Radial-base-function, Genetic-Algorithm and fuzzy logic approach for

real-time tuning of PID Controller in AVR System ABDULLAH J. H. AL GIZI

1*, M.W. MUSTAFA

1, N. ZREEN

1

1Faculty of Electrical Engineering

Universiti Teknologi Malaysia

MALAYSIA

Corresponding author: E-mail addresses: abdullh969@ yahoo.com

Abstract: - Optimal tuning of proportional–integral–derivative (PID) controller parameter is necessary

for thematic factory operation of an automatic voltage regulator (AVR) system. This study presents a novel

combined genetic algorithm (GA), radial-basis function network (RBF) identification and fuzzy logic control

approaches to determine the optimal PID controller parameters in AVR system. The problem of obtaining the

optimal AVR and PID controller parameters is formulated as an optimization problem and RBF tuning by GA

is applied to solve the optimization problem. The proposed approach has resulted in AVR and PID controller

with a good response. Whereas , RBF tuning by GA for various operating conditions are used to develop the

rule base of the Sugeno fuzzy system and design fuzzy PID controller (GRBFF-PID) of AVR system to

improve the system response. The GRBFF-PID controller is found to possess excellent features of easy

implementation, stable convergence characteristic, good computational efficiency and high-quality solution.

Our simulation provides high response of an AVR system compared to the real-code genetic algorithm (RGA),

a linear-quadratic regulator (LQR) method and GA. We assert that GRBFF-PID is highly efficient and robust in

improving the system response of an AVR system.

Key-Words: - AVR, GA, GRBRF-PID ,Sugeno fuzzy system, RBF

1 Introduction

The major purpose of the AVR is to control the

terminal voltage by regulating the generator exciter

voltage. The AVR must keep path of the generator

terminal voltage all the time under any load and

operational conditions, in order to keep the voltage

within pre-established limits. Researches concerning

the improvement of the search process to control

system engineering problems proposed different

approaches to get better solutions. [1]suggested a

new design method for determining the PID

controller parameters of the AVR system using the

real coded genetic algorithm method. Kim et al.

presented a hybrid GA and bacterial foraging

approach to tune the PID controller of an AVR[2].

Valarmathi et al. proposed enhanced GA for PI

controllers tuning in pH process [3]. Genetic

algorithm (GA) is one of these widely used

approaches since it improved its ability for solving

optimization problem [2-4]. Genetic algorithms can

be found in many applications in biogenetics,

engineering, economics, manufacturing,

mathematics, physics, chemistry, computer science,

, and other fields. For instance, Gas can be applied

to discuss the data classification, fuzzy modeling

and Omni-directional robot design problems [5].

There are some research application of fuzzy the

first one [6] proposed replaced the PI controller

by fuzzy logic controller to improve the transient

performance of the dc link under fast load variations

and the second[7]propose a new fuzzy logic control

based under- frequency load shedding scheme

implemented on mini hydro type-DG operating

in islanded mode and least one [8] Propose

the transient stability enhancement of the power

system interconnected with wind farm

by generalized unified

power flow controller (GUPFC) having grid

frequency switching similar multi-pulse converters

.Fuzzy logic theory makes it attainable to create use

of the human specialists’ data within the reliability

evaluations. [9]During this paper a neuro-fuzzy

primarily based methodology is projected to scale

back the degree of the uncertainty within the

reliability indices and thus to judge the reliability of

the composite power systems exactly. Additionally

use of RBF-NN as a result of powerful characteristic

to find out any nonlinear mapping between two

states. [10]In this study, a stochastic multi objective

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framework is proposed for distribution feeder

reconfiguration (DFR). The proposed multi

objective framework will at the same time optimize

competitive objective functions as well as total

power losses, voltage deviation and total cost. For

every settled state of affairs, a multi objective

formulation supported the adaptive changed particle

swarm improvement (AMPSO) is enforced for

every settled state of affairs of it. [11]In this study,

the operating benefits of considering thermal

recovery and hydrogen production in the economic

model of a grid-parallel proton exchange membrane

fuel cell power plant (PEM-FCPP) are investigated.

The objective functions to be optimized are the total

active power losses. [12] and [13] studied an

improved GA (IGA) for the PIO controller based on

traditional GA (TGA). In [14], a best PID controller

for a universal second-order system has been

improved using linear-quadratic regulator (LQR)

method. This approach requires a good selection of

weighting functions for acceptable performance. In

addition, nonlinear H∞ control using radial basis

function (RBF) neural networks has been proposed

in [15, 16]. Computation techniques such as GA and

PSO [17, 18] have been applied to obtain the best

controller parameters. Gaing [19] suggested a new

design method for determining the PID controller

parameters of the AVR system using the particle

swarm optimization (PSO) method. PSO is a

population-based optimization technique, which is

enthused by social performance patterns of

organisms such as bird flocking and fish schooling.

Whereas, both GA and PSO subject from

computational burden and memory condition, they

are not appropriate for on-line applications. To

overcome the above complexities, we report the

design of a novel method by integrating the Sugeno

fuzzy system rule base and the AVR system fuzzy

PID controller (GRBFF-PID) for enhancing the

system response

2 Problem Formulation To determine the optimal rule base of the Sugeno

fuzzy system for design fuzzy PID controller in

AVR system and improve the system response in

AVR system of synchronous generator under severe

disturbance.

2.1 Radial Basis Function Networks

The outer loop of AVR is a self-tuning PID

voltage controller based on the radial basis function

neural network that has an ability to adapt with

uncertain load and system conditions. Moody et al.

proposed a feed-forward two-layered RBF neural

network with single hidden layer to mimic the

systematic arrangement of restrictive readjustment

in the human mind[20]. Furthermore, the input

samples for RBF neural network do not require a

special distribution and RBF possess an on-line

learning with rapid converges. Consequently, the

control field for implementing the real time

manipulation concentrates on the neural network.

The RBF is exploited to achieve the best parameters

of the controller to maintain zero system error [21].

The schematic of radial-basis function neural

network is shown in Fig. 1. The updating algorithm

for the adaptive PID based RBF can be formulated

as,

2

3

1

)().().(.

j

j

j

m

j

jpp

kuchwkekek

(1)

2

3

1

)().().(.

j

j

j

m

j

jii

kuchwkekek

(2)

2

3

1

)().().(.

j

j

j

m

j

jdd

kuchwkekek

(3)

The PID parameters such as integral gain (Ki),

the proportional gain (Kp) and the derivative gain

(Kd) are automatically readjusted by RBF on-line

learning algorithm to maintain the system error

)(ke = 0. Two commands offered by Matlab namely

Newrb and newrbe are used to design the RBF

neural network in which Newrb adds neurons step

by step until the goal is hit with long training time

with minimal error and newrbe designs a network

very quickly with zero error [22, 23]. In the training

process, the achieved steps are: (i) neurons number

in the hidden layer, (ii) the coordinates of the center

of RBF function (iii) and the radius (spread) of each

RBF functions in each dimension.

Fig.1 Schematics of RBF neural network structure.

2.2 Automatic Voltage Regulator

2.2.1 Modeling of AVR System

An AVR system as shown in Fig. 2, mainly

comprised of amplifier, exciter, generator and

sensors is used in a synchronous generator to

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maintain constant terminal voltage at different

levels. The transfer function of the AVR

components is summarized in Table 1.

Fig. 2 Block diagram of AVR system along with

PID controller.

Table 1 the transfer functions of AVR components

An increase in the generator reactive power

load is accompanied by a drop in the terminal

voltage. A PID controller is used to minimize the

error and to achieve improved dynamic response.

The PID controllers are efficiently used to place the

manipulated variable at the set point. The transfer

function of the PID controller is given by,

sKKsG dp s

K)( i (4)

The AVR excellence affects the voltage level

through steady-state process and diminishes the

voltage oscillations during fleeting periods moving

the overall stability of the system. The transfer

function of AVR systems with PID control is given

by, ))(()1)(1)(1)(ss(1

)1)()(K(s)(2

a

d

2

)( ipdsgeasge

sgeaip

sref

t

ksKKsKKKKsss

sKKKKsK

V

sV

(5)

2.2.2 Optimization of Controller Parameters

The acceptable operation of the system is

determined by the selection of the best PID

controller parameters. Moreover, the selection

problem of the PID controller parameters is

considered as an optimization problem. The

objective function yields,

)())(1(),,K( d rsssship tteEOeKKMinF (6)

The MinF(Kp, Kd, Ki ) combines transient response

counting rise time overshoot, settling time and

steady-state error. The satisfaction of the designer

needs can be achieved by choosing suitable value of

the weighting factor β. Therefore, the optimization

problem boils down to the following constraints,

maxmin

ppp KKK , maxmin

iii KKK , maxmin

ddd KKK (7)

Following Devaraj et al. [1], RGA is applied to

optimize the values controller parameters and the

proposed GA is introduced.

2.3 Proposed GA

GA is recognized as an effective and efficient

technique to solve the optimization problems. In

comparison to the optimization techniques, such as

random search and simulated annealing, GA

performance is superior that avoids local minima

considered as a key issue in nonlinear systems [24,

25].

2.3.1 Genetic Algorithm Operators

The genetic algorithms are based on the natural

selection mechanism that allows survival of the

fittest and generate estimated solutions by

exchanging information’s to attain the optimum

solution. After generating the initial population, the

GA discovers new individuals by producing

offspring’s using the reproduction, crossover and

mutation operators, which replace the old generation

members and form the new generation. Once

several generations are produced, the algorithm

finds the best chromosome that represents the

optimum or near optimum solution. The major GA

operators such as cross-over, reproduction and

mutation are exploited. The convergence speed is

controlled by applying various probabilities on these

operators. The design of the crossover and mutation

operators are carefully managed due to their

immense impact on the performance of genetic

algorithm [24, 25]. The details of the genetic

operators used in the proposed GA are illustrated in

Table l.

2.3.1.1 Reproduction

In the process of reproduction, individuals are

selected depending on their fitness function, the

higher the fitness is, more chance for an individual

to be selected for the next generation. Three main

selection methods such as ranking method, fitness

balanced selection and tournament selection are

Component Transfer function Parameter limits

Amplifier sKTF aaamplifier 1/ ss

K

a

a

1<<02.0

40<<10

Exciter sKTF eeexciter 1/ ss

K

e

e

1<<4.0

10<<1

Generator sKTF gggenerator 1/

Kg depend on the load (0.7-

1.0) ,ss g 2<<1

Sensor sKTF sssensor 1/ ss s .060<<001.0

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utilized [1]. In this work, we employ the tournament

selection method, where ‘n’ individuals are

randomly selected from the population and the best

vale is chosen for additional genetic processing.

This process is repeatedly performed until the

mating pool is filled.

2.3.1.2 Crossover

The property of global search in GA is mostly

determined by the crossover operator, which

combines two-parent chromosomes to produce a

new one. The range of the selected probability is

typically between 0.6 – 1.0. One of the interesting

features of the crossover operators is the relation

between the generated chromosome and the location

of both the parents. The generated new chromosome

remains close to the parents in case both the parents

are close to each other. Conversely, the search is

more likely to be random [1].

2.3.1.3 Mutation

New chromosome is inserted into the

population for the mutation process. Mutation

randomly makes insignificant change in the

chromosome information. However, for inconsistent

mutation, the variable takes a consistent random

number between the lower and upper limits. In this

study ‘uniform mutation’ operator is used.

2.4 GA Implementation for Optimizing PID

Parameters of AVR

The optimum PID controller parameters are

obtained via GA tuning of PID. Two major themes

such as symbol of the choice variables (variable

representation) and arrangement of the fitness

function are used in this process.

2.4.1 Variable Representation

The solutions of all candidates are generated in

the genetic population. The solution elements of

PID controller-tuning problem include parameters

Ki, Kp and Kd. The direct representation of the

solution variables reduces the computer space for

storing the population. The values of these

parameter obtained from direct tuning of GA into

the RBF program for the optimum tuning of the PID

controller parameter are substantial for the thematic

factory operation of AVR system.

2.4.2 Fitness Function

The solution for the performance of every

candidate in the population is evaluated based on its

fitness which is defined as a non-negative value to

be maximized. Fitness is associated in a straight line

with the value of objective function. The parameter

set of the individual evaluation can be determined

using equation (6) for the performance criteria. The

value of individual fitness is calculated by the

outcome of the presentation criteria via mutual

computation. The fitness function is the presentation

of mutuality criterion F(Kp,Kd,Ki) given in equation

(6). Thus, the minimization of performance criteria

in eq. (6) can be transformed to the maximization of

the fitness function as,

ITAEKKF

kFitness

ip *),,K( d

(8)

Where k is a constant, ITAE is a time integral

multiplied by the absolute error value. This is used

to amplify the value of 1/F, which is generally

small, so that, the chromosome fitness values occur

in a wider range.

2.5 Sugeno Fuzzy Model

Recently, Devaraj et al. used fuzzy set theory, in

which a variable is a member of one or more sets,

with a membership specified degree [1]. The fuzzy

rule is expressed as,

If x is A and y is B then z = f(x,y) (9)

where A and B are fuzzy sets in the antecedent, x

and y are input variables and f (x, y) is a crisp

function in the consequent. Each variable fuzzy set

are represented by suitable membership functions.

The core of the fuzzy logic system is formed by a

set of such rules. For an exact input signal

condition, the fuzzy system defines the rules to be

fired and then calculates the efficient output in two

steps. Firstly, the minimum of the membership

functions input(wi) is obtained for each rule, where

this value is the firing value for a particular rule.

Secondly, the overall output is calculated by a

weighted average of individual rule outputs given

by,

M

1i

M

1i

iω

iziωz

(10)

The PID controller parameters under various

operating conditions are determined by the Sugeno

fuzzy system.

3 Problem Solution To determine the optimal rule base of the Sugeno

fuzzy system for design fuzzy PID controller in

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ISBN: 978-960-474-371-1 127

AVR system and improve the system response we

propose a novel combined GA, RBF-NN and fuzzy

logic control approaches. Whereas , RBF-NN tuning

by GA for various operating conditions are used to

develop the rule base of the Sugeno fuzzy system

and design fuzzy PID controller (GRBFF-PID) of

AVR system to improve the system response.

3.1 Performance of GA–PID controller

Next, the proposed GA was applied to

optimize PID controller parameters. The software

for the proposed GA was written in MATLAB and

executed on a laptop Intel core(TM) 2 Duo CPU

5550@1.83GHz and 3GB. Integral gain Ki

Proportional gain Kp and derivative gain Kd are the

optimization variables. The primary population is

produced randomly among the variable’s lower and

upper restrictions. To evaluate the fitness value of

each controller parameters set the fitness function

given by (5) is used to evaluate the fitness value of

each set of controller parameters . Simulation was

conducted with different values of . The GA

performance for various values of crossover and

mutation likelihood in the ranges 0.6–1.0 and

0.001–0.1 resprctively ,was evaluated.The top

consequences are obtained with the following

control parameters.Generations’ number: 75

,Population size: 30 ,Crossover probability: 0.6

,Mutation probability: 0.001.The GA took 33.72s to

reach the optimal solution. The GA convergence

characteristics are shown in Fig.3. During this stage,

the main focus of GA is to find feasible solutions of

the problem. It can be noted that the value increases

slowly and stabilizes near the optimum value that

most individuals in the population trying to reach.

The controller parameters optimal values obtained

by using the proposed GA for different values of

are given in Table 2.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.000

0.002

0.004

0.006

0.008

0.010

0.012

rin

.out

Time(sec)

rin.out

0 10 20 30 40 50 60 70 802.330

2.332

2.334

2.336

2.338

2.340

2.342

2.344

2.346

Best

J

Generation

Best J

Fig.3. shows the convergence characteristics of GA

algorithm

Table 2Optimal value the control parameter obtained

using the proposed GA

3.2 Performance of RBF–PID controller AVR

tuning

The proposed methodology for PID controller

tuning was tested on an AVR system . The AVR

system consists of generator, exciter, amplifier and

sensor. The parameters of AVR system are selected

as following:Ka=10 ,Ke=Kg=Ks=1.0 ,τa=0.1, τe=0.4,

τs=0.01 and τg=1.0 only Kg and τg are load

dependent . MATLAB Simulink was used to

simulate the AVR system. The MATLAB-Simulink

model of AVR system with PID controller is shown

in Fig.4. The first time PID controller was tuned

using GRBF-NN ( RBF-NN tuning by GA),

second time PID controller was tuned using (RBF-

NN tuning by RAG).

Discrete,Ts = Ts s.

powergui

Vt

Terminal voltage

in #c

Signal Scope

1

0.01s+1

Senser

Mux

Mux1

1.0

s+1

Generator

e u

GRBF-NN PID

voltge_in

FromWorkspace

1

0.4s+1

Exciter

Clock

10

0.1s+1

Amplifier

Fig.4. MATLAB-Simulink model of AVR system

along with PID controller

A step reference voltage of 0.01 p.u. is applied, and

the step response of change in terminal voltage of

AVR system in the presence of PID controller is

shown in Fig.5. From the figure, it is observed that

the AVR system response with RBF PID( RBF-NN

tuning by GA or RGA) controller increases in a

steady state until reaches to reference voltage of

0.01 p.u with little oscillatory mode and large settling time. During this stage, the main

concentrates is to find feasible solutions for the

problem. Then the value increases slowly and

stabilizes near the optimum value with small swing

dependent on tuning data to reach that point (GA or

RGA with RBF-NN). Our simulation results are

summarized in Table 3, and the terminal voltage

responses are also shown in Fig.6. We find that the

proposed RBF-NN tuning by RGA approach

minimizes the rise time, reduces settling time and

Kpidi Bestfi Best_J

dK pK

iK

0.2768 0.6877 0.1629 0.428 2.3366 0.5

0.2968 0.5563 0.1629 0.4293 2.3291 1

0.2801 0.6329 0.1785 0.4280 2.3366 1.5

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overshoots when compared with the results obtained

using methods of LQR, RAG and binary-coded GA

[1]. Conversely, GRBF-NN (RBF-NN tuning by

GA) results better minimum settling time, less rise

time and overshoot in comparsion to that obtained

using methods of LQR and binary-coded GA [1].

Conversely, GRBF-NN (RBF-NN tuning by GA)

results better minimum settling time, less rise time

and overshoot in comparison to that obtained using

methods of LQR and binary-coded GA [1].

Furthermore, the convergence time achieved by the

proposed algorithm is shorter compare to RGA

0 2 4 6 8 100.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014 RBF tuning by GA

RBF tuning by RGA

0 2 4 6 8 100.000

0.002

0.004

0.006

0.008

0.010

0.012

Delt

Vt(v

olt)

Time (sec)

RBF tuning by GA

0 2 4 6 8 100.000

0.002

0.004

0.006

0.008

0.010

0.012

Delt V

t(volt

)

Time (sec)

RBF tuning by RGA

Del

t Vt(v

olt)

Time (sec)

Fig.5. Shows characteristics of RBF PID controller

tuning by GA and, RGA [1]

0 2 4 6 8 100.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

Del

vt (p

u)

Time (sec)

GRBF-PID

LQRPID(2)

RGAPID

GAPID

.

Fig.6 comparison Step response of GRBF-PID with

LQR, RAG and binary-coded GA [1] response

Table 3 comparison of PID gains and transient response

parameters for the different methods

.

3.3 Development of Sugeno fuzzy model to design

PID controller

The optimum PID parameters for real-time

operation are obtained by developing Sugeno fuzzy

logic model, where, Ke and τe are the inputs and

Kp, Kd and Ki are the outputs. Eight fuzzy sets for

instance ‘very low (VL)’,’low(L) ,‘medium low

(ML)’, ‘medium(M)’, ‘medium high (MH)’ ,‘high

low (HL)’, ‘high medium (HM)’ and ‘high (H)’ are

defined for the variable Ke . Likewise, the fuzzy sets

defined for the variable τe are ‘very low

(VL)’, ‘low (L)’, ‘medium low (ML)’, ‘medium

high (MH)’, ‘high (H)’ and ‘very high (VH)’. They

are linked with overlapping triangular membership

functions. To formulate the table for fuzzy rule, the

values of Ke are varied from 2.0 to 9.0 in steps of

1.0 and τe are varied from 0.5 to 1 in steps of 0.1.

For each combination of Ke and τe ,the proposed

RBF-NN tuning via GA is applied to obtain the

optimal values of Kp, Kd and Ki. The fuzzy rule table

formulated for Kp, Kd and Ki using the above

approach is summarized in Table 4 as (a), (b) and

(c), respectively. During real-time operation,

corresponding to the present operating conditions,

the values of Ke and τe are found out. For this value

of Ke and τe, the optimal value of Kp, Kd and Ki can

be computed using the fuzzy rule table and the FIS

editor Sugeno inference system explained in section

2.4. Depending on the initialization (FIS editor), the

inputs of the fuzzy logic controller are Ke, τe and

the outputs are Kp, Kd and Ki. The system with three

fuzzy logic controllers Kp, Kd and Ki with rule

viewer are set in which each controller has two

inputs Ke, τe and each input has fuzzy set

associated with it. The output has 144 fuzzy set

rules for Kp, Kd and Ki, and 48 rules for each one

parameter as depicted in Fig.7 (a),(b) shown rule

viewer and surface viewer of novel GRBFF-PID

controller. MATLAB programming is used for the

proposed RBF-NN tuning via GA executed on a

Intel core (TM) 2 Duo CPU 5550@1.83GHz and

3GB RAM laptop. The optimal solution of

combination is achieved in the duration of 23.79

sec.

Fig.7. (a), (b) are Rule and Surface viewer of

Sugeno fuzzy PID controller (GRBFF-PID)

Method PID parameters )(sTs

)(sTr

shO

)10( 5

ssE

Kp Ki Kd

LQR[1] 1.01 0.5 0.1 2.3354 0.5004 0.3605 15.007

Binary-coded GA[1] 0.5692 0.2484 0.1258 1.7019 0.8093 0.0586 8.2941

RGA[1] 0.682 0.266 0.179 1.2682 1.0668 0.0004 4.3386

RBF tuning by

GA(GRBF-NN)

0.657 0.2958 0.1952 1.3766 1.0024 0.00168 5.3275

RBF tuning binary-

coded GA[1]

0.6003 0.2899 0.1626 1.4050 0.9405 0.00195 6.2490

RBF tuning by

RGA[1]

0.7136 0.3004 0.2317 1.3849 0.9522 0.00167 5.8305

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ISBN: 978-960-474-371-1 129

Table 4 (a) the fuzzy rule table formulated for Kp

using the above approach

Table 4 (b) the fuzzy rule table formulated for Ki

using the above approach

Table 4 (c) the fuzzy rule table formulated for Kd

using the above approach

3.4 Implementation of Electrical Power

Generation

The MATLAB-Simulink model of Electrical Power

Generation System along with along with Sugeno

fuzzy PID controller (GRBFF-PID) is shown in

Fig.8 and the GRBFF-PID controller used with the

excitation system is shown in Fig.9. A step

reference voltage of 1.38 kV is applied. The

GRBFF-PID controller has the ability to hold back

the oscillations in the terminal voltage and provide

high-quality damping characteristics. The test

system includes a generator excitation system, as

shown in the appendix, connected by 500 kV lines

of 650 km length and a 300 MVA-500/230 kV

transformer feeds a 230 kV-250 MW load. The

transmission line is split into two lines. The first line

is 350 km length connects between buses B1, B4,

and the second one is 300 km length connects

between buses B4 and B5. The two circuit breakers

of line 1 are CB1 and CB2 and discrete 3-Phase

PLL block measures the frequency, whereas the

PLL drives two measurement blocks considering the

variable frequency. The first block computes the

essential value of the positive-sequence load voltage

while the second block computes the active load and

reactive powers. The terminal voltage response of

excitation system with GRBFF-PID controller is

found to be highly response as shown in Fig.10.

This demonstrates the suitability of the proposed

approach to obtain the optimal PID gains during

system real-time operation. Our proposed method

renders better performance in the rise time, peak

overshoot and the steady state error. The responses

observed from the present controller have a slight

overshoot, which can be improved considerably by

increasing the rules number. We establish that the

GRBFF-PID controller has better performance in

comparison to other controllers. A three-phase to

ground fault on the 500 kV bus is evidenced at t =

1.0 s. The scope blocks clearly reveal the tracking of

the system frequency change by PLL. The

frequency of the system at moment of fault steps

down to 59.99997, at t = 1.0 s when the fault is

cleared the frequency 59.9997 at t = 1.1 s and

continuous in swing between 59.7 at time 1.2s and

60.3 Hz at time 1.24s because of the

electromechanical energy of interconnected system

(machines). Conversely, at t = 1.0 s when three-

phase to ground fault occurs on same bus, and the

system voltage at moment of fault swing between

1.3780 *104 and 1.3798*104, at t = 1.1 s when fault

is cleared ,the voltage swings between 1.3786*104

and 1.3794*104 V. The voltage reached the steady

τe Very low Low

Medium

Low

Medium

high

High

Very

high

Ke 0.5 0.6 0.7 0.8 0.9 1

(a)For proportional gain Kp

Very Low(2) 0.2944 0.6124 0.5980 0.4622 0.4728 0.6079

Low (3) 0.4153 0.3768 0.4796 0.5115 0.4887 0.3817

Medium low

(4)

0.2859 0.3304 0.3377 0.3617 0.3662 0.3835

Medium (5) 0.1039 0.2158 0.1085 0.3141 0.3099 0.3477

Medium

High (6)

0.1878 0.2422 0.2486 0.2615 0.2715 0.2037

High low(7) 0.1164 0.1123 0.2108 0.1747 0.0988 0.2570

High medium

(8)

0.1780 0.1071 0.1967 0.2068 0.2127 0.1705

High (9) 0.1391 0.1355 0.1257 0.0880 0.1823 0.1625

e

Very

low

Low

Medium

Low

Medium

high

High

Very

high

eK

0.5 0.6 0.7 0.8 0.9 1

(b)For integral gain Ki

Very

Low(2)

0.4201 0.4280 0.4276 0.4718 0.5110 0.5277

Low (3) 0.2960 0.3060 0.3218 0.3372 0.3594 0.3739

Medium

low (4)

0.2424 0.2427 0.2638 0.2671 0.2798 0.2946

Medium (5) 0.2193 0.2112 0.2370 0.2362 0.2397 0.2415

Medium

High (6)

0.1902 0.1947 0.2005 0.2114 0.2190 0.2271

High low(7) 0.1749 0.1860 0.1840 0.1937 0.2035 0.1972

High

medium (8)

0.1591 0.1650 0.1714 0.1713 0.1787 0.1916

High (9) 0.1497 0.1559 0.1599 0.1731 0.1723 0.1795

e Very low Low

Medium

Low

Medium

high

High

Very high

eK

0.5 0.6 0.7 0.8 0.9 1

(c)For derivative gain Kd

Very Low(2) 0.0241 0.0378 0.0540 0.2007 0.1916 0.2102

Low (3) 0.1733 0.1436 0.1489 0.0285 0.0284 0.2074

Medium low

(4)

0.0697 0.0199 0.0207 0.1572 0.0391 0.0897

Medium (5) 0.0144 0.1069 0.0391 0.0400 0.0221 0.0904

Medium High

(6)

0.0877 0.0160 0.0388 0.0170 0.0175 0.1035

High low(7) 0.0710 0.0179 0.0658 0.0776 0.0191 0.0168

High medium

(8)

0.0131 0.0669 0.0661 0.0321 0.0146 0.0632

High (9) 0.0353 0.0661 0.0493 0.0192 0.0136 0.0398

Manufacturing Engineering, Automatic Control and Robotics

ISBN: 978-960-474-371-1 130

state of 13790 V at t = 1.2 s whereas, frequency

reached 60 Hz at t= 1.40 s as displayed in Fig.11.

Fig.8 the MATLAB-Simulink model of Electrical

Power Generation System along with Sugeno fuzzy

PID controller (GRBFF-PID)

1

u

Scope

kp

ki

kd

e

out

PID

-K-

Gain1

0.5

Gain

Fuzzy Logic Controller

with Ruleviewerdu/dt

Derivative

1

e

Fig.9 Sugeno fuzzy PID controller

0.0 0.5 1.0 1.5 2.00

2000

4000

6000

8000

10000

12000

14000

16000

Time (sec)

Vt with GRBFF-PID controller

Del

vt(

vo

lt)

Fig.10 terminal voltage response of excitation

system with GRBFF-PID controller

Fig.11 shows the system terminal voltage and

frequency response under severe disturbance with

GRBFF-PID controller.

3.5 Comparison with other similar method

The optimal gains and transient response parameters

obtained using the models for a new set of operating

condition are given in Table 5.

Table 5 Optimal PID gain and transient response

using GA and RBF tuning by GA technique.

0 2 4 6 8 100.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

delt

Vt(

pu)

Time (sec)

LQR PID

RGAPID

GRBFF-PID

GAPID

Fig.12 seen comparison of overall method of LQR,

RAG and binary-coded GA [1] with GRBFF-PID

controller response

To validate the results obtained by the using GA and

RBF tuning by GA technique was applied for the

same values of Ke and te and the results are given in

Table 5. From the table, it is observed that the

values of controller parameters obtained are enhance

all cases because of RBF-NN. The proposed fuzzy

Ke τe Type Kp Ki Kd

2 0.5 GA 0.8348 0.4888 0.0238

RBF tuning by GA 0.8663 0.5155 0.08098

4 0.6 GA 0.8954 0.4995 0.0416

RBF tuning by GA 0.9272 0.52 0.1141

6 0.7 GA 0.6041 0.4936 0.1622

RBF tuning by GA 0.6369 0.5316 0.1947

8 0.8 GA 0.6696 0.4614 0.0073

RBF tuning by GA 0.7013 0.4964 0.04831

9

0.9 GA 0.7243 0.4844 0.1085

RBF tuning by GA 0.7569 0.5157 0.1575

9 0.95 GA 0.4125 0.4790 0.2519

RBF tuning by GA 0.4425 0.512 0.295

The 'Ts' parameter used in this modelis set to 10e-6 by the Model Properties Callbacks

Aircraft Electrical Power Generation

ContinuousIdeal Switch

powergui

fsys1

1

Volts > pu Va (pu)

v+-

Va

VabcA

B

C

abc

Three-Phase

V-I Measurement2

Synchronous generator

Scope5

Scope4

RT

speed supply

Prime Mover

GLC controlVabc

Iabcin_a

in_b

in_c

out_a

out_b

out_c

Primary Distribution(measurements & main

contactor)

?

More Info

Line 2

(300 km)1

L1 350 km

Iabc

Vabc_B1

Vabc_B2

P_B25

Q_B25

V1_Plant

I1_Plant

Motor_Speed

Grid

Data acquisition

Grid

Generator Control Unit (GCU)

-K-

?

Double click here for more info

Freq

Sin_Cos

abc

Mag

Phase

Discrete 3-phase

PLL-Driven

Positive-Sequence

Fundamental Value1

Vabc(pu)

Freq

wt

Sin_Cos

Discrete

3-phase PLL1

A

B

C

a

b

c

CB2

A

B

C

a

b

c

CB1

A

B

C

a

b

c

B5

A

B

C

a

b

c

B4

A

B

C

a

b

c

B1

Activate PrimaryContactor

A

B

C

a2b2c2a3b3c3

300 MVA

500/230 kV

A

B

C

30,000 MVA

500 kV1

A B CA B C

3-Phase Fault

A B C

250 MW

A

B

C

a

b

c

1000 MVA

13.8 kV/500 kV1

Field

Vabc

Iabc

Vabc_B120 (pu)

Vabc_B25 (pu)

P_B25 (MW)

Q_B25 (Mv ar)

Motor Speed (pu)

I Plant pos. seq. (pu/2 MVA)

V_Plant 2.3kV pos. seq. (pu)

Freq (Hz)

Freq (Hz)Mag. pos. seq. (pu)

Phase pos. seq. (deg.)

wt Va (pu)Va (pu)

Copyright 2004-2009 The MathWorks, Inc.2

GLC

1

Field voltage

0

abc

sin_cos

dq0

abc_to_dq0

Transformation

1

Vref

cos

sin

Terminator1

-K-

SI_PU

Relay

30/pi

Rad_Rpm

-K-

PU_SI1

s

Integrator

2

Gain

e u

FUZZY_PID

v ref

v d

v q

v stab

Vf

Excitation

System

3

PMG

2

voltage sensing

1

current sensing

Three-phase diode rectifier

Three-phase inverter 1

speed supply

-K-rad2rpm

speed

To Workspace1

torqueTo Workspace

N

N*

MagC

Flux*

Torque*

Ctrl

Speed Controller

Scope1

Scope

A

B

C

+

-

I_ab

V_abc

Ta

Tb

Tc

V_Com

Mta

Mtb

Mtc

Measuresg

A

B

C

+

- mA

B

C

Tm

Inductionmachine

MotorSpeed

load_torque

From

Workspace1

speed_in

From

Workspace

Torque*

Flux*

V_abc

I_ab

MagC

Gates

DTC

Meas.V L+

V L-

V +

V -

Braking chopper

A

B

C

460V 60Hz <Electromagnetic torque Te (N*m)>

<Rotor speed (wm)>

Manufacturing Engineering, Automatic Control and Robotics

ISBN: 978-960-474-371-1 131

PID controller is found to possess minimum time of

settlement, less rise time and overshoot in

comparison to that obtained by using the method of

LQR, RAG and binary-coded GA [1] as seen from

Fig.12.

4 Conclusion

We present a combined approach of GA, Sugeno

fuzzy logic and RBF-NN to determine the optimal

PID controller parameters in AVR system. The

RBF-NN is used to enhance the PID parameters

obtained from GA to design Sugeno fuzzy PID

controller tuned by excitation parameter (Ke,τe). The

GRBFF-PID controller possess preferable features

such as easy implementation, stable convergence

characteristic, good computational efficiency and

high-quality solution that keeps the system error

closer to zero. A novel combination can directly

deals with the real variables have been applied to

get the optimal parameter of PID fuzzy controller in

AVR. The dynamic performance of the AVR is

much improved with the proposed GRBFF-PID

controller. Furthermore, the results for the numerical

simulation offer a high response of the AVR system

compare to the RGA, LQR and GA, and the RBF

can generate the optimal PID values accurately in a

fraction of second, which solves the problems,

associated with evolutionary computation

techniques when used in an on-line application. The

excellent features of our method suggest that the

new technique automatically averts the over fitting

problem, which is adverse for many optimizations

and learning algorithms.

References: [1] Devaraj, D. and Selvabala, B. Real-coded

genetic algorithm and fuzzy logic approach for real-

time tuning of proportional-integral - derivative

controller in automatic voltage regulator system.

Generation, Transmission & Distribution, IET, 3, 7

2009), 641-649.

[2] D.H. Kim, A. A., and J.H. Cho A hybrid genetic

algorithm and bacterial foraging approach for global

optimization .Int. J. Inf. Sci., 177, 18 2007), 3918–

3937.

[3] K. Valarmathi, D. D., and T.K. Radhakrishnan

Enhanced genetic algorithm based proportional

integral controller tuning for pH process.

Instrument. Sci. Technol., 35, 6 2007), 619-635.

[4] Nasir, A. N. K., Tokhi, M. O., Abd Ghani, N. M.

and Ahmad, M. A. A novel hybrid spiral-dynamics

bacterial-foraging algorithm for global optimization

with application to control design. City, 2012.

[5] M.Shady. Gadoue, D. G. a. J. W. F. Genetic

Algorithm Optimized PI and Fuzzy Mode Speed

Control for DTC drives. London, U.K Proceedings

of the World Congress on Engineering 2007, 1,

WCE 2007 p. 2007, 1, WCE 2007, July 2-4, 2007.

2007).

[6] Gupta N, S. S., Dubey SP, Palwalia DK Fuzzy

logic controlled three-phase three-wired shunt active

power filter for power quality improvement.

International Review of Electrical Engineering

[Internet], 6, 3 2011), 1118-1129.

[7] Mokhlis H, L. J., Bakar AHA, Karimi M A

fuzzy based under-frequency load shedding scheme

for islanded distribution network connected with

DG. International Review of Electrical Engineering

[Internet], 7, 4 2012), 4992-5000.

[8] Vural AM, B. K. Transient stability

enhancement of the power system interconnected

with wind farm using generalized unified power

flow controller with simplex optimized self-tuning

fuzzy damping scheme. International Review of

Electrical Engineering [Internet], 7, 4 2012), 5091-

5107.

[9] Kavousifard, A. and Samet, H. Consideration

effect of uncertainty in power system reliability

indices using radial basis function network and

fuzzy logic theory. Neurocomput., 74, 17 2011),

3420-3427.

[10] T. Niknam, A. K. F., Jamshid Aghayi Scenario-

Based Multiobjective Distribution Feeder

Reconfiguration considering Wind Power Using

Adaptive Modified PSO. IET Renewable 6, 4 2012),

236?247.

[11] Niknam, T. and Kavousifard, A. Impact of

thermal recovery and hydrogen production of fuel

cell power plants on distribution feeder

reconfiguration. Generation, Transmission &

Distribution, IET, 6, 9 2012), 831-843.

[12] R. Yu, Z. C. a. H. Z. Optimal PID Controller

Design in PMSM Based on Improved Genetic

Algorithm 2nd International Conference on

Industrial Mechatronics and Automation 2010).

[13] L. Fan, E. M. J. D esign for auto-tuning PID

controller based on genetic algorithms. . Industrial

Electronics and Applications.2009), 1924-1928.

[14] Gwo-Ruey, Y. and Rey-Chue, H. Optimal PID

speed control of brush less DC motors using LQR

approach. City, 2004.

[15] Darken, J. M. a. C. Learning with Localized

Receptive Fields. Proceedings of the 1988

Connectionist Models Summer School1988), 133-

143.

Manufacturing Engineering, Automatic Control and Robotics

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[16] M.S.Ahmed Neural controllers for nonlinear

state feedback L2- gain control. IEE Proceedings of

Control Theory Applications, 147, 3 2000).

[17] Khandani, K., Jalali, A. A. and Alipoor, M.

Particle Swarm Optimization based design of

disturbance rejection PID controllers for time delay

systems. City, 2009.

[18] Krohling, R. A. and Rey, J. P. Design of

optimal disturbance rejection PID controllers using

genetic algorithms. Evolutionary Computation,

IEEE Transactions on, 5, 1 2001), 78-82.

[19] Zwe-Lee, G. A particle swarm optimization

approach for optimum design of PID controller in

AVR system. Energy Conversion, IEEE

Transactions on, 19, 2 2004), 384-391.

[20] Al Gizi, A. J. and Mustafa, M. Hybrid Neural

Genetic and fuzzy logic approach for real-time

tuning of PID Controller in AVR System. Life

Science Journal, 10, 4 2013).

[21] Yao-Lun, L., Chia-Chang, T., Wu-Shun, J. and

Shuen-Jeng, L. Design an Intelligent Neural-Fuzzy

Controller for Hybrid Motorcycle. City, 2007.

[22] Sang Jeen, H., May, G. S. and Dong-Cheol, P.

Neural network modeling of reactive ion etching

using optical emission spectroscopy data.

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[23] Shu-Kun Zhao, M.-W. K., Yi-Seul Han, Se-

Youn Jeon, Yun-Keun Lee, and Seung-Soo Han

Radial Basis Function Network for Endpoint

Detection in Plasma Etch Process. Springer-Verlag,

672010), 253–263.

[24] R. Anulmozhiyal and Dr. K. Baskarn Speed

Control of Induction Motor Using Fuzzy PI and

Optimized Using GA. International Journal of

Recent Trends in Engineering, 2, 5 2009), 2009.

[25] Neenu Thomas, D. P. P. Position Control of

DC Motor Using Genetic Algorithm-based PID

Controller. London, U.K Proceedings of the World

Congress on Engineering, , July 1-3, 2009. , 2,

WCE 2009 2009).

Appendix

Generation parameters

)(VAPn 1000E6 ][Hzfn 50 Inertia 0.02

)(VrmsVn

13800 Pairs of poles 2 Internal

impedance

R(ohm)

0.0204

Damping

factor

0 Initial

condition[dw,th(deg),ia,ib,ic(A)

,pha,phb,phc(de

g)]

[-99,0

0,0,0 0,0,0]

Sample time -1

L(H) 0.08104e-3 Regulator gain

and time

constant

[ 300, 0.001 ]

Excitation System

[vt0 (pu)

vf0(pu)

[1 0] Low_pass filter

time constant

20e-3 [Kf() Tf(s)] [ 0.001, 0.1 ]

Exciter

[Ke()

Te(s)]

[1,0] Transient gain

[Tb(s) Tc(s)]

[0,0] [Efmin,Efmax(

pu),Kp()]

[ -2, 2, 0 ]

Rotor parameters

)(VAPn 1100 ][Rs 0.435 ][Hzfn

50

)(VrmsVn 200 ][rR

0.816 ].[ 2mKgJ 0.089

0.78 ][HrLl 2e-3 ]..[ smNF 0.005

cos 0.8 ][HLls 2e-3 p 2

)..( mprN 3600 ][HLm

69.31e-

3

Manufacturing Engineering, Automatic Control and Robotics

ISBN: 978-960-474-371-1 133