International Journal of Computer Applications (0975 – 8887)

Volume 3 – No.8, June 2010

Real Time Application of Ants Colony Optimization

Dr.S.M.GiriRajkumar Dr.K.Ramkumar Sanjay Sarma O.V

Senior Assistant Professor Senior Assistant Professor Department of Mechatronics
School of Electrical & Electronics School of Electrical & Electronics School of Mechanical Engineering
Engineering Engineering SASTRA University, Thanjavur
SASTRA University, Thanjavur SASTRA University, Thanjavur Tamilnadu-613402
Tamilnadu-613402 Tamilnadu-613402

ABSTRACT function properly, the PID loop must be properly tuned. Standard
Automatic control has played a vital role in the advancement of methods for tuning include Ziegler-Nichols Ultimate-cycle tuning
engineering and science. It is also essential in such industrial [5], Astrom and Hagglund [6], Cohen-Coon‟s method [7], and
operations as controlling pressure, temperature, humidity, many other traditional techniques. Although new methods are
viscosity and flow in the process industries. Proportional Integral proposed for tuning the PID controller, their usage is limited due
Differential (PID) controllers marked its place in many of the to the complexities arising at the time of implementation and their
industrial processes. Tuning a controller is the adjustment of its incompetence towards nonlinear systems.
control parameters. Computational Intelligence (CI) an off shoot However, despite decades of development work,
of Artificial Intelligence relies on heuristic algorithms mainly surveys indicating the state of the art of control industrial practice
evolutionary computation. Swarm intelligence (SI) a derivative of report sobering results. For example, Ender (1993) states that, in
CI, describes the collective behaviour of decentralized, self- his testing of thousands of control loops in hundreds of plants, it
organized systems. Ant behaviour was the inspiration for the Meta has been found that more than 30% of installed controllers are
heuristic optimization technique. This paper presents an operating in manual mode and 65% of loops operating in
application of an Ant Colony Optimization (ACO) algorithm to automatic mode poorly tuned. The Handbook of PI and PID
optimize the parameters in the design of a (PID) controller for a controller Tuning Rules by Aidan O.Dwyer has recorded 408
highly nonlinear conical tank system. The proposed work separate sources of tuning rules since the first such rule which was
discusses in detail, the ACO, a CI technique, and its application published by Callender et al. in 1935. In a striking statistic, 293
over the parameter tuning of a PI controller in a real time process. sources of tuning rules have been recorded since 1992 reflecting
The designed controller‟s ability in tracking a given set point is the upsurge of interest in the use of the PID controller recently.
compared with an Internal Model Control (IMC) tuned controller. Although these many tuning rules are available in literature, most
of the rules are applicable only for a first order system with a time
Keywords: PID controllers, Computational Intelligence, Ants delay. So clearly they are not meant to be applied for higher order
Colony Optimization, Internal Modal Control, Meta heuristic
nonlinear systems. In order to apply them we may go for
optimization.
approximating the system to a FOPTD (first order with time
1. INTRODUCTION delay).This can primarily be done either using Taylor‟s
The widely used PID industrial controller uses a combination of approximation or Skogestad‟s approximation. But the word
proportional, integral and derivative action on the control error to approximation itself suggests that the parameters obtained using
regulate its output. Owing to its simple structure, easy tuning and the application of these traditional tuning rules on the
effectiveness, this technology has been a mainstay for long among approximated system will also be a very big compromise. The
practicing engineers [1]. PID control is a generic feedback control intensity of compromise depends on the magnitude of degree
technology and it makes up 90% of automatic controllers in diminution. This approximation could itself fail if the higher order
industrial control systems. The PID control was first placed in the system has a complex time constant where it will be a tedious
market in 1939 and has remained the most widely used controller process and sometimes impossible.Certain methods are available
in process control until today. The basic function of the controller in applying over specific systems. And hence reduces the
is to execute an algorithm based on the control engineer‟s input acceptance of the method.
and hence to maintain the output at or around the set point [2]. Tuning a PID controller means setting the proportional, integral
The popularity of PID controllers is due to their functional and derivative constant to get the best possible control for a
simplicity, reliability and cost effectiveness. They provide robust particular process. Adjusting the controller gains, to satisfy the
and reliable performance for most systems and the PID parameters performance specifications like margin of stability, transient
i.e. the proportional, integral and differential constants are tuned response and bandwidth, improves the system robustness. The
to ensure a satisfactory closed loop performance [3]. A PID performance of the tuned controller can be represented as a
controller improves the transient response of a system by reducing function of error for quantitative analysis. The commonly
the overshoot, and by shortening the settling time of a system [4]. employed performance indices are Integral Absolute Error,
The PID control algorithm is used to control almost all loops in Integral Squared Error, Integral of time multiplied by absolute
process industries and is also the cornerstone for many advance value of error and Integral of time multiplied by squared error.
control algorithms and strategies [2]. For this control loop to
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Control design is called “optimal control” when a predefined 2. DEVELOPMENT OF MATHEMATICAL

criterion is optimized .Optimality is just with respect to the
MODEL FOR THE REAL TIME PROCESS.
criterion at hand and the real performance depends on the
suitability of the chosen criterion. The Ant Colony Optimization Feedback control systems are often referred to as closed-loop
(ACO) algorithm is a meta-heuristic algorithm for the control systems. In a closed-loop control system the actuating
approximate solution of combinatorial optimization problems that error signal, which is the difference between the input signal and
has been inspired by the foraging behavior of real ant colonies [9- the feedback signal, is fed to the controller so as to reduce the
11]. In this algorithm, computational resources are allocated to a error and bring the output of the system to a desired value.
set of relatively simple agents that exploit a form of indirect The conical tank system, which exhibits the property of non-
communication mediated by the environment to find the shortest linearity, is taken for the real time analysis of the designed
path from the ant nest to a set target. Ants can follow through to a controllers. The process dynamics are analysed in four segments
food source because, while walking, they deposit pheromone on so as to obtain effective models for the operating ranges. The
the ground, and they have a probabilistic preference for paths with operating ranges are concluded for 0-15cm as model-1, 15-27cm
larger amount of pheromone [12-13]. as model-2, 27-36cm as model-3 and 36-43 cm as model-4. And
The model of the process under study is very important the corresponding mathematical models are obtained for these
for its tuning as the accuracy of the tuned controller parameters is sections.
greatly dependent upon the degree of accuracy of the system
model with that of the real system. As per the fundamentals, it is 2.1. Experimental Setup
possible to approximate the actual input-output mathematical The real time experimental system consisting of a conical tank,
model of a very-high order, complex, dynamic process with a reservoir and water pump, current to pressure converter,
simple model consisting of a first or second order process compressor, Differential Pressure Transmitter(DPT), ADAM
combined with a dead-time element. Thus, a common practice module, and a Personal Computer which acts as a controller forms
followed in industries for the purpose of control design and a closed loop system. The inflow rate to the conical tank is
process analysis is to model the dynamics of the process near the regulated by changing the stem position of the pneumatic valve by
operating point by simpler models such as first order process with passing control signal from computer to the I/P converter through
time delay (FOPTD). digital to analog converter (DAC) of ADAM module. The
Analysis of the proposed controller design gives a operation current for regulating the valve position is 4-20 mA,
satisfactory performance over a wide range of process operations. which is converted to 3-15 psi of compressed air pressure. The
Control design is called “optimal control” when a predefined water level inside the tank is measured with the differential
criterion is optimized .Optimality is just with respect to the pressure transmitter which is calibrated for 0-43 cm and is
criterion at hand and the real performance depends on the converted to an output current range of 4-20 mA. This output
suitability of the chosen criterion. Using ACO approach, global current from DPT is passed through 1K ohms resistance
and local solutions could be simultaneously found for the better converting it to 1-5V range, which is given to the controller
tuning of the controller parameters. The controller designed is through analog to digital converter (ADC) of ADAM module.
independent of the mathematical model of networks, thus getting The ADAM module is used for interfacing the personal
rid of adverse effects. Hence, in industries, the difficulties to computer with the conical tank system thus forming a closed loop.
achieve an optimal PID gain without prior expert knowledge can It has four slots for four converter cards. In the current process,
be overcome. two slots are used, one containing Analog to Digital Converter
The proposed work‟s objective is to use Ants Colony (ADC) card and the other containing the Digital to Analog
Optimisation in order to obtain optimal values for control Converter (DAC) card. The ADC card has 8 analog input
parameters, Kp and Ki of a PI controller for a conical tank channels with a range of 4-20 mA and DAC has 4 analog output
process, which is highly non-linear. The problem of non-linearity channels with a range of -10V to +10V accommodating both
is overcome by linearizing over four suitable ranges. Hence four positive and negative terminals. The sampling rate of the module
sets of PI parameters are proposed in this paper. Each of the is 10 samples/sec and the baud rate is set to 9,600 bytes per sec
parameters proportionality constant Kp and integral constant Ki with a 16 bit resolution. The ADAM module is connected to the
represents a particle which changes in the search space in order to personal computer through RS-232, serial cable. The module can
minimize the error function (objective function in this case). The be operated manually through console software provided and also
error function used here is Integral Time of Absolute Errors with programming software like LABVIEW, MATLAB etc., Here
(IAE). The proposed work deals with the development of the MATLAB based script files are used in interfacing the controller
mathematical model for the non-linear conical tank process. The with the real time system.
tuning results of conventional techniques are discussed in section
3. Sections 4 deal with the explanation of the ACO algorithm and MATLAB software gives us the flexibility of interfacing
its implementation. The comparative studies and results are given the ADAM module with the personal computer. The system is
in section 5. prepared to access the module through m-files. The controller
equation which is discussed further in this paper is accessed
through this programmed frame work.
The piping and instrument diagram of the system is shown in
Figure 1. The system specifications are shown in the Table 1. The
ADAM interfacing module, control valve, differential pressure

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transmitter are shown in the Figure 2.The real time system

developed is shown in the Figure 3.

Table 1: System specifications

PART NAME DETAILS

Conical tank Stainless steel body, height – 45 cm,

Top Diameter – 33.74cm, Bottom Diameter-0.8 cm, α=34.40.
Differential Pressure Transmitter Capacitance type, Range 2.5-250 mbar,
Output 4-20 mA Figure 2: Images of ADAM module, Control valve,
Differential Pressure Transmitter.
Pump Centrifugal 0.5 HP
Control Valve Size ¼” Pneumatic actuated,
Type: Air to open, Input 3-15 psi
Rotameter Range 0-18 lpm
Air regulator Size 1/4” BSP, Range 0-2.2 bar
I/P converter Input 4-20 mA, Output 0.2-1 bar
Pressure gauge Range 0-30 psi
Compressor 20 psi

Figure 3: Photograph of experimental setup.

2.2 Process Modeling:
System identification is normally done by applying step
response methods. In application of these methods, response of
the conical tank for a given flow is required. Through this
response, suitable model and model parameters are estimated.
model selection is based upon the open loop step response of the
system, for which the inflow valve is set to different positions by
manual operation through ADAM console software. Owing to the
non-linearity in the shape of the conical tank, a single range
response cannot cover the entire range.
So, various trials were conducted for different flow
ranges and valve openings to obtain a typical response curve.
Four responses covering the full height of the conical tank were
obtained for 0-15cm as model-1, 15-27cm as model-2, 27-36cm
as model-3 and 36-43 cm as model-4.
Figure 1: Piping and instrument diagram of the process system The models were checked with the two point method
and Sunderesan Kumaraswamy [14] method. The models checked
with the two point method were not close to the real time response
where Sundaresan Kumaraswamy method is found to be more
coinciding. So, in this work we follow the Sunderesan
Kumarasamy method, with the models obtained as the response
curves of the open loop response with the time delay inclusion
directly, instead of Pade‟s approximation techniques.
As per the structure of the curves, the model is predicted
to be of the form similar to FOPTD,

Eq(2.1)

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Where K= process gain

=first order time constant

d = delay time
The maximum inflow rate to the tank is maintained at 5.467 lpm.
The comparative response curves between the real time and
simulated model, with reference to the range 0-15 cm .The model
was estimated as

G(s)model 1 Eq(2.2)

For the region 15-27 cm the mathematical model is given below .

G(s)model 2 Eq(2.3)
Figure 5: Comparison of real time and simulated responses of
model 2
For the region 27-36 cm the mathematical model and the
validation curves are given below . .

G(s)model 3 Eq(2.4)

For the region 36-43 cm the mathematical model is given below.

G(s)model 4 Eq(2.5)

The validation curves for the four models are given in Figures 4-
7. The so framed model is simulated for a step input for the set
points whose graphs are presented in the figures. The system is
then subjected to a step input for all the four set points and the
corresponding real time graphs are presented comparing with the
simulated graphs.

Figure 6: Comparison of real time and simulated responses of

model 3.

Figure 4: Comparison of real time and simulated responses of

Figure 7: Comparison of real time and simulated responses of
model 1.
model 4.

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3. CONVENTIONAL DESIGN TECHNIQUE

The basic PI controller parameters are proportional
gain, Kp and integral gain Ki. Numerous methods were developed
over last fifty years for setting the parameters of a PID controller.
In this paper, it is considered to proceed the tuning with Internal
Model Control(IMC), a tuning technique proposed by Skogestad
for PI tuning.
The IMC technique is one of the recent traditional
tuning techniques that yield better values among the techniques
available for conventional methods [2]. For a FOPTD model of
the mentioned form in Equation-1, the IMC tuning values based
on Skogestad proposal is given as
Eq(3.1) Figure 8: Path traced by ants without and with obstacle

Where τc=τd as per Skogestad, and integral time constant Ti is Ants Colony algorithm can be applied for the
continuous function optimization problems. Here, the domain has
given as, Ti = , and hence, we have Ki=Kp/Ki. Applying the to be divided into a specific number of R randomly distributed
technique for both the models, we get the IMC tuning parameters regions. These regions are indeed the trial solutions and act as
as in Table 2. local stations for the ants to move and explore. The fitness of
Table 2: Control parameters for PID controller for the four these regions are first evaluated and sorted on the basis of fitness.
models by conventional design technique When an algorithm designed for combinatorial optimization is
used to tackle a continuous problem, the simplest approach would
PARAMETERS Model1 Model 2 Model 3 Model 4
be to divide the domain of each variable into a set of intervals.
Kp 0.0727 0.1453 0.2456 0.3011 However, when the domain of the variables is large and the
required accuracy is high, this approach is not viable. For this
Ki 0.0171 0.0163 0.0201 0.0193 reason, ACO algorithms have been developed, which are
specifically designed for continuous and mixed continuous-
discrete variable [19-20] Totally a population of ants explores
these regions; the updating of the regions is done locally and
4. ANTS COLONY ALGORITHM globally with the local search and global search mechanism
respectively. The distribution of local and global ants is illustrated
The Ant System is a new kind of co-operative search
in Figure 9 and the flowchart of the Ants Colony algorithm is
algorithm inspired by the behavior of colonies of real ants. The
presented in Figure 10.
ants colony algorithm was applied to travelling salesman problem
[15-17] The blind ants are able to find astonishing good solutions
to shortest path problems between food sources and their home 4.2 Global Search
colony. The medium used to communicate information among The global search creates G new regions by replacing
individuals regarding paths, and decide where to go, was the the weaker portions of the existing domain. In the ACO random
pheromone trails. A moving ant lays some pheromone on the path walk and trial diffusion are utilized for global search. By random
they move, thus marking the path by the substance. While an walk procedure, the ants move in new directions in search of
isolated ant moves essentially at random, it can encounter a newer and richer stocks of food source. In the ACO simulation
previously laid trail and decide with high probability to follow it, such a global search in the entire domain is done by process
and also reinforcing the trail with its own pheromone. The equivalent to crossover operation and mutation operations in G.A.
collective behavior that emerges in a form of autocatalytic Adding or subtracting with a probability proportional to the
behavior where the more the ants following a trail, the more mutation probability carries out the mutation step in ACO. The
attractive that trail becomes for being followed. mutation step is reduced as per the relation.
4.1 The Path of Ants
There is a path along which ants are walking from nest Where „r‟ is a random number from [0, 1] „R‟ is the maximum
to the food source and vice versa. In the forties and fifties of the step size. „T‟ is the ratio of the current iteration number to that of
twentieth century, the French entomologist Pierre-Paul Grass´e the total number of iterations; „b‟ is a positive parameter
[18] observed that some species of termites react to what he called controlling the degree of nonlinearity.
“significant stimuli”. If a sudden obstacle appears and the path is
cut off, the choice is influenced by the intensity of the The mutation radius is nonlinearly reduced with increasing
pheromone trails left by proceeding ants. On the shorter path iterations. The scaling down enables enhanced probability of
more pheromone is laid down. The Figure 8 details the behavior locating maximum by concentrated search procedure called trial
of ants when faced with an obstacle in its search path. diffusion. The trial diffusion is quite similar to arithmetic cross
over. In this step two parents are selected at random from the
parent population space. The elements of the child‟s vector can
have either (1) The corresponding element from the first parent,

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Volume 3 – No.8, June 2010

(2) The corresponding element from the second parent and (3) A parameter in the ACO algorithm. The size of the ant movement in
combination arrived from a weighted average of the above. i.e. If the local search depends on the current age.
the random number is less than 0.5 •Initially all the regions are assigned with the pheromone value of
1.0
X ( child ) Xi parent1 1 Xi parent 2
•It better results are obtained the pheromone of region i is
where α is a uniform random number in the range (0 –1). modified by

If the random number is in between 0.5 and 0.75 then:

•Now again the average pheromone for each region is calculated

And if the random number is in between 0.75 and 1.00 then
and the procedure is repeated as many number of times as they are
local ants.
•The termination criterion is the total number of iterations.
4.3 Local Search
4.4 IMPLEMENTATION OF ACO
In the local search, the ants have the capability of selecting
regions proportional to the current pheromone values of superior The parameters Kp and Ki of a PID controller are optimised using
and inferior regions. Local updating is applied only on superior ACO.
regions. In an ACO, local ants select a region „i‟ given by
4.4.1 Selection of ACO parameters
To start up with ACO, certain parameters need to be defined.
Selection of these parameters decides, to a great extent, the ability
of global minimization. The population size balances the
where „i‟ is the region index and τi is the pheromone trail on requirement of global optimization and computational cost.
region i at time t. After selecting the destination, the ant moves Initialising the values of the parameters is as per Table 3.
through a short distance. The direction of the movement will be
the same as that of the previous direction if there is an
improvement in the fitness. It there is no improvement it searches
in a random direction. If improvement in fitness is found in the
above procedure, the regions position vector is updated.

Figure 9: Distribution of Ants for Local and Global search

The Pheromone deposited by the ant is proportional to the

increase in fitness. The age of the region is another important
Figure 10: Flowchart of Ants Colony Optimization algorithm

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Table 3: Initial values of the parameters

Parameter Specification

Learning constant,c1 2

Learning constant,c2 2

4.4.2 Performance Index of ACO Algorithm

The objective function considered is based on the error criterion.
The performance of a controller is best evaluated in terms of error
criterion. A number of such criteria are available and, in the
Figure 13: Kp distribution for model2
proposed work, the controller‟s performance is evaluated in terms
of an Integral of Absolute Errors (IAE) criterion, given by

IIAE =
The IAE weights the error with time and hence emphasizes the
error values over a range of 0 to T, where T is the expected
settling time.
4.4.3 Termination Criteria
Genetic Algorithm termination can take place either
when the maximum numbers of iterations are performed, or when
a satisfactory fitness value is attained. The fitness value is the
reciprocal of the error, since we consider for a minimization of Figure 14: Ki distribution for model2
objective function. In this work, the termination criterion is
considered to be the maximum number of iterations. The
distribution of the values for the first iteration for Kp and Ki are
given below for all the models as shown in Figures 11 - 18. It is
clearly seen that the values are well distributed.

Figure 15: Kp distribution for model3

Figure 11: Kp distribution for model1

Figure 16: Ki distribution for model3

Figure 12: Ki distribution for model 1

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Figure 17: Kp distribution for model4

Figure 20: Best solutions of Ki to model 1 for 100 iterations

Figure 18: Ki distribution for model4

For each iteration, the best among the 100 particles considered as
potential solution are chosen. Therefore the best values for 100 Figure 21: Best solutions of Kp to model 2 for 100 iterations
iterations are sketched with respect to iterations for Kp and Ki and
are shown in Figures 19-26 for all the four models.

Figure 19: Best solutions of Kp to model 1 for 100 iterations

Figure 22: Best solutions of Ki to model 2 for 100 iterations

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The PI controller was formed based upon the respective

parameters for 100 iterations, and the gbest (global best) solution
was selected for the set of parameters which had minimum error.
A sketch of the error based on IAE criterion for 100 iterations is
given in Figures 27 - 30. It is seen that the error value tends to
decrease for a larger number of iterations. As such, the algorithm
was restricted to 100 iterations beyond which there was only a
negligible improvement. Based on the ACO algorithm for the
application of the PI tuning, we get the PI tuning parameters for
the model is given in the Table 4.

Figure 23: Best solutions of Kp to model 3 for 100 iterations

Figure 27: IAE values for 100 iterations of model 1

Figure 24: Best solutions of Ki to model 3 for 100 iterations

Figure 28: IAE values for 100 iterations of model 2

Figure 25: Best solutions of Kp to model 4 for 100 iterations

Figure 29: IAE values for 100 iterations of model 3

Figure 26: Best solutions of Ki to model 4 for 100 iterations

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Table 7: Comparison of performance index for Model 3

METHOD IMC ACO

IAE 249.8921 216.21
ISE 221.2638 200.1470
MSE 0.1158 0.1008
ITAE 6237.9 3905.3

Table 8: Comparison of performance index for Model 4

Figure 30: IAE values for 100 iterations of model 4

METHOD IMC ACO

Table 4: Control parameters for PI controller for the four IAE 305.2351 270.119
models got from global best by ACO technique ISE 290.908 268.5775
PARAMETERS Model1 Model 2 Model 3 Model 4 MSE 0.0969 0.0895
Kp 0.21805 0.31813 0.4797 0.5502 ITAE 9469.1 6135.9
Ki 0.02606 0.02278 0.0264 0.0252

5.1 REAL TIME RESPONSE OF THE

5. RESULTS AND COMPARISION
EXPERIMENTAL SETUP FOR SET POINT
After the tuning process is done through traditional CONDITIONS
methods and proposed techniques, analysis was done for their The parameters designed for the experimental setup were
responses to a unit step input, with the help of real time implemented for 4 set points. The real time response of the system
application for the conical tank. The performance index was observed by giving set points of 12cm, 22cm and a servo
comparison for the obtained models with the designed controllers process including the points 32cm and 39 cm. The corresponding
variation of level from a reference value of zero was recorded.
is presented in Tables 5-8 for all the four models.
The outflow valve of the tank was kept partially open and the
position was maintained same for the various trails of controller
Table 5:Comparison of performance index for Model 1 settings. The responses of the conical tank for all the set points
with various controller settings are presented in the figures 31-33.
METHOD IMC ACO
IAE 192.3461 145.47
ISE 156.8276 134.07
MSE 0.0786 0.0671
ITAE 2638.9 1258.4

Table 6: Comparison of performance index for Model 2

METHOD IMC ACO

IAE 235.8107 201.8154
ISE 208.3621 184.86
MSE 0.0694 0.0616
ITAE 4251.3 2885.4
Figure 31: Real time response for a set point of 12 cm.

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G1(s)model 1 Eq(5.1)

Modified model 2 for segment 15-27 cm as

G1(s)model 2 Eq(5.2)

Modified model 3 for segment 27-36 cm as

G1(s)model 3 Eq(5.3)

Modified model 4 for segment 36-43 cm as

G1(s)model 4 Eq(5.4)

Figure 32: Real time response for a set point of 22 cm. Table 9: Comparison of performance index for 15% change in
Model 1

METHOD IMC ACO

IAE 192.3461 130.984
ISE 156.8276 260.64
MSE 0.0786 0.0587
ITAE 2638.9 1095.9

Table 10: Comparison of performance index for 15% change

in Model 2

METHOD IMC ACO

IAE 235.8107 180.77
ISE 208.3621 162.07
MSE 0.0694 2423.4
Figure 33: Real time servo response for ACO and IMC
ITAE 4251.3 1095.9
5.2 Robustness Investigation
The PI controllers tuned by the GA based method is compared
with the performance index from the four major error criterion Table 11: Comparison of performance index for 15% change
techniques of Integral Time of Absolute Error (ITAE), Integral of in Model 3
Absolute Error (IAE), Integral Square of Error (ISE), and Mean
Square Error (MSE). Robustness of the controller is defined as its METHOD IMC ACO
ability to tolerate a certain amount of change in the process IAE 249.8921 197.24
parameters without causing the feedback system to go unstable. In
ISE 221.2638 179.14
order to investigate the robustness of the proposed method in the
face of model uncertainties, the model parameters were altered. MSE 0.1158 0.0908
Here the values of gain constant K, time constant, and delay ITAE 6237.9 3467.2
time are deviated by as much as ±15% of nominal values, In
the proposed models for the experimental setup, the value of K is
incremented by 15% , the value of is incremented by 15% and
that of d is reduced by 15%. Thus, we have the models with the
proposed uncertainties as, modified model 1 for segment from 0-
15 cm as

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Table 12: Comparison of performance index for 15% change system for a plant of a first-order system with a time delay and
in Model 4 deriving the possible results.

METHOD IMC ACO

IAE 305.2351 252.0237 REFERENCES
ISE 290.908 237.0833
[1] Novel Approach to Nonlinear PID Parameter Optimization
MSE 0.0969 0.0790 Using Ant Colony Optimization Algorithm , Duan Hai-bin',
ITAE 9469.1 5153.1 Wang Dao-bo2, Yu Xiu-fen3, Journal of Bionic Engineering
3 (2006) 073-078
[2] M Araki: Control systems, Robotics and Automation-Vol II –
PID Control –,Kyoto University ,Japan

Table 13: Comparison of time domain specifications for 12cm [3] Kim Dong Hwa and Park Jin Ill: Intelligent PID Controller
Tuning of AVR system using GA and PSO: Springer-Verlag
Berlin Heidelberg: ICIC 2005, Part II, LNCS 3645, pp 366-
Height IMC ACO 375.(2005).
Over shoot 1.81 1.81 [4] Ziegler, G. and Nichols, N. B, 1942.Optimum settings for
Raise Time 41.3339 37.2207 automatic controllers, Trans. ASME, 64,759-768.
Delay Time 9 7 [5] K.J.Astrom, T.Hagglund, The future of PIDcontrol, Control
Eng.Pract.9(11)(2001)1163–1175.

Table 14: Comparison of time domain specifications for 22cm [6] Astrom, K J.;. Hagglund .T,1984, Automatic tuning of simple
regulators with specifications on phase and amplitude
margins, Automatica, 20,645-651.
Height IMC ACO
[7] G.H Cohen and G.A Coon: Theoretical Consideration of
Over shoot 3.91 2.91 Retarded Control , Trans ASME 75,pp.827/834,(1953)
Raise Time 18.4013 15.9150 [8] Haber , Rodolf., Toro1, Raúl M. and. Alique, José R, ‟ Using
Delay Time 9 7 Simulated Annealing for Optimal Tuning of a PID Controller
for Time-Delay Systems. An Application to a High-
Performance Drilling Process‟, Springer.
6. CONCLUSION [9] Colorni A. Dorigo M, Maniezzo V. Distributed optimization
The developed controller tuning for various set points can be by ant colonics. Proceedings of the First European
suitably tracked by providing a program which can allow the Conference on Artjficial Life.Elsevier Publishing, paris.
system to choose that value based on the set point selected. The 1992, 134-142.
ACO tuning for model 1 will be used for set points between 0-15 [10] Bonabeau E. Dorig M, Theraulaz G. Inspiration for
cm, model 2 for set points between 15-27 cm, model 3 for set optimization from social insect behavior. Nature, 2000, 406.
points between 27-36 cm and model 4 for set points between 36
and 43 cm. The servo response of the system shows its stability [11] Katja V, Ann N. Colonies of learning automata. IEEE
over continuous change in set points at regular intervals. Transactions on Systems, Man, and Cybernetics-Part B,
2002,32,772-780.
The various results presented prove the betterness of the
ACO tuned PI settings than the IMC tuned ones. The simulation [12] Dorigo M, Gambardella L M. Ant colony system: A
responses for the models validated reflect the effectiveness of the cooperative learning approach to the traveling salesman
GA based controller in terms of performance index. The problem. IEEE Transactions on Evolutionary
performance index under the various error criteria for the Computation,1997,1,53-66.
proposed controller is always less than the IMC tuned controller.
Above all, the real time responses confirm the validity of the [13] James M, Marcus R. Anti-pheromone as a tool for better
proposed ACO based tuning for the conical tank. exploration of search space. Proceedings of the 3rd
International Workshop ANTS, Brussels, 2002, 100-1 10.
ACO presents multiple advantages to a designer by
operating with a reduced number of design methods to establish [14] Sundaresan, K. R., Krishnaswamy, R. R., Estimation of time
the type of the controller, giving a possibility of configuring the delay, time constant parameters in Time, Frequency and
dynamic behaviour of the control system with ease, starting the Laplace Domains, Journal of Chemical Engineering., 56,
design with a reduced amount of information about the controller 1978, p. 257.
(type and allowable range of the parameters), but keeping sight of [15] Dorigo M, Maniezzo V, Colomi A. Ant system: Optimization
the behaviour of the control system. These features are illustrated by a colony of cooperating agents. IEEE Transactionson
in this work by considering the problem of designing a control Systems, Man, and Cybernetics-Part B, 1996,26,29-41

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 International Journal of Computer Applications (0975 – 8887)
Volume 3 – No.8, June 2010

[16] Duan H B, Wang D B. A novel improved ant colony [19] K. Socha, “ACO for continuous and mixed-variable
algorithm with fast global optimization and its optimization,” in Ant Colony Optimization and Swarm
simulation.Information and Control, 2004,33,241-244, (in Intelligence, 4th International Workshop, ANTS 2004, ser.
Chinese). LNCS, M. Dorigo et al., Eds., vol. 3172. Springer Verlag,
2004, pp. 25–36.
[17] Duan H B, Wang D B, Zhu J Q, Huang X H. Development
on ant colony algorithm theory and its application. Control [20] K. Socha and M. Dorigo, “Ant colony optimization for
and Decision, 2004, 19, 1321-1326, 1340, (in Chinese). continuous domains,” European Journal of Operational
Research, 2006,
[18] P. P. Grass´e, Les Insectes Dans Leur Univers. Paris, France:
Ed. Du Palais de la d´ecouverte, 1946.

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