optimization of fuzzy controller parameter by using …ijesta.com/upcomingissue/08.03.2016.pdfvolume...

Volume 02, No. 3, March 2016

Pa

ge5

3

Optimization of Fuzzy Controller Parameter by Using

A Firefly Algorithm

Soumya Chauhan

Department of Electrical Engineering, Deenbandhu Chhotu Ram University of Science and Technology,

Murthal, Sonepat (Haryana) India

ABSTRACT:

Firefly Algorithm (FA) is one of the latest nature-inspired algorithms. Finding the best global

optimal point, speed up the convergence by tuning the FA parameters and the ability of

dealing with multimodality are some merits of FA. In this paper, FA is applied to tune

optimal fuzzy parameters for FLC which are used in plant for liquid level and temperature

control. MATLAB/ Simulink program has been used to achieve the optimal parameters of the

membership functions. The results show clearly that the optimized FLC using FA has better

performance compared to manually adjustments of the system parameters for different

datasets.

KEYWORDS: Firefly algorithm, Fuzzy logic controller, Particle swarm optimization,

1. INTRODUCTION

FLC is a popular technique that has been increasing interest in the past decades since it has a

linguistic based structure and its performance is quite robust for nonlinear system, complex

systems or system whose mathematical model is not known. However, FLC including some

parameters such as linguistic control rules and limits and type of membership functions has

to be tuned for a given system. A major drawback of FLC is that the tuning process becomes

more difficult and very time consuming when the number of the system inputs and outputs

is increased. Evolutionary algorithms regarding tuning the membership function parameters

of FLC have been studied extensively in the literature. These studies can be divided into

three groups as genetic algorithm [5], PSO [3,13], and cuckoo algorithm [20, 21]. In many

industrial processes, control of liquid level is required. Several researchers have investigated

the problem of controlling liquid flow [22–28]. A constrained predictive control algorithm

based on feedback linearization applied to a coupled tank apparatus is given in [29]. In [30],

several sliding mode control schemes for the coupled tanks system and liquid level control

are proposed. Fuzzy logic is as a powerful problem-solving methodology with a great

number of applications in level control. Intelligent control including fuzzy control [31–36],

neural network control [37], and genetic algorithms [5] has also been applied to liquid level

system. Water level control is highly important in industrial applications such as boilers in

nuclear power plants. In many industrial processes, control of liquid level and temperature

control is required for e.g., in water purification systems; boilers; industrial chemical

processing and automatic liquid dispensing .The typical actuators used in liquid level control

and temperature control systems include pumps, stepper motor, on-off valves, etc.

stabilizing the water level of a plant around a predetermined level is an important problem

since dynamics of coupled system some amount of delay which can be increased by delay.

The right choice of an optimization algorithm can be crucially important in finding the right


Pa

ge5

4

solutions for a given optimization problem. There exist a diverse range of algorithms for

optimization.

Firefly Algorithm (FA) is one of the latest nature-inspired algorithms. Finding the best

global optimal point, speed up the convergence by tuning the FA parameters and the ability

of dealing with multimodality are some merits of FA[39]. Fireflies cover the search space by

random and information based steps which present two random search and local search to

the algorithm respectively which conveys exploration and exploitation in firefly algorithm

[33]. But, important point in firefly algorithm is keeping balance between exploration and

exploitation. In standard firefly algorithm, controlling parameters of these two kinds of

searches are initialized at the beginning and these values don‘t change until end of the

searching process and this cannot indicate proper balance between these two kinds of

searches considering different conditions that algorithm will be faced in different steps of

solving problem. Therefore, we have used a fuzzy controller for tuning the parameters

which control balance between random search and local search dynamically in each step of

solving problem (with considering progress of solving problem). This method increases

performance of the firefly algorithm in finding optimal solution by keeping balance between

these two kinds of searches. We have used the proposed method for optimization of fuzzy

controller parameters for a temperature and water level system.

In this paper, fuzzy controller (Mamdani type) to control of liquid level and temperature in

tanks are used. We present optimization of Mamdani-type fuzzy regulator parameters using

FA. MATLAB software is used for designing and simulating. This paper is organized as

follows. In Section2, system model is presented. In Section3, the controller design based on

Mamdani system is given. In Section4, Simulink model is presented. In Section5,FA is

described. Finally, the results, conclusion and future direction are illustrated.

II. GENERAL FORMULATION OF THE SYSTEM MODEL OF LIQUID LEVEL

AND TEMPERATURE

1. System Model for Level

The tank system [1-2] is shown in Fig. 1

Fig. 1: Schematic diagram of coupled tank system

By applying the laws of physics to get a mathematical model of the system to become the

dynamic equation of the system, as in equations (1)&(2).


Pa

ge5

5

= (1)

= - (2)

Where:

F =steady-state liquid flow rate, c /sec.

F = out flow rate from first tank, c /sec.

= out flow rate from second tank, cm3/sec.

And = coefficients, c /sec.

( = level first tank, cm. = level second tank, cm).

=the cross sectional area for first tank, c .

=the cross sectional area for second tank, c

2. SYSTEM MODEL FOR TEMPERATURE [29]

Fig. 2 depicts the circuit configuration for a simple Triac circuit where the primary power

control device is the Triac whose gate firing device is the Diac (Skvarenina, 2002). The Diac

is a fixed break-over voltage device compared to the Triac that permits a variable firing angle

through its gate terminal. Compared to the Silicon Controlled rectifier (SCR) which is also

gate controlled, the Triac permits device firing on the positive and negative half-cycles of the

AC waveform.

Fig 2: Triac circuit

III. DESIGNING OF FUZZY LOGIC CONTROLLER

A. Fuzzy Logic Controller Review [1-2]

The basic fuzzy structure is shown in fig 3. The development of FLC consists following

steps-

a) Specify the range of controlled variable and manipulated variables;

b) Divide these ranges into fuzzy sets and attach linguistic labels which can be used to

describe them;


Pa

ge5

6

c) Determine the rule base to specify control action;

d) Application of suitable defuzzification method.

The number of necessary fuzzy sets and their ranges were designed based upon the

experience gained on the process. The standard fuzzy set consists of three stages:

Fuzzification, Decision- Making Logic and Defuzzification.

Fig 3: Block Diagram of basic structure of fuzzy control system.

The controller in present work is Mamdani based one. It uses a rule based in linguistic terms.

There are two inputs: error in liquid level and rate of change of liquid level and one output

parameter: the inlet valve control angle in level control. Triangular membership functions are

selected to fuzzify the inputs and output variables. The membership functions with five

linguistic values for error (e) and change in error (de) is used and is shown in fig.4, 5.

Fig 4: Membership function for error Fig 5: Membership function for change in error

The Linguistic Variable are MN (Medium Negative), SN (Small Negative), Z (Zero), MP

(Medium Positive), and SP (Small Positive) ,FLCOSE (Fully Close),SCLOSE (Slightly

Close), HF (Half), PCLOSE (Partially Close), FOPEN (Fully Open), SOPEN(Slightly Open).


Pa

ge5

7

Fig 6: Membership function for output (rotation)

2. HAND-TUNED MEMBERSHIP FUNCTION FOR TEMERATURE

Fig 7: Membership function for error Fig8: Membership function forchange-in-

error

Fig 9: Membership function of output


Pa

ge5

8

IV. SIMULINK BLOCK DIAGRAM DESCRIPTION

1. For Level

Simulink model for liquid level control and Fuzzy Logic Controller and by using program

MatlabR2013. Based on the dynamic equations (1) and (2) a Simulink block diagram. Fig.2

showing the nonlinear model of the plant can be formed successively .Fig.3 shows the

subsystem the Simulink block diagram of the nonlinear model of the plant. For pumping

liquid is pumping capacity (F = 588 c \sec). Fig.4 showing the subsystem of stepper motor.

Fig.10 showing subsystem of flowrate using stepper motor and valve control and Fig.11

shows the subsystem 1 of valve control.

Fig 10: Simulink for Water level Control System with FLC

Fig 11: Coupled two tanks model in Simulink


Pa

ge5

9

Fig 12: Subsystem of stepper motor

Fig: Subsystem of flow rate using stepper motor and valve control

Fig 13: Subsystem 1 of valve control

2. For Temperature

The flow of water is supplied via a pump from a storage tank and water flow rate is adjusted

with an actuator. The level of liquid is measured. Here, the implementation of the fuzzy logic

controller in process control is based on the fuzzy logic based term, output = F [(e (t),) Δ e


Pa

ge6

0

(t)]. In this the fuzzy sets e (t) (Temperature error) and de (t) (Change in temperature error)

acts as the input. And the output is a firing angle which lies in the interval of [ ]. Here

through fuzzy output, get the firing angle which triggers the triac. Then fuzzy is further

connected with triac circuit and through this firing angle calculate the value of TRAIC

voltage (load voltage) from this formula(1).

V=f ( (1)

V=triac voltage

f ( = function of firing angle

Through this triac voltage, we have to calculate (Rms voltage) from TRIAC circuit.

Then, the value of will be put in the formula of power which is shown in formula (2)

P= (2)

In this formula, the value of R will be taken as a constant value. And the changes

according to the firing angle. The value of power will put in this formula (3) to get rise in

temperature ( =100 ) which is shown in formula (3)

(3)

, P= power, t= time, density=1,

Fig 14: Simulink model of Temperature Control


Pa

ge6

1

Fig 15: Subsystem 1 of AC source and measuring unit

Fig 16: Subsystem 2 of measuring unit

Fig 17: Subsystem 3 of measuring unit


Pa

ge6

2

Fig 18: subsystem 4 of triac

Fig 19: Subsystem 5 of rise in temperature

V. FIREFLY OPTIMZATION ALGORITHM (FA)

In the firefly algorithm, the flashing light of fireflies is an amazing sight in the summer sky in

the tropical and temperate regions. There are about two thousand firefly species, and roost

fireflies produce short and rhythmic flashes. The pattern of flashes is often unique for a

particular species. The flashing light is produced by a process of bioluminescence, and the

true functions of such signaling system are still being debated. However, two fundamental

functions of such flashes are to attract mating partners (communication), and to attract

potential prey. In addition, flashing may also servo as a protective warning mechanism to

remind potential predators of the bitter taste of fireflies. The rhythmic flash, the rate of

flashing and the amount of time form part of the signal system that brings both sexes

together. Females respond to a male‘s unique pattern of flashing pattern of other species

while in some species such as photuris, female fireflies can eavesdrop on the bioluminescent

courtship signals and even mimic the mating flashing pattern of other species so as to lure

and eat the male fireflies who may mistake the flashes as a potential suitable mate. Some


Pa

ge6

3

tropic fireflies can even synchronise their flashes, thus forming emerging biological self-

organized behaviour. We know that the light intensity at a particular distance r from the light

source obeys the inverse square law. That is to say, the light which becomes weaker and

Fig 20: Flowchart of Fa

Weaker as the distance increases. These two combined factors makes most fireflies visual to

a limit distance, usually several hundred meters at night, which is good enough for fireflies to

communicate. The flashing light can be formulated in such a way that it is associated with the

objective function to be optimized, which makes it possible to formulate new optimization

algorithms. Use the following three idealized rules:[39]

1) All the fireflies are unisex so it means that one firefly is attracted to other fireflies

irrespective of their sex.

2) Attractiveness and brightness are proportional to each other, so for any two flashing

fireflies, the less bright one will move towards the one which is brighter. Attractiveness and


Pa

ge6

4

brightness both decrease as their distance increases. If there no one brighter than other firefly,

it will move randomly.

3) The brightness of a firefly is determined by the view of the objective function.

Input: f(X), X= ( )

m, // user defined constant

= f(X)

Output ;

For i=1: m

= initial _solution ( )

End

While (termination requirements are not met) do

min argmi (f( )

fori= 1: m do

for j 1 : m do

if j 1 : m do

if f( then

distance ( , )

attractiveness ( , )

(1- ). + + α. (random ()-1/2)

end if

end j

endi

+ α. (random ()-1/2)

end

Fig 21: Pseudo codes of FA

A. DESIGN ISSUES FOR CONSTRUCTION OF mfs [38]

Following design points are considered while constructing rule base and sfs for FAFLC:

1. Choice of Input Variables: We considered only 2 input variables, E(n) and R(n), each

with 5 mfs and thus total number of rules & output mfs being 25 and 9 resp.

2. Choice of Input And Output Mfs: Exponential type of mfs (such as sigmoidal, Gaussian

etc.) were avoided as their infinitely long tails add to noise only. For outermost fuzzy sets on

UOD, particularly suited are non-exponential type zmf and smf (requiring only two defining

parameters, each) and for the rest, triangular mfs, trimf, (requiring 3 parameters, each) were

adopted. Defining equations are:

zmf(x;a,b) = 1 for x<=a,

= 1-2((x-a)/(b-a))2 for a<= x <=(a+b)/2


Pa

ge6

5

= 2((x-b)/(b-a))2 for (a+b)/2 <= x <= b

= 0 for x >=b.

where parameters a and b locate extremes of sloped portion of curve.

smf(x;a,b) = 1 – zmf(x;a,b)

trimf(x;a,b) = max(min((x-a)/(b-a), (c-x)/(c-b)), 0)

where a,b,c respectively locate start, peak and end points.

B. DESIGN OF ADAPTIVE FITNESS FUNCTION

A performance criterion such as ISE is although quite general but has disadvantage of being

unable to distinguish between persisting errors (even though well within tolerance band) and

initial sluggishness. To cover more facets of time-response, a synthetic, more comprehensive

fitness-function as follows is adopted:

Fitness-function= (w1+w2+w3+w4)/ (w1*ISE +w2*Mp+w3*tr+ w4*ts) (1)

where w1,…,w4 are user-settable weights (free-parameters) to lay emphasis on different

facets of response. Design of such a comprehensive fitness function needs much more

attention in case FA-FLC is to operate at SPC. We considered following points in its design:

i) In synthesizing a comprehensive fitness function for a FA meant to tune an FLC

operating at SPC, one cannot be oblivious of numerical properties/ scale of different factors

constituting the fitness function. For instance, at higher SPCs, ISE can get numerically too

dominant over Mp, tr and ts, so static chosen weights can mean that ISE is getting the tilt in

its favour, totally eclipsing other performance indices. In other words, firefly good on all

other accounts (viz. Mp, tr and ts) will keep on getting superseded by firefly poor on these

accounts but dominant merely on account of ISE. We, therefore, felt a need to adapt fitness

function by choosing weight w1 as follows: w1 = 0.2/(SPC)2.

ii) Values of w3 and w4 were held constant at 0.5 and 2 respectively, as these indices are

relatively independent of SPC; latter weight is kept much higher as ts is generally more

crucial than tr.

iii) w2 is adapted as follows depending upon whether Mp is within tolerance band (normal

weight) or Mp exceeds it (heavily de-weighted):

If (Mp>0.05*abs(SPC)),

w2 =0.1/abs(SPC);

else w2 = 0.5/sqrt(abs(SPC)

VI. EXPERIMENTAL RESULTS

In this section results of experiments and simulations will be presented. We have solved the

problem of tuning of fuzzy controller parameters for water level and temperature control by

using firefly algorithm which provides desired solution using MATLAB. Fig 5.3 shows the

response of fuzzy controller of water level of tank 2 under simulation environment. The

controller stabilizes the desired water level very quickly.


Pa

ge6

6

Fig 28: Response of Level control with FLC

Fig 5.4 shows the response of fuzzy controller of water level of tank 2 with load disturbance at t

= 5 sec under simulation environment

Fig 29: Response of water level of tank 2 with load disturbance

Fig 30: FA-Tuned Membership function of error Fig 31: FA-Tunedmf of Change-in-error


Pa

ge6

7

Fig 32: Membership function of Output

Fig 33: Response of water level of tank 2 with FA-FLC

FAFLC: Evolved mfs shown in Fig and correspond to following bestf firefly:

[-60, -36, -60, -36, 0, -36, 0, 24, 0, 24, 59.4, 24, 59.4, -1200, -720, -1200, -720, 0 ,-720,0,

480, 0,480, 1188, 480, 1188, 0,480.0,0,480.0,864,480.0,864,1104, 864, 1104, 1200, 1104,

1200, 1320, 1200, 1320, 1824, 1320, 1824, 2064, 1824, 2064, 2376, 2064, 2376]

Fig 34: Result for FA-FLC for temperature control


Pa

ge6

8

The greatest reductions in settling time has occurred which is a proof to great ability of FA

for finding global search of a problem. After optimization of controller membership function,

the main obvious changes can be interpreted as a significant lowering in rise time as shown in

figure

FAFLC: Evolved mfs shown in Fig and correspond to following bestf firefly:

[-100, -60, -100, -60, 0, -60, 0, 40, 0, 40, 99, 40, 99, -2000, -1800, -2000, -1800, 0, -1800, 0,

1200, 0, 1200, 2970, 1200, 2970, 0, 1020, 0, 1020, 2160, 1020, 2160, 2760, 2160, 2760, 3000,

2760, 3000, 3300, 3000, 3300, 4560, 3300, 4560, 5160, 4560, 5160, 5940, 5160, 5940]

Table 1: Comparison between FA-FLC and FLC for temperature

FA-FLC FLC

Rise time ( ) 0.0355 0.1421

Settling time 0.5211 0.582

Overshoot 4.115 4.775

Table 2: Comparison between FA-FLC and FLC for water level

FA-FLC FLC

Rise time 0.3572 0.3760

Settling time 1.15 1.245

Table 3: Values of FA Parameters

Number of optimization variables 19

Number of alpha 0.55

Number of firefly (n) 30

Number of delta 0.97

Number of dimension(d) 51

Number of beta 0.20

Number of gamma 1

TABLE 4: Bounds for mfs of input and output variables and for input and output scaling factors of FLC

Note 1: (a,b)= points of zmf of smf

(a,b,c) =points of trimf

Note 2; m =Multiplying Factor. Its value is SPC for E(n);

20*SPC for R(n) & 50*SPC for u(n)

lb ub

Bounds for

mfs of inputs

E(n) and R(n)

MN

SN

ZE

SP

[-1, -0.6]*m [0.99, -0.4]*m

[-1, -0.6, 0]*m [-0.99, -0.4, 0.2]*m

[-0.6, 0, 0.4]*m [-0.4, 0.2, 0.6]*m

[0, 0.4, 0.99]*m [0.2, 0.6, 1]*m

[0.4, 0.99]*m [0.6, 1]*m


Pa

ge6

9

V. CONCLUSION AND FUTURE DIRECTION

With a large number of parameters (51 points of mfs for a two-inputs and one-output FLC),

FLC design truly represents a search problem in high-dimensional, multi-modal hyperspace

typically suited for FA. In this work, simulation experimental results on the control of level

and temperature using firefly algorithm have been provided and it has been demonstrated that

FA is an efficient method. FA-FLC outperforms a hand-tuned FLC.

Following new directions can be pursued: (a) adapting FLC for temperature and level control

systems subjected to wide range of set-points. (b) adapting control parameters of FA.

REFERENCES

i. Dharamniwas, Aziz Ahmad, Varun Redhu and Umesh Gupta, ―Liquid Level Control by

Using Fuzzy Logic Controller‖, pp. 537-549, July 2012

ii. Evelia Lizárraga Olivas, Oscar Castillo, Fevrier Valdez and José Soria, ―Ant Colony

Optimization for Membership Function Design for a Water Tank Fuzzy Logic

Controller‖ IEEE Transaction, 2013

iii. Majid Joshani, Rubiyah Yusof, Marzuki Khalid, A. Imam Cahyadi, ―Swarm

Intelligence Based Fuzzy Controller – A Design for Nonlinear Water Level Tank‖,

International Conference on Intelligent Systems Modelling and Simulation, 2012

iv. PROCYK, T. J AND MAMDANI, E. H. ―A Linguistic self-organizing process

controller‖, Automatica, Vol. 15., pp. 15-30,1979

v. B. SUBUDHI AND A. K. SWAIN, ―Optimization of Membership Functions of Fuzzy

Logic Controller for Controlling Liquid Level Using Genetic Algorithm‖, pp.77, Jan.—

Feb. 1997.

vi. Ahmad Hatta bin Abdullah, ―Design and Development of Fuzzy Logic Based Level

Controller‖, UniversitiTeknikal Malaysia Melaka, May 2008

vii. Harshdeep Singh, ―Design of Water Level Controller Using Fuzzy Logic System‖,

National Institute of Technology Rourkela, Department of Mechanical Engineering.

viii. J.S. Saini and Y.P. Singh, ―Use of Causal Knowledge in a Real-time Fuzzy Logic

Controller‖, IEEE Transaction, 1995

MP

Bounds for

mfs of output

u(n)

VLN

LN

MN

SN

ZE

SP

MP

LP

VLP

[0, 0.17]*m [0.1, 0.18]*m

[0, 0.17, 0.36]*m [0.1, 0.20, 0.39]*m

[0.17, 0.36, 0.46]*m [0.20, 0.39, 0.47]*m

[0.36, 0.46, 0.5]*m [0.39, 0.47, 0.57]*m

[0.46, 0.5, 0.55]*m [0.47, 0.57, 0.67]*m

[0.5, 0.55, 0.76]*m [0.57, 0.67, 0.87]*m

[0.55, 0.76, 0.86]*m [0.67, 0.87, 0.99]*m

[0.76, 0.86, 0.99]*m [0.87, 0.99, 1]*m

[0.86, 0.99]*m [0.99, 1]*m


Pa

ge7

0

ix. W. Tan, ‗Water level control for a nuclear steam generator‘, Nuclear Engineering and

Design, vol.241, pp.1873-1880, 2011

x. A. Shome and D. Ashok, ‗Fuzzy Logic Approach for Boiler Temperature and Water

level Control‘, International Journal of Scientific and Engineering Research, vol.3, pp.

1-6, 2012

xi. O. Safarzadeh, A.Kahki Sedigh and A.S. Shirani, ―Identification and robust water level

Control of horizontal steam generators using quantitative feedback theory‖, Energy

Conversion and Management, vol.52, pp.3103-3111, 2011

xii. M.S Das Gupta, ―Fuzzy and ANN Controller Design and Implementation on a level

control setup‖, UGC National Conference on advances on industrial automation, vol.2,

March 2004.

xiii. Majid Joshani, RubiyahYusof, Marzuki Khalid, A. Imam Cahyadi, ―Swarm Intelligence

Based Fuzzy Controller – A Design for Nonlinear Water Level Tank‖, International

Conference on Intelligent Systems Modelling and Simulation, 2012

xiv. NamrataDey, Ria Mandal, M Monica Subashini, ―Design and Implementation of a

Water Level Controller using Fuzzy Logic‖, International Journal, Vol 5 No 3, Jun-Jul

2013

xv. M.S.M Aras, M.F. Basar, N. Hasim, M.N. Kamaruddin, H.I. Jaafar, ―Development and

Modeling of Water Tank System Using System Identification Method‖ ,International

Journal, Volume-2, August 2013.

xvi. ZHAO Taoyan, LI Ping and CAO Jiangtao, ―Study of Interval Type-2 Fuzzy Controller

for the Twin-tank Water Level System‖,Chinese Journal of Chemical Engineering, Vol.

20, Dec 2012.

xvii. K.Govinda, Sreekar.ch, Sandilya .k, ―Reservoir Water Level Indicator using UM66

Microcontroller‖,International Journal for Scientific Research & Development, Vol. 2,

2014

xviii. Daniel Wu, FakhreddineKarray, Insop Song, ―Water Level Control by Fuzzy Logic and

Neural Networks‖, University of Waterloo

xix. P. Singhala, D. N. Shah, B. Patel, ―Temperature Control using Fuzzy Logic‖,

International Journal of Instrumentation and Control Systems (IJICS) Vol.4, No.1,

January 2014.

xx. Saeed Balochian, EshaghEbrahimi, ―Parameter Optimization via Cuckoo Optimization

Algorithm of Fuzzy Controller for Liquid Level Control‖, Hindawi Publishing

Corporation Journal of Engineering Volume, 2013

xxi. NaaJu Na, Zeugnam Bien, ―A Fuzzy Controller for the Steam Generator Water Level

Control and its Practical Self-Tuning Based on Performance‖, Journal of Korean

nuclear society, vol.27, no.3, 1995.

xxii. SurachaiPanich, ―Development of Fuzzy Controller for Water Level in Stream Boiler

Tank‖, Journal of Computer Science 6 (11): 1233-1236, 2010.

xxiii. ChulHwan Jung, Kee-Choon Kwon, ―A fuzzy controller with a real-time tuning

algorithm and its application to a steam generator water level control‖, Control and

Cybernetics vol. 27, No. 4, 1998.


Pa

ge7

1

xxiv. Isizoh A. N., Okide S. O, Anazia A.E., Ogu C.D, ―Temperature Control System Using

Fuzzy Logic Technique‖, (IJARAI) International Journal of Advanced Research in

Artificial Intelligence, Vol. 1, No. 3, 2012.

xxv. Seyed Kamaleddin Mousavi Mashhadi, Elham Sareban, Amir Aminian, ―Design Fuzzy

Controller for Synthesis Water Level‖, Journal of mathematics and computer

Science,vol.9 ,2014.

xxvi. P. J. King and E. H. Mamdani, ―The application of fuzzy control systems to industrial

process,‖ Automatica, vol. 13, pp. 235–242, 1977

xxvii. W. J. M. Kickert and H. R. Van Nauta Lemke, ―Application of a fuzzy logic controller

in a warm water plant,‖ Automatica, vol. 12, pp. 301–308, 1976

xxviii. Sven Fagerstrom and Nagy Bengiamin, ―Modelling and Characterization of Power

Electronics Converters Using Matlab Tools‖, vol.1, pp. 133-165, 2012

xxix. Teccor electronics, ―Phase Control Using thyristors,‖ pp 1-9, 2002

xxx. Rabisankar Roy, Susmita Das, Jayanta Kumar Ray, Shreyashi Barat, BiswarupNeogi,

―Automatic Speed Control of Single Phase Induction Motor with the Variation of

Ambient Temperature‖, ISSN 2250-3153,Volume 2, Issue 11, November 2012

xxxi. Disha, Mr.Pawan Kumar Pandey, Rajeev Chugh, ―Simulation of Water Level Control in

a Tank Using Fuzzy Logic‖, ISSN: 2278-1676 Volume 2, Issue 3 ,PP 09-12,Sep-Oct

2012

xxxii. Zaid Abed AljasimMuhasain and Saif Abed AljasimMuhasain, ―Analysis and Design of

Controller for Level Process Control without Sensor‖, (NUCEJ), Vol.13 No.1, pp.84-

97, 2010

xxxiii. Xin-She Yang and Xingshi He, ―Firefly Algorithm : Recent Advances and

Application‖, Int. J. Swarm Intelligence,2013, Vol. 1, No. 1, pp. 36-50.

xxxiv. Adelson Menezes Lima∗, Samequefariascunha De Oliveira, Missilene Da Silvafarias,

Tarcisio Da Silvabarreto, Elmer Rolando Llanos Villarreal, ―Application the control in

tanks using fuzzy theory‖, 2012

xxxv. Aniket B. Kabde, A. Dominic Savio, ―Position Control of Stepping Motor‖,Vol. 3,

Issue 4, April 2014

xxxvi. Vasilija Sarac, ―Application of Matlab/Simulink in hybrid stepper motor modelling‖,

2013

xxxvii. Ahmad Johan Mahbob, MahanijahMd Kamal and FaiezaHanumYahaya, ―Water

Temperature Using Fuzzy Logic‖, IEEE Transaction on CSPA, 2009

xxxviii. J.s. Saini, Dr. M.gopal, Dr. A.P. Mittal, ―Evolving Optimal Fuzzy Logic Controllersby

Genetic Algorithms‖, Volume 50, Issue 3, pp.179-190, 2004

xxxix. X. S. Yang, Nature-Inspired Metaheuristic Algorithm, Luniver Press, Beckington, UK,

2nd edition, 2010

xl. Xin-She Yang and Xingshi He, ―Firefly Algorithm: Recent Advances and Application‖,

Int. J. Swarm Intelligence,2013, Vol. 1, No. 1, pp. 36-50.

http://www.tandfonline.com/loi/tijr20?open=50#vol_50

http://www.tandfonline.com/toc/tijr20/50/3

optimization of fuzzy controller parameter by using …ijesta.com/upcomingissue/08.03.2016.pdfvolume...

Documents