Constrained GA Based Online PI Controller Parameter Tuning

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



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



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



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



↓ ↓

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



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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[13] W. Jie-sheng, Z. Yong and W. Wei, “Optimal Design of PI/PD

Controller for Non-Minimum Phase System,” Transactions of the

Institute of Measurement and Control, vol. 28, no. 1, 2006.

[14] S. Mohd Saad, hishamuddin jamaluddin and Z. Intan, M. Darus, “PID Controller Tuning Using Evolutionary Algorithms,” Wseas

Transactions on Systems And Control, vol. 7, no. 4, 2012, pp. 139-149.

[15] J. Zhang, J. Zhuang, H. Du and S. Wang, “Self‐ Organizing Genetic Algorithm Based Tuning of PID Controllers,” Information Sciences,

vol. 179, no. 7, 2009, pp. 1007 – 1018. [16] S.M. GirirajKumar, R. Sivasankar, T.K. Radhakrishnan, V.

Dharmalingam and N. Anantharaman, “Genetic Algorithms for Level

Control in a Real Time Process; Sensors and Transducers,” vol. 97, no. 10, 2008, pp. 22-33.

[17] S. Nithya, N. Sivakumaran,T. Balasubramanian and N. Anantharaman,

“Design of Controller for Nonlinear Process using Soft Computing”, Instru. Science And Technology, vol. 36, 2008, pp. 437-450.

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.



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


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)


Servo response (Initial set point = 10 cm) Regulatory response

Set Point Changes

from 10 cm to 13cm


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



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)



Set Point Changes

from 35 CM to 38 CM


38 CM to 34 CM

35 CM (Load change

for 15 Sec)


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)



Set Point Changes

from 21 CM to 24 CM


24 CM to 20 CM

20 CM (Load change

for 15 sec)


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



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



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



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



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



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

Documents

Constrained GA Based Online PI Controller Parameter Tuning