
DESIGN AND IMPLEMENTATION OF PI CONTROLLER USING GENETIC
ALGORITHM AND ANT COLONY OPTIMIZATION FOR A SPHERICAL TANK
PROCESS
Mr. G. SAKTHIVELLecturer (selection grade)Department of
Instrumentation EnggAnnamalai university chidambaram.ByA.
KRISHNAMOORTHYM.E. (Process Control & Instrumentation Engg.)
(20092011)

OBJECTIVES OF THE PROJECT WORKTo identify the model of the
spherical tank process by black box modeling for various operating
region.Low LevelMiddle LevelHigh LevelTo tune the PI controller by
Ziegler Nichols method.To optimize the designed PI controller
using ACO (Ant Colony Optimization) Technique for various cost
function like IAE, ITAE, ISE.To tune the PI controller by Genetic
algorithm.

To compare the results of ACO tuned PI controller with ZN tuned
PI and GA tuned PI controller in terms of time domain specification
and performance indices like ISE, MSE, ITAE, IAE. To obtain the
results form both simulation and real time process for the
corresponding models. To check to robustness of the above designed
controller and test the ACO under white noise.

PI CONTROLLER It consist of proportional and integral action PID
can be implemented as a stand alone controller (or) part of the
controller e.g. DDC (or) DCS Various actions PACTION P = Kp* e
IACTION I = ki e dt DACTION D = Kd d(e)/ dt whereKp =
proportional gain KI = Integral gain

Closed loop ZN tuned PI Controller
The transfer function of PI controller looks like following: U=
Kp* e (t)+kie(t)Block diagram of PI controller Recommended PID
Value Setting
TYPE OF CONTROLLERKpTiTdP0.5 Ku0PI0.45 KuPu/1.20PID0.6
KuPu/2Pu/8

OBJECTIVE FUNCTIONSThe following objective function we are using
for both GA and ACO optimization. 1. Integral Absolute error
2. Integral square error 3. Integral time Multiplied by Absolute
error

It is a type of machine learning technique
Mimics the biological process of evolution Genetic algorithms
Software programs that learn in an evolutionary manner, similar to
the way biological systems evolve
An efficient, domainindependent search heuristic for a broad
spectrum of problem domains
Main theme: Survival of the fittes. Moving towards better and
better solutions by letting only the fittest parents to create the
future generations

Reproduction Multiple copies of the same string may be selected
for reproduction and the fittest string should begin to dominate
e.g. roulette wheel selectionDepiction of roulette wheel
selection

CROSSOVER Once the selection process is completed, the crossover
algorithm is initiated. The crossover operations swaps certain port
of the two selected strings in a bid to capture the good parts of
old chromosomes and create better new ones. Singe point Multi point
Uniform

Single point crossover
Multi point crossover
Uniform crossover

MUTATION Mutation is the occasional random alternation of a
value of a string position. Eg.

Ant Colony Optimization (ACO) is a paradigm for designing meta
heuristic algorithms for combinatorial optimization problems.
Ants travel from node to node until end decision based on
transition probability (called state transition)
Once all ants travel finished Solutions compared
Pheromone evaporation applied to all edges Pheromone increased
along each edge of best/each ants path
Original ant system: at each iteration, the pheromone values are
updated by all the ants that have build a solution in the iteration
itself.
Daemon activities can be run (like local search)
Redo until termination criteria met
They have an advantage over simulated annealing and genetic
algorithm approaches when the graph may change dynamically. The ant
colony algorithm can be run continuously and can adapt to changes
in real time.

Ants choose paths depending on pheromoneAfter collecting food,
paths are marked After some time, the shortest path has the highest
probability

When ants travel they mark their path with substance called
pheromoneAttracts other ants
When an ant reaches a fork in its path the direction it follows
is based on amount of pheromone it detectsDecision
probabilistically made
This causes positive feedback situation (i.e. Choosing a path
increases the probability it will be chosen)

While ( termination not satisfied )create antsFind
solutionsTransition probability:
Pheromone updateDaemon activities {optional}
Quantity of pheromoneHeuristic distance, constants

While ( termination not satisfied )create antsFind
solutionsPheromone update
Daemon activities {optional}Evaporation ratePheromone laid by
each ant that uses edge (i,j)

RESULTS AND DISCUSION In this section the result of the
implemented ACO (ant colony optimization) tuned PI Controller was
obtained. The ACO designed PI controller is initialized with 10
Ants and 100 iterations then response is analyzed. From the ACOPI
controller Reponses it is compared with GA designed PI and ZN tuned
PI controller. The various cost functions are plotted belowin the
given figure with different tabulations.

Initialization of ParametersTo start up with GA, certain
parameters need to be defined. Initializing value of the parameters
for this project for is as follows: Population size80Bit length of
considered chromosome6 Number of Generations100Selection Method
Roulette wheel selectionCrossover typeSingle point
crossoverCrossover probability0.8Mutation typeUniform
mutationMutation probability 0.05

Comparison of Performance index and time domain
specification
KpKi%MpTptstrIAEISEMSEITAEZN0.73330.001842.93761320106315.71195.950.03929.22x104
ACOITAE0.44790.0008782.825041030209261.27196.240.03925.54x104ACOIAE0.58250.001116.1412930143258.72181.850.03646.64x104ACOISE0.61620.001118.4398915135264.40180.380.03619.22x104
GAITAE0.52350.001216.1448849157256.64187.370.03754.72x104GAIAE0.68860.001328.0370989108276.57181.560.03637.03x104GAISE0.66690.001736.3393114011295.01191.110.03827.56x104
ZN0.73330.001842.93761320106315.71195.950.03929.22x104ACOITAE0.44790.0008782.825041030209261.27196.240.03925.54x104GAITAE0.52350.001216.1448849157256.64187.370.03754.72x104

Step response for the closed loop system for the PI controller
tuned with different methodsStep response for the closed loop
system for the ACO PI controller tuned with different cost
function

Step response for the closed loop system for the GA PI
controller tuned with different cost function

Initial distribution of Kp, Ki for AC

Kp, Ki settled for ACO

Kp, Ki settled for GA

ACO ITAE setteled

Comparison of Performance index and time domain
specification
KpKi%MptptstrIAEISEMSEITAEZN1.38460.003269.84251920105465.61279.930.05602.0565x105
ACOITAE0.96780.002038.4516940153371.14234.600.04691.1809x105ACOIAE1.09780.001837.74611450130346.04220.200.04401.1059x105ACOISE1.13240.001940.54621430133349.93222.390.04451.1900x105
GAITAE1.15280.002552.34641440120388.66246.060.04921.3028x105GAIAE1.18690.003365.14701750122454.97280.660.05611.8600x105GAISE1.24880.002960.84461400128420.10260.000.05211.5838x105
ZN1.38460.003269.84251920105465.61279.930.05602.0565x105ACOITAE0.96780.002038.4516940153371.14234.600.04691.1809x105GAITAE1.15280.002552.34641440120388.66246.060.04921.3028x105

Step response for the closed loop system for the PI controller
tuned with different

Step response for the closed loop system for the ACO PI
controller tuned with different cost function

Step response for the closed loop system for the GA PI
controller tuned with different cost function

Initial distribution of Kp, Ki for AC

Kp, Ki settled for ACO

Kp, Ki settled for GA

ACO ITAE settled

zKpKi%MptptstrIAEISEMSEITAEZN2.29000.004663.74862140124499.58300.230.06002.3669x105
ACOITAE1.48520.002019.06161230210374.53245.520.04911.3270x105ACOIAE1.69020.002528.85621590176375.28245.190.04901.2660x105ACOISE1.83000.003045.45101600158389.48251.790.05031.3200x105
GAITAE1.85860.002430.25251530160361.09238.410.04701.1800x105GAIAE1.90720.003443.85281610150408.08261.230.05221.4300x105GAISE2.02370.003437.55361560140408.28258.890.05181.4750x105
ZN2.29000.004663.74862140124499.58300.230.06002.3669x105ACOITAE1.48520.002019.06161230210374.53245.520.04911.3270x105GAITAE1.85860.002430.25251530160361.09238.410.04701.1800x105

Step response for the closed loop system for the PI controller
tuned with different methods

Step response for the closed loop system for the ACO PI
controller tuned with different cost function

Step response for the closed loop system for the GA PI
controller tuned with different cost function

Initial distribution of Kp, Ki for AC

Kp, Ki settled for ACO

Kp, Ki settled for GA

ACO ITAE settled

Robustness of the controller is defined as its ability to
tolerate a certain amount of change in the process parameters
without causing the feedback system to go unstableIn order to
investigate the robustness of the proposed method in the model
parameters were altered. henceGain constant K,Time const T,Delay
time TdAre deviated by 15% of its nominal values. Therefore k is
incremented by 15% T is incremented by 15% Td is reduced by 15%
of

ACTUAL MODELSALTERED MODELS

ALTERED MODELSCase (i)Gain, K value is incremented by 15%.The
value of is incremented by 15%.The value of td is decremented by
15%. Case (ii) Gain, K value is incremented by 10%.The value of is
incremented by 10%.The value of td is decremented by 10%.

Case (iii)Gain, K value is incremented by 25%.and , td values no
changes.Case (iv)Time constant is incremented by 25%.and k, td
values no changes.Case (v)Time delay td is incremented by 25%.and
k, values no changes.

Robustness check with various cost functions for various
model
CASE 1 Model 1 Model 2 Model 3 Kp Ki %Mp tp Ts tr Kp Ki %Mp tp
Ts tr Kp Ki %Mp tp Ts tr ZN 0.7333 0.0018 33.5 347 1000 105 1.3846
0.0032 53.8 390 1230 105 2.29 0.0046 49.6 448 1390 123 ACO 0.4479
0.00087 1.96 484 380 201 0.9678 0.0020 30.8 504 1225 157 1.4852
0.0020 28.6 618 1310 195 GA 0.5235 0.0012 11.7 439 729 162 1.1528
0.0025 39.5 437 1230 128 1.8586 0.0024 33.9 509 1350 155

CASE 2 Model 1 Model 2 Model 3 Kp Ki %Mp tp Ts tr Kp Ki %Mp tp
Ts tr Kp Ki %Mp tp Ts tr ZN 0.7333 0.0018 36.9 356 1040 105 1.3846
0.0032 59.4 402 1260 105 2.29 0.0046 52.9 464 1440 125 ACO 0.4479
0.00087 2.16 520 552 215 0.9678 0.0020 32.9 506 1140 155 1.4852
0.0020 30 628 1290 197 GA 0.5235 0.0012 13.4 433 668 157 1.1528
0.0025 43.8 545 1330 127 1.8586 0.0024 36.2 524 950 157

CASE 3 Model 1 Model 2 Model 3 Kp Ki %Mp tp Ts tr Kp Ki %Mp tp
Ts tr Kp Ki %Mp tp Ts tr ZN 0.7333 0.0018 65.7 348 2050 84 1.3846
0.0032 93.9 391 3560 85.7 2.29 0.0046 85.2 450 3400 102 ACO 0.4479
0.00087 14.7 423 935 150 0.9678 0.0020 53.2 451 1410 121 1.4852
0.0020 46.8 546 1650 153 GA 0.5235 0.0012 30.8 393 1100 120 1.1528
0.0025 70.7 416 1900 102 1.8586 0.0024 60.4 485 1800 125

CASE 4 Model 1 Model 2 Model 3 Kp Ki %Mp tp Ts tr Kp Ki %Mp tp
Ts tr Kp Ki %Mp tp Ts tr ZN 0.7333 0.0018 36.7 401 1170 118 1.3846
0.0032 55.6 478 1500 128 2.29 0.0046 49.3 554 1680 153 ACO 0.4479
0.00087 2.42 587 667 244 0.9678 0.0020 33.1 624 1290 192 1.4852
0.0020 31.4 773 1050 242 GA 0.5235 0.0012 13.4 499 809 181 1.1528
0.0025 42 539 1110 156 1.8586 0.0024 34.8 638 1240 194

CASE 5 Model 1 Model 2 Model 3 Kp Ki %Mp tp Ts tr Kp Ki %Mp tp
Ts tr Kp Ki %Mp tp Ts tr ZN 0.7333 0.0018 20.5 326 648 109 1.3846
0.0032 40.8 370 1140 107 2.29 0.0046 35.2 428 1270 129 ACO 0.4479
0.00087 0 0 985 272 0.9678 0.0020 22.2 508 1310 166 1.4852 0.0020
20.4 641 1440 213 GA 0.5235 0.0012 3.19 450 550 182 1.1528 0.0025
29.3 424 1170 133 1.8586 0.0024 22.9 505 1034 186

Robustness Investigation for model 1(Case1)

Robustness Investigation for model 2(Case1)

Robustness Investigation for model 3(Case1)

The following results shows different PItuned methods are
implemented from real time process for above said models.
Comparison of Performance index and time domain
specification
%MptsISEZN0.23.58.5274 x108GA0.1635.3635x 106ACO0.122.57.3456x
105

Step response for the closed loop system for the PI controller
tuned with deferent methods

In order to test the PI tuning with ant algorithm in the
presence of noise, ACO ITAE is usedThe above system is tested for
three different variances 2=0.0025 2=0.025, 2=0.25Ant algorithm was
run 5 times with 10 ants and 100 iterations due to the
probabilistic nature of AA and noise.
White noise for variance0.0025

White noise for variance0.025White noise for
variance0.00025

In phase 2 of this project work, the conventional PI controller
was tuned by ZN tuning method and compared with proposed GA and
ACO methods.
Then it is implemented to the first order with dead time
process. Then simulation studies are carried out to analyze the
performance of the spherical tank process and Robustness of above
mentioned controller for the different set points.
It is also implemented in real time for the real time results of
GA, ACO, ZN same set points. The result of both simulation and real
time process were compared.
From the output response obtained using ACO tuned PI controller
gives less over shoot, fastest settling time, fastest rise time
then the other techniques.
Time domain specification and performance indices were tabulated
for the above said models.

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Thank you
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