PID controller Separate Excited DC motor with Matlab simulink.

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Contents
1 INDRODUCTION ......................................................................................................... 1
2 Separately Excited DC Motor ........................................................................................ 1
2.1 The DC Motor Model ............................................................................................. 2
2.2 Simulink Modelling DC Motor............................................................................... 3
3 TURNING OF PID CONTROLLER USING................................................................ 4
4 GENETIC ASGORITHM.............................................................................................. 6
5 TUNING METHODOLOGY ........................................................................................ 7
5.1 Conventional PID controller Tuning Method......................................................... 7
5.2 GA-based optimization........................................................................................... 8
6 SIMULATION RESULTS AND DISCUSSION .......................................................... 9
7 CONCLUSIONS.......................................................................................................... 10

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List of Figures
Figure 1 The schematic diagram of DC motor...................................................................... 2
Figure 2 Simulink Modeling of DC motor............................................................................ 3
Figure 3 PID Controller with System.................................................................................... 5
Figure 4 Flowchart of GA for PID tuning............................................................................. 7
Figure 5 Step input of uncontrolled DC motor drive system ................................................ 8
Figure 6 PID-GA Controller with system ............................................................................. 8
Figure 7 Step input of PID controlled DC motor drive system............................................. 9
Figure 8 Step input of PID-GA controlled DC motor drive system...................................... 9
Liat of Tables
Table I. Motor of Parameters................................................................................................. 4
TABLE. II.ZEIGLER-NICHOLS TURNING RULE BASE................................................ 4
TABLE. III.EFFECT OF INCREASING THE PID CONTROLLER PARAMETERS ...... 5
TABLE.IV. PERFORMANCE COMPARISION OF PARAMETER PID & PID TUNED
......................................................................................................................................... 10

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1 INDRODUCTION
The DC motor has been generally utilized as a section of industry not withstanding despite
the way that it’s up keep charge is higher than the inciting. Relating Integral Derivative (PID)
controllers have been generally utilizes for speed and position control of DC motor
framework. The paper accomplishment is to design a control inspiration utilizing Genetic
Algorithm with taking into consideration of nonlinearity capable of for the construction.
Acquired Algorithm or in diminutive (genetic algorithm) GA is a stochastic compute making
an allowance for the models of standard structure and less expensive The target of this paper
is to look at the execution of Genetic Algorithm (GA) for flawless tuning of PID controllers
parameters and number their reasons of excitement over the basic tuning framework Genetic
Algorithms (GA) are adaptable heuristic solicitation considering transformative
contemplations of conventional choice and inherent qualities. Characteristic Algorithms are
proficient and clever decisions under the best conditions game-plan among the rate of each
achievable blueprint. The Genetic Algorithms were utilized to overview the ideal PID
controller extension values where execution records, IAE were utilized as far as possible. It
was probably settled that the Integral of Absolute Magnitude of the error (IAE) execution
foundation delivers the best PID controller when contrasted and other execution paradigm.
The proposed procedures were confirmed utilizing a second request physical model of plant
as DC motor (separately excited DC motor) where tuning calculations were driven for the
most part by the obtained framework information and the coveted execution parameters
determined by the client are effectively fulfilled. Resultant upgrades on the stride reaction
conduct of DC motor speed control framework are appeared for two cases. This paper is
composed as takes after: system modelling of DC motor is displayed in section II, PID
controller brief describe in section III, brief prologue to genetic algorithm is talked about in
Section IV, main work of this paper describe in Section V and last two Section VI and VII
individually describe simulation result and conclusion of this paper speed control of dc
motor.
2 Separately Excited DC Motor
The section diagram of an independently energized DC motor drive speed control framework
with a PID controller is appeared in Fig.3.The Separately Excited DC (SEDC) motor drive
system structure through armature control and the voltage apply to armature of the is
instantly recognizable without rearrangement the voltage productive to the field. Fig.1.
shows a generously breathed life into DC climbs to outline (SEDC). It is created of the circuit
model of dc using MATLAB/Simulink as showed up in Figure.2. In this uncommon case
through the supply gave an energetically to armature winding and field winding. The tenet
another or demanding make-up in these sorts of dc motor is with the key foundation taking
after the field reshaping in does not stream the armature current in light of the way that, the
field winding is displeased from another outside source of dc current. DC motor gives
astounding rate for motor of control require of their regulation parameters, for outline,
position, speed, broadening pace thus on [5]. DC motor is a world class drive. The DC motor
drive relies on upon the key, while a in attendance departing on conductor is to be found in

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an involving with fields, it experiences a force which tends to move. This is known as
motoring improvement or turning limit, when drawing in field and electric field group up
they make a mechanical force.
2.1 The DC Motor Model
Figure 1 The schematic diagram of DC motor
( )
( ) ( )a
a a a a b
di t
V R i t L e t
dt
  
( ) ( )b be t K t (1)
( ) ( )
( )
( ) ( )
m m a
m ma m
T t K i t
d t
T t J B t
dt



 
Laplace Transform
( )
( ) ( ) ( )
( ) ( )
( )
( ) . ( ) . . ( )
( ) . ( ) . . ( ) . ( )
a
a a a a b
b b
a
a a a a b
a a a a a b
di t
V t R i t L e t
dt
e t K t
di t
V t R i t L K t
dt
V s R i s L s i s K s



  

  
   
( ) . ( )
, ( )
.
a b
a
a a
V s K s
so i s
R L s



(2)
( ) . ( )
_
( ) . ( )
m m a
m m a
T t K i t
Laplace transform
T s K i s


(3)
( )
( ) . . ( )
_
( ) . . ( ) . ( )
( )
( )
.
m ma m
m ma m
m
m ma
d t
T t J B t
dt
Laplace transform
T s J s s B s
T s
s
B J s


 

 
 



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2
( )
( )
( ) . . ( . ). .
out m
in a a m a m a m a m m b
V Ks
H s
V V s L J s L B R J s R B K K

  
   
(4)
1
( ) . ( )s s
s
  (5)
Where
Ra = armature resistance
La = armature inductance
Ia = armature current
Va = armature voltage
Eb = back emf
W = angular speed
Tm = motor torque
 = angular position of rotor shaft
Jm = rotor inertia
Bm = viscous friction coefficient
Km = motor torque constant
Kb = back emf constant
2.2 Simulink Modelling DC Motor
Figure 2 Simulink Modeling of DC motor

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TABLE I. Motor of Parameters
Parameters Value
Armature inductance (Henry) La = 0.1215H
Armature resistance (ohm) Ra = 8.2Ω
Rotor inertia (kg m2
) Jm = 0.02215 kgm2
Armature voltage (Volt) Va = 240V
Viscous friction coefficient (Nm s/rad) Bm = 0.002953Nms/rad
Motor torque constant (Nm/A) Km = 1.28Nm/A
Back emf constant (V s/rad) Kb = 1.28Vs/rad
Speed (rpm) ω = 1500rpm
3 TURNING OF PID CONTROLLER USING
There are two strategies for determination of the parameters of PID controllers called
Ziegler-Nichols tuning rules. Be with the purpose of as it may, the broadly acknowledged
strategy for tuning the PID controller is clear technique. In the first place, set the controller
to P mode as it were. Next, set the gain of the controller (KP) to a little esteem. If KP the off
chance that is low the reaction should be Sluggish. Increment KP by a component of two
and Continue expanding KP (by a component of two) until the reaction gets to be oscillatory.
At long last, change until a reaction is acquire that creates nonstop motion. This is known as
a definitive addition (KU) or. Note that the time of the motions is known as extreme period
(TU).
The strides compulsory for the technique are given underneath: -
 The necessary and subordinate coefficients need to set (increases) to zero.
 Gradually build the corresponding coefficient from zero to until the framework just
starts to sway persistently (maintained wavering) Ku
The relative coefficient as of right now is known as a definitive the distinctive reactions of
DC motor, for instance, scattering and creation can corrupt the execution of standard
controllers. [6].
The Ziegler-Nichols Tuning Rule are then obtained from the following Table (II),
TABLE. II.ZEIGLER-NICHOLS TURNING RULE BASE
Controller
Type
KP KI KD
P Ku/2
PI Ku/2.2 Tu/1.2
PID Ku/1.7 Tu/2 Tu/8

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The PID controller taking an attempt at the adjustment in misunderstanding its usefulness,
to control the structure all jointly such with the motive for the chaos up is reductions. Tuning
of PID give complete data about the suspicion and controllers [7]. The goal of the tuning
technique is to pick the PID controller parameters that fulfill the execution purposes of
liveliness of the controlled configuration, for case, the rising time, the most stagger overshot,
the settling time and the steady condition commit an error. Regardless, it is hard to get the
boggling estimations of these requirements for the moment. As appeared in Table I, for case,
more principal estimations of relative change results in speedier reaction while overshoot is
opened up. In this way, an immaculate tuning method is of amazing criticalness. PID
Controller is a basic control circle of information instrument and is extensively used as a
touch of control framework. The novel signs of the DC motor, for instance, spreading and
change can decay the execution of standard controllers [8]. PID controller is all around called
the three-term of standard controller parameter, whose trade most distant point is routinely
made in the parallel structure given by relationship (6) or the ideal structure is given by
numerical representation (1) [9]. An undertaking PID controller is things being what they
are known as the three-term of key controller parameter, whose exchange most remote point
is ordinarily made in the parallel structure given by examination (6) or the perfect structure
is given by exploratory declaration (1). General kind of the Transfer furthest reaches of a
PID controller is given as,
 
1
. .P I DG S K K K S
S
   (6)
2
. .1
. . D P I
P I D
K S K S K
K K K S
S S
 
   (7)
Figure 3 PID Controller with System
Where: e = Error signal
KP = Proportional Constant
KI = Integral Constant
KD = Derivation Constant
0
( )
( ) ( ) ( )
t
P I D
de t
V t K e t K e t K
dt
   (8)
TABLE. III.EFFECT OF INCREASING THE PID CONTROLLER PARAMETERS

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Parameter Rise Time Overshoot Settling time
Steady state
error
KP Decrease Increase Small Change Decrease
KI Decrease Increase Increase Reduce
KD Small Change Decrease Decrease Small Change
From the above reaction, we can break down the framework. We can examine the
accompanying parameters:
 Maximum Overshoot (Mp)
 Settling time (ts)
The system of Maximum Overshoot (Mp) of is Approximately 59.2%. And the Settling times
are relation to 0.121second or after the analysis on top of, the system has not been turn to its
optimum.
4 GENETIC ASGORITHM
The genetic algorithm is a strategy for illustrative both obliged and unconstrained update
issues that depends on upon ordinary choice [10]. hereditary calculation fit in with the more
noteworthy class of transformative computations, which produce answers for improvement
issues using techniques pushed by standard headway, for instance, legacy, change, quality
of brain, and crossover [11]. The GAs were at essential proposed by ohm Holland in 1970
[12]. As a way to deal with find uncommon reactions for issues that were all round
computationally unmanageable. Holland's piece hypothesis, this theory is in like
methodology called the principal hypothesis of hereditary calculations, is thoroughly taken
to be the foundation for elucidations of the power of procured numbers. It says that short,
low demand schemata with above-standard wellbeing growth exponentially in component
times [9]. In this paper, GA is utilized to pick the ideal estimations of the PID controller
parameters that fulfil the required segment execution attributes of the DC motor drive
system. Fig. 3 demonstrates the movements of system GA based tuning of PID controller
parameters. In the key, GA is introduced. By then, it makes starting individuals of PID
controller parameters. The general population are made recklessly, covering the whole
degree of conceivable arrangements. The general population are made out of chromosomes.
Every chromosome is a contender reaction for the issue. Fig.4 demonstrates the chromosome
structure, in which the three parameters (Kp, Ki and Kd) are melded. The chromosomes are
related in the DC drive system and the dynamic execution qualities of the structure are
resolved for every chromosome. By then, the wellbeing respect for every chromosome is
assessed utilizing as far as possible. In light of the wellbeing estimations of the initial, a get-
together of best chromosomes is made the going with masses. After choice, cream and
change are connected with these surviving individuals to enhance the going with time [13].
The framework proceeds until the end standard is capable or the measure of times is gone to
its most significant worth. Acquired estimation is in like way examined to some degree 3 the
stream chart of GA is appeared in figure (5). Making the beginning masses is the initial step
of GAs. The masses are made out of the chromosomes that are parallel piece string. The
relating examination of masses is known as the (wellbeing work) the wellbeing quality is
more noticeable and the execution is better.

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Figure 4 Flowchart of GA for PID tuning
5 TUNING METHODOLOGY
5.1 Conventional PID controller Tuning Method
Remembering the finished objective to choose the parameters of the standard PID controller
using sensitive figuring tuning as a part of a MATLAB is made. The step response of the
uncontrolled DC motor drive is showed up in Fig. 5. It is clear that the uncontrolled DC
motor has a sensible step response since the settling time is exceptionally poor and not
appropriate working condition second of the reference speed. At that point applying PID
controller whose velocity might be explored utilizing the Proportional, Integral, Derivative
(KP, KI, and KD) addition of the PID controller. Since, established controllers PID are
neglecting to control the drive when load parameters are additionally changed [16]. We have
dissect, for example, most extreme overshoot around 59.2% and the settling time is about
0.121sec from the underneath Fig.7. The framework has not been tuned to its ideal. So, we
START
INITIAL POPULATION
EVALUATE FITNESS
SELECTION
CROSSOVER
MUTATION
ELITIST MODEL
NO
YES
TERMINATION
CONDITION
END

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need to go for hereditary calculations approach. The primary point of this paper is to break
down the execution of Evolutionary Computation (EC) procedures viz. genetic Algorithm
(GA) for upgrade PID controller parameters for pace control of dc and count their points of
interest over the ordinary tuning procedures. The accentuation point is determined, the
straying line is drawn.
Figure 5 Step input of uncontrolled DC motor drive system
5.2 GA-based optimization
The fitness function is the best approach to use the Genetic Algorithm [14]. The most key
stride in applying GA tuning method is to accept the target work that is utilized to review
the health assessment of every chromosome. In this paper, target limits are utilized and their
execution is looked at. The key depends endless integral of the absolute error (IAE)
document and these papers in target work additionally organize through the MATLAB
coding. The parameters of GAs in this study are set as in Table IV. The GA progress process
based IAE record Fig. 8. For every case, the PID controller parameters are resolved. The
objective function (target limit) is given as:
0
( )
T
IAE e t dt  (8)
Figure 6 PID-GA Controller with system

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6 SIMULATION RESULTS AND DISCUSSION
This paper in objective function a devoted programming utilizing "C" programming dialect
is created for this issue in MATLAB. The extent of.Kp, Ki and Kd is picked between (0-
100) separately. Estimations of Kp, Ki and Kd are plotted through a the objective function
in Fig.6. demonstrates the variety of the wellness of the best arrangement with era, where
best arrangement is characterized as the one which gives least ascent time, settling time, zero
overshoot and almost zero consistent zero steady state error in the wellness of the best
arrangement in every era until it achieves a most extreme conceivable worth can be credited
to the novel choice strategy embraced to be specific blend of Tournament choice with
Elitism.
Figure 7 Step input of PID controlled DC motor drive system
Figure 8 Step input of PID-GA controlled DC motor drive system

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TABLE. .IV. PERFORMANCE COMPARISION OF PARAMETER PID & PID TUNED
Parameters
PID
Conventional Tuned IEA
Kp 100 2.182 5
Ki 100 35.81 80
Rise time (sec) 0.00542 0.0663 0.03357
Settling time (sec) 0.121 0.257 --
Overshoot (%) 59.2 10.5 19.88
Peak 1.59 1.11 1.2
7 CONCLUSIONS
It is clear that the ordinary PID controller is not getting the exact result but rather through
the developmental calculation procedures to the ideal tuning of PID controller prompted an
agreeable close circle reaction for the framework under thought. Examination of the
outcomes as appeared in Table V and Fig.7 & Fig. 8. This paper exhibits another turning
technique for velocity control of DC motor utilizing genetic algorithm (GA) based The PID
controller. Target of this paper of PID parameters upgrade through the genetic algorithm
based distinctive target work, this tuning technique keeping in mind the end goal to
accomplish least ascent time, settling time, Overshoot and almost zero steady state error.
The final results show in Fig. 7 & Fig. 8 that give more enhanced execution when contrasted
with traditional PID controller for the considered system and thus, demonstrated the
prevalence of the genetic algorithm.

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