Iaetsd position control of servo systems using pid

POSITION CONTROL OF SERVO SYSTEMS USING PID
CONTROLLER TUNING WITH SOFT COMPUTING
OPTIMIZATION TECHNIQUE
P.RAVI KUMAR
M.Tech (control systems)
Gudlavalleru engineering college
Gudlavalleru,Andhra Pradesh,india
Pravikumara9@gmail.com
V.NAGA BABU
ASSISTANT PROFESSOR
Gudlavalleru engineering college
Gudlavalleru,Andhra Pradesh,india
Nagababu243@gmail.com
Abstract: in this paper, position control of servo motor using PID controllers with soft
computing optimization techniques is discussed .PID controllers widely used in the industry.
Different methods are available for tuning the PID controllers. In this paper ZN method, GA
and PSO are used for the position control of the servo motor.
KEY WORDS: servo motor, position control, tuning methods, ZN, GA and PSO methods.
INTROUDUCTION
Position control systems are
normally unstable when they are
implemented in closed loop configuration.
Now a day’s PID controllers are widely
used in the industry. About 85-90% of the
controllers are used in the industry are of
PID type.PID controllers tuning for
positional control systems is a time
consuming task , therefore much effort has
been given to analyse the servo systems.
The main aim of this paper is to
analyse the soft computing methods and
enumerate their advantages over
conventional PID tuning methodologies.
Position control of a 3rd
ordered plant
(Servomotor) using Conventional and soft
computing methods with their
comparisons is analysed. Conventional
PID tuning method Ziegler-Nichols, soft
computing methods like genetic algorithm
and PSO is used for the position control of
servo systems.
Except for miner difference in
constructional features a dc servo motor is
essentially an ordinary dc motor. Physical
requirements of servo motor are Low
inertia and High starting torque. Low
inertia is attained with reduced armature
diameter with consequent in armature
length such that the desired power output
is reached.
SYSTEM MODELLING
In this paper considering an armature
controlled dc motor. In this dc servo motor
can be consider as a linear SISO system
having 3rd
order transfer function. Relation
between shaft position and armature
voltage is derived from the physical laws.
The air gap flux is given by
Torque is proportional to product of Flux
and Armature current
Or
Back EMF of the motor is given by
FIG1: separately exited dc motor
By apply Laplace transform to the
armature loop
( ) = ( ) + ( ) + ( )
)()(1 tItIkkT aff
)(tIKT am
bb kV 
)(1 tIkT a
ff ik
Proceedings of International Conference On Current Innovations In Engineering And Technology
International Association Of Engineering & Technology For Skill Development
ISBN : 978 - 1502851550
www.iaetsd.in
88

Where Vb(s) is back EMF voltage
proportional to the motor speed. Therefore,
we have
( ) = ( )
The armature current is expressed as
( ) =
( ) − ( )
+
The motor torque is expressed as
( ) = ( ) + ( )
Where Tl is the load torque
( ) = ( ) + ( )
The relation between speed and position is
given by
( ) = ∗ ( )
The above equations can be represent in a
block diagram as
Fig2 :equivalent block diagram
From the above block diagram the relation
between shaft position and armature
obtained as
by assuming the Td=0,
( )
( )
=
⌈( + )( + ) + ( )⌉
J=0.01kg/ ,b=0.1n.m.s, kb=0.01
v/rad/sec, km=0.01n.m/amp, Ra=1
ohm,L=0.5H
Substitute above values in the above
equation,
( )
( )
=
0.01
0.005 + 0.06 + 0.1001
ZN Method:
Set Kd=0 and Ki=infinity. ku and Pu are
determined by using R-H criteria. Ku is
determined by equating the row containing
‘s’ in R-H row to zero. Pu is determined b
equating the row containing ‘s^2’ in R-H
row to zero. Evaluate parameters described
by Z-N method. Find kp, ki ,and kd using
the formulas Kp=0.6*Ku ,Ki=Kp/Ti
,Kd=Kp*Td .
Kp, Ti, Td are calculated using the
formulas given in below table
Control
type
kp Ti Td
P 0.5 Ku
PI 0.45
Ku
1.6(Kp/Ku)
PID 0.6 Ku 2*(Kp/Ku) (Kp/Ku)
The advantage of this method is applying
easy rules to simple mathematical models.
But the disadvantage of this method is Do
not provide as good results as expected.
GENETIC ALGORITHM:
A genetic algorithm is a powerful
searching capabilities and heuristic
characteristics. GA has also been used in
control tuning applications, being shown
to obtain better results than classical
techniques
The components of GA are
A problem definition as input, and
encoding principles (gene, chromosome),
initialization procedure followed by cross
over, mutation and selection operators for
reproduction with the help of an objective
function.
Simple Genetic Algorithm:
{
Initialize population;
Evaluate population;
While Termination Criteria Not Satisfied
{
Select parents for reproduction;
Perform recombination and mutation;
Evaluate population;
}
}
GA parameters:
In this paper the following genetic
algorithm parameters are used
ISBN : 978 - 1502851550
www.iaetsd.in
89

parameters Values
Lower bounds [kp ki kd] [0 0 0]
Upper bounds [kp ki kd] [100 100 100]
Stopping criteria 100
Population size 40
Cross over fraction 0.4
Mutation fraction 0.08
These are the parameters of the genetic
algorithms.
PSO
PSO is a robust stochastic
optimization technique based on the
movement and intelligence of swarms. The
components of PSO are Swarm Size, Velocity,
position components and maximum no of
iteration. Here I have consider the
following objective function
F=(1-exp(-0.5))*(Mp+Ess)+exp(-0.5)*(ts-tr)
Algorithm of PSO
1. Create an initial population of particles
with random positions and velocities
within the solution space.
2. For each particle, calculate the value
of the fitness function.
3. Compare the fitness of each particle
with local- best. If current solution is
better than its local- best, then replace
its local best by the current solution.
4. Compare the fitness of all the particles
with global best. If the fitness of any
particle is better than global-best, then
replace global-best.
5. Update the velocity and positions of all
particles using velocity update
equations.
6. Repeat steps (2)-(5) until a stopping
criterion is met.
FLOW CHART OF PSO
Block diagram of servo motor with PID
controllr :
Fig3: Block diagram of servo motor
ISBN : 978 - 1502851550
www.iaetsd.in
90

STEP RESPONSE OF Z-N METHOD:
Fig4: Step response of Z-N method
STEP RESPONSE OF GA
Fig 5:step response of GA
STEP RESPONSE OF PSO
Fig 6:step response of PSO
Comparisons of all Wave forms
Fig7: Comparisons of all Wave forms
Comparisons of all methods
parameters ZN GA PSO
Settling
time(sec)
5.0139 1.6 0.56
Rise
time(Sec)
0.2901 0.25 0.35
Peak over
shoot (%)
61.74 30 3
ISE 0.43 0.0847 0.1539
IAE 0.153 0.1905 0.4312
CONCLUSION:
By comparing the all methods
PSO gives better response in terms of
performance indices. Also for the position
control of servo systems the genetic
algorithm method gives better response.
This may be extending by using advanced
genetic algorithm, particle swarm
optimization and also using evolutionary
algorithms.
References:
1. DC motor angular position control
using PID controller for the
purpose of controlling the
hydraulic pump. International
conference on control, Engineering
&information technology (ICIT-
13).
2. modelling and control of motorized
robotic arm using hybrid PSO
algorithm.2012 nimra university
ISBN : 978 - 1502851550
www.iaetsd.in
91

international conference on
engineering (NUICONE-2012)
3. Emphasis on genetic algorithm
(GA) over different PID tuning
methods for controlling the servo
systems using MATLAB.
International journal of scientific
research in computer science
engineering.
4. Dc motor control by using genetic
algorithm. International journal of
digital applications &
contemporary research 2012.
5. Design and implementation of
discrete augmented Ziegler-Nichols
PID controller.(ACEEE
international journal of control
systems and instrumentation- 2013)
ISBN : 978 - 1502851550
www.iaetsd.in
92

Iaetsd position control of servo systems using pid

More Related Content

What's hot (19)

Similar to Iaetsd position control of servo systems using pid (20)

More from Iaetsd Iaetsd (20)

Recently uploaded (20)

Iaetsd position control of servo systems using pid