Performance Indices Based Optimal Tunining Criterion for Speed Control of DC Drives Using GA

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 4, No. 4, December 2014, pp. 461~473
ISSN: 2088-8694  461
Journal homepage: http://iaesjournal.com/online/index.php/IJPEDS
Performance Indices Based Optimal Tunining Criterion for
Speed Control of DC Drives Using GA
Deepti Singh*, Brijesh Singh**, Nitin Singh***
* Departement of Electrical Engineering, Ashoka Institute of Technology and Management, Varanasi-India
** Departement of Electrical Engineering, IIT (BHU) Varanasi-India
*** Departement of Electrical Engineering, MNNIT, Allahabad-India
Article Info ABSTRACT
Article history:
Received May 27, 2014
Revised Jul 2, 2014
Accepted Jul 25, 2014
This paper presents a framework to carry out a simulation to tune the speed
controller gains for known input of DC drive system. The objective is to find
the optimal controller gains (proportional and integral) in a closed loop
system. Various performance indices have been considered as optimal
criterion in this work. The optimal gain values have been obtained by
conventional and Genetic Algorithm (GA) based optimization methods. The
study has been conducted on a simulink model of three phase converter
controlled direct current (DC) drive with current and speed control strategy.
The results show that the GA based tunning provided better solutions as
compared to conventional optimization methods based tunning.
Keyword:
DC motor drives
Gains tuning
Genetic Algorithm
Optimization
Performance indices
Speed controller Copyright © 2014 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Brijesh Singh,
Departement of Electrical Engineering,
IIT (BHU) Varanasi, India-225001.
Email: singhb1981@gmail.com
1. INTRODUCTION
The introduction of variable-speed drives increases the automation, productivity and efficiency of
process and control industries. Nearly 65% of the total electric energy has been consumed by electric motors
world-wide. This is a known fact that the energy consumption can be reduced by decreasing the energy input
or by increasing the efficiency of the mechanical transmission during processes. The system efficiency can be
increases from 15 to 27 % using variable speed drives in place of constant speed drives. At present, most of
the electric drives (75-80%) still run at constant speed. Only some smaller numbers of drives (20-25%) are
used in process and control industries whose rate of change of speed and torque is varied to match the
mechanical load. These drives are basically DC drives which have been used in electric traction. The DC
motors can be considered as single input and single output systems (SISO) systems. In these motors, the
torque/speed characteristics are compatible with most of the mechanical loads. The modern electric drives are
capable to control the speed and obtained variable speeds for the loads. Mainly, an electric drive has various
important parts such as electric motor, power electronic converter (PEC), drive controllers and load. A
number of modern industries require variable speed drives for there efficient and economical operations. The
variable speed DC motors have been frequently preferred by these industries. Also, the brushless DC motors,
nduction motors and synchronous motors have provides a variable speeds which is widly used in electrical
traction. However, the behaviour of DC motors with respect to dynamic loading conditions is good as
compared to thses motors and also there speed control strategies are simpler. Consiquenly, the DC motors
have also been provides a good ground to apply the advanced control algorithms in its speed control

 ISSN: 2088-8694
IJPEDS Vol. 4, No. 4, December 2014 : 461 – 473
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operations. Therefore, DC drives using DC motors are more preffered as compaterd to AC drives in process
and control industries.
Normally closed loop operation with PI controllers in the inner current loop and the outer speed loop
is employed for speed control. In fact, the Proportional-Integral-Derivative (PID) controllers are widely used
in the process industries even though more advanced control techniques have been developed. Mostly, these
advanced control stretegies have been used to determine the parameters of PID controller in single input
single output (SISO) systems. In this work, a comparision has been presented in between applications of
conventional and modern optimization techniques based on Gradient-Decent and Gentic Algorithm (GA) on
speed control strategies of DC drives. A considerable number of works on application of GA in process and
control industries have been reported by various recherchers in different time frames. Mostly, the GA based
methodology has been applied for identification of both continuous and discrete time systems [1]-[4]. First
time, Man & tang was introduced applications of GA in engineering fields [5]. A design method which
determines PI/PID parameters of motion control systems based on genetic algorithms (GAs) has been
presented in [7]-[12]. These papers propose an analytical procedure to obtain the optimal PI/PID parameters.
The implementational issue related to premature convergence of GA in some applications have been
examined and reported in [13]-[16]. Thereafter, the applicability of GAs as an optimization tool for process
controllers and the solution of premature converges in GA based optimization has been explained in [6]. The
GA method cans easily interated with other optimization techniques. A GA and neuro-fuzzy based
optimizations have been presented to solve the speed control problems of DC motors [17]-[22]. A multi-
objective and performance indices based optimization for tunning of PID controllers have been simulated by
different researchers [24]-[32]. The speed control of a linear brushless DC motor using soft computing based
optimization for determining the optimal parameters PID controller has been reported in [33]. Recently, some
of the new advancements have been carried out in the field of brushless DC drive control using adaptive and
robust control theories [40]-[42]. The work presents a study of steady–state behavior of DC motors supplied
from power converters and their integration to the load. The paper was repotrted a comparative study of
conventional PI controllers such as PI speed and current controller over GA based PI controller using transfer
function approach.
In fact, the speed control methods of a DC drives are simpler and less expensive in comparision to
AC drives. The speed control of DC drives below and above rated speed can also be easily achieved. The two
types of controls have been used for controlling the speed of DC drives, armature control and field control.
Sometimes, these methods have been combined to yields a wider range of speed control. Usually, the speed
control operation of DC drives have been classified into three types; single, two and four quadrant operations.
In each operation a unique set voltage and current have been applied to the armature and field winding of DC
motors. In this work, the main emphasis has been given on two quadrant operation of DC drive [34]-[36]. In
two quadrant operation, a converter–controlled separately excited DC motor has been used for obtaining the
variable speed. The current or speed signals are processed through a proportional plus integrator (PI)
controller to determine the control command which provides a desired speed opretion. In this operation, the
control command kept within the safe limits. These control commands also required proper scaling [37] and
[38]. In this, if the rotor achives a recommended value then the control command will settle down to a value
which is equal to the sum of load torque and other motor losses. This condision is required to keep the motor
in steady state condition. The proper selections of gains and time constants of the speed and current
controllers is also utmost important criterion for meeting the dynamic specifications of drives [39]-[45]. In
this work, the design of controllers and their implementation for DC drives have been presented. The system
analysis and design of the motor drive are kept in perspective with regard to current practice. The present
work uses the performance indices as one of the optimization criterions for optimal tunning of PID
controllers in a DC drive system. The control algorithms and analysis have been developed to facilitated
dynamic simulation with personal computers. Also, the applications of motor drives have illustrated with
selections from industrial environment.
2. PROPOSED METHOD
In this work, seperataly exicited DC motor drive has been considered as a test system model. To
investigate the effects of conventional and GA based tunning, the MATLAB simulink model of a separately
excited DC motor with speed and current controllers have been developed on the basis of mathematical
formulations. The mathematical and simulink models for separately excited dc drive system using transfer
function approach have been dissucussed in subsequent sections.

IJPEDS ISSN: 2088-8694 
Performance Indices Based Optimal Tunining Criterion for Speed Control of DC Drives… (Deepti Singh)
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2.1. Mathematical Concepts of Speed Control of DC Motor using Electromechanical Coversion
For simplicity, the load is modeled as a moment of inertia, J, in kg – m2
/sec2
, with a viscous friction
coefficient B1 in N.m/(rad/sec) then the acceleration torque, Ta, in N.m drives the load and is given by:
J(dω/dt) + B1 ωm = Te – T1 = Ta (1)
Where T1 is the load torque. Equation (1) constitutes the dynamic model of the DC motor with load. Now, the
motor equation can be represented with neglecting all the initial conditions as:
Ia (s) = [V(s) – Kb ωm (s)] / [Ra + sLa] (2)
ωm (s) = [Kb Ia (s) – T1(s)] / [B1 + sJ] (3)
These equations can be representred in block–diagram forms as shown in Figure 1 [43]. Thus, the transfer
functions ωm (s) / V(s) and ωm (s) / T1(s) can be derived from block diagram shown in Figure 1.
These transfer fuctions are as:
Gωv(s) = ωm (s) / V(s) = Kb / [s2
(JLa) + s (B1La + JRa) + (B1 Ra + Kb
2
)] (4)
Gω1(s) = ωm (s) / T1(s) = - (Ra + sLa) / [s2
(JLa) + s (B1La + JRa) + (B1 Ra + Kb
2
)] (5)
Figure 1. Block diagram of the D.C. motor
It is a known fact that the separately–excited DC motor is a linear system. Therefore, the variation in
speed due to simultaneous voltage input and load torque disturbance can be written as a sum of their
respective individual speeds.
ωm (s) = GωV(s) V(s) + Gω1(s) T1(s) (6)
The induced voltage due to field flux and speed can be derived as:
e = K Φf ωm (7)
Where e = back e.m.f., K = motor constant, Φf = field flux and ωm = motor speed.
Usually, the field flux is proportional to the field current if the iron is not saturated and is
represented as.
Φf α if (8)
By substituting (7) in Equation (8), the speed is expressed as:
(9)
Where v and ia are the applied voltage and armature current, respectively. From (9), it is seen that the rotor
speed is depence on the applied voltage and field current. Since, the voltage drop in resistive armature is very
small as compared to the rated applied voltage and the armature current becomes a secondary effect. Mostly,
in a current control operation, the armature current should create dominating effects and to make a
dominating armature current, an external resistor has been connected in series with armature winding. The
speed of the motor has been controlled by varying the value of external resistor in step wise. As an effect, the
power dissipation in the external resistor leads to lower efficiency. Therefore, in the present work the
converter control has been used to obtain the desire speed using optimal tunning of PI current and speed
controllers. In the present work, two methods, armature voltage control and field current control have been

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considered for speed control of a DC motor [36]. It is known that, the applied armature voltage is maintained
constant during field current control method. Then the speed of motor can be represented as:
ωm α 1 / if (10)
This equation shows that the rotor speed is inversely proportional to the field current. Since, by
varying the field current, the rotor speed is changed and if the field current is reversed then the rotational
direction has also been changed. Therfore, the speed can be increased or decressed by weakening or
stranghting the field flux. Similarly, the field current is maintained constant in the armature control method
and the speed is derived from (9) as:
ωm α (v – ia Ra) (11)
The speed of drive can be varying by changing the applied voltage across the armature windings.
Equation (11) shows that the reversal of applied voltage changes the direction of rotation of the motor. The
armature current control method has an advantage to control the armature current rapidly by adjusting the
applied voltage. As a result, a wide range of speed control is possible by combining the armature and field
control for speeds below and above the rated speed respectively. To obtain the speed lower than its rated
speed, the applied armature voltage is varied while the field current is kept at its rated value in this
combination. On the other hand, to obtain speeds above the rated speed, field current is decreased while
keeping the applied armature voltage constant. Now, the torque of the motor can be drived as:
Te = K Φf ia (12)
Equation (12) can be normalized if it is divided by rated torque, which is expressed as:
Ter = K Φfr iar (13)
Where the additional subscript r denotes the rated or nominal values of the corresponding variables. Hence
the normalized version of (12) is:
, (14)
Where the additional subscript n express the variables in normalized terms, commonly known as per unit
(p.u.) variables.
2.2. Transfer Function Modeling of DC Drive System
In the present case study, a contant field flux has been considered for the DC motor operation. The
DC motor parameters, rating and the mathematical models of different subsystems of the test maodel are as
follows
DC motor specifications:
DC motor input voltage = 220V; Armature current rating = 8.3A; Rated speed = 1470 rpm;
Armature resistance Ra = 4Ω; Moment of inertia J = 0.0607 kg – m2; Armature Inductance La = 0.072 h ;
Viscous friction coefficient Bt=0.0869 N – m/rad/ sec and Torque constant Kb = 1.26 V/rad/sec.
Converter specifications:
Supplied voltage = 230 V, 3 – phase A.C.; Frequency = 60 Hz; Maximum control input voltage is ±
10 V. The speed reference voltage has a maximum of 18 V. the maximum current permitted in the motor is
20 A. For the simulation, the transfer function of all subsystems of given plant model as follows:
Motor-Load connected system transfer function
(15)
(16)
1 2 2
0.0869
0.0449
1.26 4 0.0869
t
b a t
B
K
k R B
  
  
2
2
1 2
1 1 1 1
,
2 4
t a t a b a t
a a a
B R B R K R B
T T J L J L JL
     
           
     

465
(17)
So the motor and load subsystem transfer functions are:
1
1 2
( ) (1 )
Motor transfer function
( ) (1 )(1 )
0.0449(1 0.7 )
(1 0.0208 )(1 0.1077 )
a m
a
I s sT
K
V s sT sT
s
s s


 


  (18)
( ) / 14.5
Load transfer function
( ) (1 ) (1 0.7 )
m b t
a m
s K B
I s sT s

 
  (19)
Converter transfer function:
The rated DC motor voltage required is 220 V, which corresponds to a control voltage of 7.09 V.
(20)
(21)
The transfer function of the converter is:
(22)
(23)
(24)
Current controller transfer function:
(25)
(26)
(27)
So,
(28)
(29)
1
2
0.1077 sec.
0.0208sec.
0.7 sec.m
t
T
T
J
T
B


 
1 .3 5 1 .3 5 2 3 0
3 1 .0 5 /
1 0
r
c m
V
K V V
V

  
(max) 310.05dcV V
( )
( )
( ) 1
a r
r
c r
V s K
G s
V s sT
 

60 / 2
(time period of one cycle)
360
rT  
1 1
,sec. 1.388 . 0.00138sec.
12 s
ms
f
   
31.05
( )
1 0.00138
rG s
s


(1 )
( ) c c
c
c
K sT
G s
sT


2 0.1077 sec.cT T 
2
2 r
T
K
T

0 .0 0 1 3 8rT 
0.1077
38.8
2 0.00138
K  


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(30)
So,
(31)
(32)
(33)
Current control loop approximation:
(34)
(35)
(36)
(37)
(38)
(39)
(40)
So,
(41)
(42)
Speed controller transfer function:
(1 )
( ) s s
s
s
K sT
G s
sT


(43)
2
2 4
1
;
2
i b
s
t m
K K H
K K
K T B T

 
(44)
4 4; 4i w sT T T T T  
(45)
1
2.33c
c
c r m
KT
K
K H K T
 
138.8; 0.208sec; 0.0449; 0.355 /c cK T K H V A   
31.05 / ; 0.7 sec.r mK V V T 
21.63(1 0.107 )
Therefore ( )c
s
G s
s


*
( )
( ) 1
a i
a i
I s K
I s sT


1
.
(1 )
fi
i
c fi
K
K
H K


1
38.8c r m c
fi
c
K K K T H
K
T
 
2.75
c
iK 
3
1
i
fi
T
T
K


3 1
where
0.109rT T T  
0.0027sec.iT 
( )
1
i
c
i
K
G s
sT


2.75
Therefore with current loop approximation ( )
1 0.0027
cG s
s



467
4 0.0027 0.002 0.0047i wT T T    
(46)
2 3.70i b
t m
K K H
K
B T

 
(47)
2 4
1
28.73
2
sK
K T
 
(48)
44 0.0188sec.sT T 
(49)
28.73(1 0.0188 )
( )
0.0188
s
s
G s
s


(50)
Current transducer gain:
The maximum safe control voltage is 18V, and this has to correspond to the maximum current error.
Here in present case study, it has been accepted as unity value. Therefore,
(51)
The Tacho-generator transfer function is given in problem”
(52)
Now, develop a Simulink plant model in MATLAB/SIMULINK with these subsystem transfer
functions, which is shown in Figure 2 and find the different simulation results for various cases on this plant
model for a variable speed operation. Also, analyze the effect of different controller on dynamics of DC
motor control operation.
(a) (b)
Figure 2. Typical Plant model with (a) speed and (b) current control based methodologies
2.3. Problem Objective and Optimal Criterion
The main objective function in this work is to minimize the steady state error, rise time, overshoot
and settling time during speed control of DC drive. The objective function can be represented as:
Minimize
(53)
Where,
1
In this, the objective function J provides an operating point which is generally a relation of four
weighted terms of PID controller and depending on the values of weights α1, α2, α3 and α4. The weights, α1,
α2, α3 and α4 are the weighting factors of the steady state error, rise time, overshoot and settling time. In the
present work, the performance indicies of ITAE, ISE, IAE, ITSE, and IT^2SE have been considered as
optimization criteria. These performance indicies are as follows:
1.0 /cH V A
( ) 1G s 

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a) Integral of square of the error
∞
b) Integral of the absolute magnitude of the error | |
∞
c) Integral of time multiplied by absolute error | |
∞
d) Integral of time multiplied by squared error | |
∞
e) Integral of time squared multiplied by squared error ^2
∞
The optimized controller parameters have been obtained by minimizing these performance indices.
The main objective of this work is to improve the performance of the test system model.
3. RESEARCH METHOD
In this work, Zigeler-Nichols, Gradient-descent and Genetic Algorithm based optimization
techniques have been used to tune the PI controller parameters for the test model of DC motor drive with
various performance indices based optimization criterions. The results obtained through simulation using
proposed techniques have been compared with each other. The MATLAB PID optimizer tool has been used
to apply these optimization techniques for tuning the PI controllers. The proposed solution methodology
based plant model has been shown in Figure 3.
Figure 3. Proposed solution methodology based plant model
3.1. Zieger-Nichols (Z-N) PID Tuning Using Trial and Error Based Optimization
In the present work, the Zieger-Nichols (Z-N) tuning has been used to obtain the initial tunning
values for PID controllers and then design the controllers for the study of system. Once, the initial tuned
values of PID parameters have been obtained, and then it has been optimized by the trial and error method.
This method is based on calculation of critical gain Ker and critical period Per. Initially, the integral time Ti
has been set to infinity and the derivative time Td is to zero. This has been used to get initial PID setting for
the test system. In Z-N method, only the proportional control action would be used and the Kp has been
increased to a critical value Ker which has been exhibited the case of sustained oscillations of system output.
In this method, if the system output does not exhibiting the sustained oscillations then it is not useful for the
application. These are the following steps to obtain the tuned value of PID parameter for a given plant.
Steps1: Substitute Ti = ∞ and Td = 0 for reducing the complete transfer function of a close loop
transfer system.
Step 2: Check that the system is marginally stable by Routh’s Criterion:
If sytem output offeres sustained oscillation, then system is marginally stable,
Else not marginally stable.
Step 3: Determined the value of Kp by Routh’s Stability criterion and set Kp = Critical gain Ker.
Step 4: Calculate the frequency (ω) of sustained oscillation by substituting jω in place of s in
characteristic equation.
Step 5: Calculate the period of sustained oscillation as Per = 2π / ω.
Step 6: Estimate the parameters of Kp, Ti and Td by the second Z-N frequency method.
Step 7: Obtain the complete transfer function of PID controller.
3.2. A Classical Optimization Technique – Gradient-Descent Optimization Algorithm Based Approach
In fact, this is a first-order optimization method. The main idea of this optimization method is to
reach the minima by the shortest path. In order to achieve the shortest path, the steepest gradient have moving
down and then this will lead to reach the minima. Fundamentally, when the gradient changes from point to
point then significantly choose a new direction and make changes accordingly to ensure the steepest path. In

469
this method, the minimization of the error function has been achieved by analyzing the function of error
function. To find a local minimum of a function, select the steps at the current point in proportional to the
negative of the gradient (or of the approximate gradient) function. This method is also known as steepest
descent, or the method of steepest descent. Fundamentally, the gradient descent is based on the observation
that if the multivariable function F(x) is defined and differentiable in a neighborhood of a point a, then F(x)
decreases fastest if one goes from a in the direction of the negative gradient of F at a, ( )F a . It follows
that, if ( )b a F a   for 0  a small enough number, then F(a) ≥ F(b). Using this observation, the
solution starts with a guess X0 for a local minimum of F, and considered that the sequence X0 and X1, such
that 1 ( ), 0n n n nX X F X n     . Here 0 1 2( ) ( ) ( ) ...........F X F X F X   and due to this the sequence (Xn)
converges to the desired local minimum. It is also noted that the value of the step size γ is changes in every
iteration with certain assumptions on the function F (for example, F convex and F Lipschtz) and particular
choice of γ (e.g., chosen via a line search that satisfies the Wolfe conditions). In this way the convergence to
a local minimum can be guaranteed. Now, if the function F is convex then all the local minima have also
been global minima then in this case the gradient descent has been converged to the global solution. This
process has been illustrated by Figure 4. Here it is assumed that the function F has been defined on a plane
and its graph has a bowl shape. In the Figure 4, the curves show the contour lines and these are lies on that
region in which the value of F is constant. The arrow originating at a point shows the direction of the
negative gradient at that point. It is noted that the (negative) gradient at a point is orthogonal to the contour
line going through that point. It has been seen that gradient descent leads to the bottom of the bowl which is
the point where the value of the function F is minimal.
Figure 4. Illustration of gradient descent optimization technique
3.3. Genetic Algorithm Optimization Based Approach
Genetic algorithms (GAs) have been based on search mechanisum based on biological organisms
which have been adapted and flourished changing and highly competitive environment. This can also be
applied to optimize the parameters of complex non-linear process controllers. The adpotibility of non-
linearity in the computational process makes it one of the more efficient techniques compared to other
traditional optimization techniques. GAs plays an important role in process control applications for the
optimization of parameters. This method can quickly solve the various complex optimization problems such
as problems of reliablity and accuracy. These are some of the mojor qualities of GAs are
a) Genetic algorithms search a population of points in parallel, not from a single point.
b) Genetic algorithms do not require derivative information or other auxiliary knowledge; only the
objective function and corresponding fitness levels influence the direction of the search.
c) Genetic algorithms use probabilistic transition rules, not deterministic rules.
d) Genetic algorithms work on an encoding of a parameter set not the parameter set itself (except
where real-valued individuals are used).
e) Genetic algorithms may provide a number of potential solutions to a given problem and the
choice of the final is left up to the user.
In the present work, some of the important issues have been considered for optimizing the plant
behaviour with proper implementation of GA such as decision of population size. Mostly, the population size
has been considered in between 20 to 30 chromosomes. It is a well known fact that the big population size
consumes more computational time for finding the optimum solution and this may cause of deterioration in
performance of GA. Sometimes, the problem of premature convergence has been arised due to improper
selection of crossover rates. The premature convergence problems have been minimized by considering the

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recommended higher rate of crossover of about 85 percent to 95 percent. The low mutation rate of about 0.5
percent to 1 percent is generally recommended to obtain optimized results from GA. In fact, the mutation is
an artificial and forced method of changing the numerical value of the chromosome. Mutation should be
avoided as far as possible because it is totally random in nature. Small mutation rates prevent genetic
algorithms from falling into local maxima or minima. Deciding of selection method for selecting good
chromosomes is another important issue while applying genetic algorithms for process control applications.
Rank selection method and roulette wheel selection methods have shown good results over other methods of
selection.
4. RESULTS AND DISCUSSION
In the present work, conventional and optimal tuning methods of PI controller with both control
strategies (speed control and current control) for DC motor drive system have been considered as test cases.
In the convetional tunning method the trial and error based Z-N methodology has been used to tune the PI
controllers. On the other hand, the Gradient-Descent (GD) and GA based optimization methods have been
considered for PI tunning. The performance of suggested techniques has been tested on a DC motor drive
system. The overall transfer function of system model has been reduced into second order transfer function
system model using truncation based methodology. In this method, the higher orders have been neglected
from the overall transfer function. As a result, the overall transfer function of converter and motor-load
connected system or in other word the plant model for current control and speed control strategy has been
given as:
TF Current control
. .
. .
TF Speed control
. .
. .
Case: 1 The PI Tuning by using conventional trial and error based Z-N methodology
The performance of the system with Z-N based tunning in the control loop has been tabulated in
Table 1.
Table 1. Performance of system with trial and error method based on Z-N method
Performance parameters Current control Speed control
Set value (p.u.) 1 1 p.u.
Settling time (sec) 12.228 12.10
Overshoot -- --
KP 0.04463 0.00125
KI 0.51939 0.0251
Case: 2 Optimal tuning of PI controller parameter using Evolutionary optimization based method
(GD and GA based)
In this section, the results obtained using GD and GA based optimization algorithm has been
disscussed. These results have been analyzed for the smallest overshoot, fastest rise time and the fastest
settling time response of the designed PI controller for test system. The best tuned values have been selected
for the system operations. The responses obtained by GD designed PI and GA designed PI have been
compared. The Table 2 and 3 shows the performance of system with GD based optimization method for
current and speed loop respectively. Similarly, Table 4 and 5 shows the performance of GA based
optimization for current control and speed control. The results shown in Table 1 to 5 are revels that the GA
based optimization provides better solutions using ITAE performance index as an optimal criterion as
compared to GD based optimization method.
Table 2. Performance of system using GD based optimization in current control
Optimization criterion Kp Ki Mp (p.u.) Ts (Sec.) e2
(t) ∫e2
(t)
ITAE 0.0390 0.4962 1.14 7.286 0.72 1.68
ISE 0.0781 0.5227 1.25 9.36 0.74 1.10
IAE 0.0504 0.5088 1.18 7.33 0.72 1.50
ITSE 0.0612 0.5103 1.2 7.88 0.72 0.70
IT^2SE 0.0448 0.4983 1.15 7.07 0.71 0.70

471
Table 3. Performance of system using GD based optimization in speed control
Optimization Criterion Kp Ki Mp (p.u.) Ts (Sec.) e2
(t) ∫e2
(t)
ITAE 0.0157 0.0330 1.03 6.35 0.048 1.4
ISE 0.0259 0.0354 1.17 10.85 0.048 1.2
IAE 0.0185 0.0336 1.03 6.11 0.049 1.5
ITSE 0.0222 0.0357 1.11 8.6 0.05 0.69
IT^2SE 0.0195 0.0350 1.06 6.13 0.049 0.73
Table 4. Performance of system using GA based optimization in current control
(t) ∫e2
(t)
ITAE 0.0167 0.4793 1.08 6.775 0.72 1.55
ISE 0.0863 0.4996 1.21 9.29 0.73 1.13
IAE 0.0489 0.5118 1.19 8.72 0.71 1.5
ITSE 0.0710 0.5163 1.22 9.35 0.73 0.71
IT^2SE 0.0396 0.5120 1.17 7.6 0.72 0.79
Table 5. Performance of system using GA based optimization in speed control
(t) ∫e2
(t)
ITAE 1.0133 0.0302 -- 5.4 0.05 1.51
ISE 0.0203 0.0514 1.428 11.9 0.049 1.40
IAE 0.0311 0.0326 1.21 13.05 0.05 1.7
ITSE 0.0155 0.0429 1.25 10.93 0.05 1.0
IT^2SE 0.006 0.0212 -- 7.3 0.06 2.5
5. CONCLUSION
In the present work, optimal PI tuning based controller using current control and speed control
strategies have been modeled and simulated on MATLAB/SIMULINK package for complete DC drive
system. These controllers have been tuned for motor load connected system by using current control and
speed control loop of the transfer function models. The tuning of PI controllers has been tuned using Z-N,
GD and GA based optimization techniques. The current control and speed control loop of the drive was
simulated with a conventional PI controller in order to compare the performances to those obtained from the
respective GD and GA based drive system. The steady state performance of the GA based controlled drive is
much better than the conventional and GD based optimal PI controlled drives.
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BIOGRAPHIES OF AUTHORS
Deepti Singh belong to Allahabad, DOB is 04.10.1985, Recived her B.Tech in Electrical and
Electronics Engineering in 2008 from UP Technical University, Lucknow. Presently she is
working as faculty member in department of Electrical Engineering, AITM, Varanasi. Her field
of interest includes optimization in control systems and AI applications.
(deeptisingh1434@gmail.com)
Brijesh Singh belong to Jaunpur, DOB is 05.12.1981, Received his B.Tech in Electrical
Engineering in 2003 from IET, Purvanchal University Jaunpur, M.Tech (Power system) in 2009
from KNIT Sultanpur (UP). Presently he is Ph.D. (power system) research scholar in department
of Electrical Engineering, IIT (BHU), Varanasi. His field of interest includes Power system
operation & control, optimization and Artificial Intelligence.
(singhb1981@gmail.com)
Nitin Singh born in 20.08.1981, Recived his M.Tech. from D.I.E. Agra (UP). Presently he is
working as faculty member in department of Electrical Engineering, MNNIT, Allahabad. His
field of interest includes Power systems, Artificial Intelligence and Electrical Machines.
(nitins@mnnit.ac.in)

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