual parameter
(Tournament selection)
Matting/reproduction
(Single point crossover)
Mutation satisfying
the given constraints
(Delta operator)
New population generated and fitness evaluatedfor each
solution
If
Solution is satisfactory? Or
Maximum iteration reached?
No
End