Speed Control of Dc Motor using Adaptive PID with SMC Scheme

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 09 | Sep -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 163
SPEED CONTROL OF DC MOTOR USING ADAPTIVE PID WITH
SMC SCHEME
Abhishek Pintu Kollabathula1, Dr. K. Padma2
1,2 Dept. of Electrical Engineering, AUCE (A), Andhra University.Visakhapatnam-530003, A.P
---------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - Direct Current (DC) motors have been used
extensively in industry mainly because of the simplestrategies
required to achieve good performance in speed or position
Control applications. The sliding mode control approach is
recognised as an efficient tool to design robust controllers for
complex high-order nonlinear dynamic plant operatingunder
uncertain conditions. The research in this area initiated in the
former Soviet Union about 40 years ago, and the sliding mode
control methodology has subsequently received much more
attention from the internationalcontrolcommunitywithin the
last two decades. Due to the robustness of Sliding Mode
Control (SMC), especially against parameters variations and
external disturbances, and its ability in controlling linearand
nonlinear systems. This thesisdealswiththeAdaptivePIDwith
sliding mode control adjustment of a speed control for DC
motor. Firstly, the thesis introduces the principle of sliding
mode control method. Then, design SMC controller for DC
motor after that design Adaptive PID withSMCcontrollerthen
the performance of dc motor with adaptive PID with SMC is
compared with SMC and PID controllers is made on the real
model of the DC motor. After obtaining the entire model of
speed control system, Performance of these controllers has
been verified through simulation results using
MATLAB/SIMULINK software. The simulation results shows
that Adaptive PID with SMC controller was a superior
controller than SMC and PID controllers for speed control of a
separately excited DC motor. The performance of DC motor
with these controllers, clearly observe Settling time, Rise time
and Overshoot. Adaptiv*e PID SMCcontrollergivesbestresults
considering above three conditions and also this controller is
very robust controller. That is irrespective of any disturbances
Adaptive PID SMC produce the same output.
1.INTRODUCTION
The development of high performance motor drives is very
important in industrial as well as otherpurposeapplications
such as steel rolling mills, electric trains and robotics.
Generally, a highperformancemotordrivesystemmusthave
good dynamic speed command tracking and load regulating
response to perform task. DC drives, because of their
simplicity, ease of application, high reliabilities, flexibilities
and favorable cost have long been a backbone of industrial
applications, robot manipulators and home appliances
where speed and position control of motor are required.
DC drives are less complex with a single power conversion
from AC to DC. Again the speed torque characteristics of DC
motors are much more superior to That of AC motors. A DC
motors provide excellent control of speed for acceleration
and deceleration. DC drives are normally less expensive for
most horsepower ratings. DC motors have a longtraditionof
use as adjustable speed machines and a wide range of
options have evolved for this purpose. In these applications,
the motor should be precisely controlled to give the desired
performance. The controllers ofthespeedthatareconceived
for goal to control the speed of DC motor to execute one
variety of tasks, is of several conventional and numeric
controller types, the controllerscanbe:proportional integral
(PI), proportional integral derivative (PID),sliding mode
controller etc…The proportional –integral – derivative(PID)
controller operates the majority of the control system in the
world. It has been reported that more than 95% of the
controllers in the industrial process control applicationsare
of PID type as no other controller match the simplicity, clear
functionality, applicability and ease of use offered bythe PID
controller. PID controllers provide robust and reliable
performance for most systems if the PID parameters are
tuned properly. The major problems in applying a
conventional control algorithm (PI, PD, PID) in a speed
controller are the effects of non-linearity in a DC motor. The
nonlinear characteristics of a DC motor such as saturation
and fiction could degrade the performance of conventional
controllers. Generally, an accurate nonlinear model of an
actual DC motor is difficult to find and parameter obtained
from systems identification may be only approximated
values. The field of sliding mode control has been making
rapid progress in recent years. Interests in the applicationof
sliding mode control technique invariablespeeddriveshave
increased in recent years. It is well known that a
distinguished property ofa slidingmodecontrol techniqueis
its insensitivity to system uncertainties and external
disturbances. Compared to the conventional PI controller,
the system is sensitive to the parameter variations and
inadequate rejection of external disturbances or load
variations. Furthermore in order to design PI controller, the
challenge faced by the researchers due to multi loop system
structure and trial and error design approach which make
the control design time consuming and expensive. This has
lead to the development of the sliding modes control
technique, which is very attractive for its excellent
performance, easy to implement with simple control
algorithm. It is desirable to achieve robust performance
against external disturbances especially sudden orstepload
applications.

Volume: 04 Issue: 08 | Aug -2017 www.irjet.net p-ISSN: 2395-0072
This paper deals with the Adaptive PID with sliding mode
control adjustment of a speed control for DC motor. Firstly,
the paper introduces the principle of sliding mode control
method. Then, design controller for DC motor after that the
performance is compared with the performance of PID and
SMC is made on the real model of the DC motor .The main
result of the paper is the analysis the adaptive sliding mode
control. After obtaining the entire model of speed control
system, the model is utilized with MATLAB(SIMULINK). The
simulations of the performance comparisons between
Adaptive PID with sliding mode control and PID control
show that variable structure system with sliding mode
control approach is less sensitive to parameter variations,
produce faster dynamic response, eliminate overshoot and
performs better in rejecting disturbance. The excellent
features of the sliding mode control based on variable
structure system are mainly due to the high gain effect,
which suppresses influence of disturbances and
uncertainties in system behavior.
2.MODELLING OF DC MOTOR
A separately excited dc motor has the simplest
decoupled electromagnetic structure. A schematic diagram
of the separately excited DC motor is shown in Fig.1.
Figure 2.1: A Separately excited DC motor
The armature controlled method for speed control
of DC motor is considered here. The armature current is
controlled to generate desired electromagnetic torque and
the armature voltage is controlled for the load. The field
excitation is kept constant to produce rated flux. For a
constant field excitation the armature circuit electrical
equation of a separately excited
DC motor is written as:
a
a a a b a
dI
L I R E E
dt
   (1)
where Ea is the Applied Voltage, Ra is the armature
resistance, La is the Equivalent armature inductance, Ia
current flowing through armature circuit, Eb is the back emf
and. The dynamics of the mechanical system is given by the
torque balance equation :
2
2
K Il m t a
d d
J B T T
dt dt
 
    (2)
where Tm is the developed torque, Tl is the load torque, J
is the moment of inertia, B is the damping constant, and Kt =
Torque constant. Eb represents electromotive force in V
given by
E (t) K (t)b b  (3)
Where Kb is the back emf constant in Vs/rad. The input
terminal voltage Va is taken to be the controlling variable.
one can write state model with the ω and Ia asstatevariables
and Va as manipulating variable, as given below
Let
1x 
1 2x x    
3 ax I
11
1 2 22
0
0 1
m
xx
uK
A A xx
JL
 
                   
 
(4)
1.2aR ohm K 0.6 /b V s rad
L 0.05a H 2 2
0.1352 /J Kg m s
K 0.6 /t Nm Amp 0b Nms
Table. 1 : Parameters of DC motor
 2
( )
( )
m
g m
k
s JL
U s Rb K kb R
S S
J L JL


                      
(5)
Using the parameters given in Table 1, transfer function
of the DC motor with angular velocity as controlled variable
and input terminal voltage as manipulating variable is
determined as given below
2
( ) 88.76
V ( ) 24 53.25a
s
s S S


 
(6)
(5) in time domain is as follows:
 2
2
g m m
Rb K K Kd b R d
u
dt J L dt JL JL
 

    
       
    
(7)
However, if the state variables consider and =
= .The system described by equation(4)by equation(8)
will be expressed, Where the only variable is the angular
velocity and derivative.

Therefore the state space model is,
11
1 2 22
0
0 1
m
xx
uK
A A xx
JL
 
                   
 
(8)
Where
 
1
g mRb K K
A
JL
 
 
 
 
(9)
1
b R
A
J L
    
      
    
(10)
3.PID CONTROLLER
Proportional, integral and derivative are the basic
modes of PID controller. Proportional modeprovidesa rapid
adjustment of the manipulating variable reduces error and
speeds up dynamic response. Integral mode achieves zero
offset. Derivative mode provides rapid correction based on
the rate of change of controlled variable. The controller
transfer function is given by
1
( ) K 1PID p dC s T s
T s
 
   
 
(11)
where, Kp, Ti and Td are the proportional, integral
and derivative constants of PID controller respectively. PID
controller tuning algorithm is based on Ziegler-Nicholsopen
loop method. And the preference is given to the load
disturbance rejection.
4.SLIDINGMODE CONTROLLER DESIGN
A linear system can be described in the state space
as follows:
x Ax Bu  (12)
Where
n
x R , u R ,
*n n
A R ,
n
B R and B is full
rank matrix. A and B are controllablematrixes.Thefunctions
of state variables are known as switching function:
sx  (13)
The main idea in sliding mode control is
• Designing the switching function so
that 0  manifold (sliding mode) provide the
desired dynamic.
• Finding a controller ensuring sliding mode of the
system occurs in finite time First of all, the system
should be converted to its regular form:
x Tx (14)
T is the matrix that brings the system to its regular form
1 11 1 12 2xx A A x 
2 21 1 22 2 2x A x A x B u   (15)
The switching function in regular form is:
1 1 2 2s x s x   (16)
On the sliding mode manifold ( 0  ):
1
2 2 1 1x s s x
  (17)
From (17) & (15)
 1
1 11 12 2 1 1x A A s s x
  (18)
One of matrixes in product: should be chosen
arbitrary. Usually (19) is used to ensure that S2 is invertible
1
2 2s B 
 (19)
can be calculated by assigning the Eigen value of (18)
by pole placement method. Hence, switchingfunctionwill be
obtained as follows:
 1 2s s s T (20)
The control rule is:
c du u u  (21)
Where and are continuous and discrete parts,
respectively and can be calculated as follows:
21 1 22cu A x A    (22)
sgnd s pu K K    (23)
Where sgn is sign function. , and are constants
calculated regarding to lyapunov stability function.
We are going to set the angular velocity over a certain value
r, so switching function is
 1 1 2 2rs x s x   (24)
If the controller switching function isdesignedto beplaced
on the surface 0  then Solving equations (24)
assume 0  , and are obtained by
1
2
s
t
s
r e

  (25)
1
21
2
s
t
ss
e
s


 (26)
As equation (8) it is regular form, so the transformation
matrix is equal to the unit matrix Factor according to
equation (19) must be calculated

2
m
JL
s
K
 (27)
Also according to (12-19) 1 s calculated and w Pole
placement method using (12-21) .Suppose we have to
placed system poles in so we have
1
2
s
s
  (28)
As (25), (26) and (28) shown determines the
speed of convergence of the system output So it is better to
choose a small negative value Thus, the switching function
was designed as follows
  
m
JL
r
K
      (29)
B. Controller design:
If the equation (8) can be rewritten based on the state
variables  and  1 1X x r  The following is reached
11 11 12
21 22
0
1
n
XX A A
u
A A 
      
       
      
(30)
That (30) has the following parameters and variables.
1
11
2
s
A
s
  
12
2
1
A
s

2
21 1 2A A A    
22 2A A  
1
2 1nu s u A r
  (31)
Thus the relations (21), (22) and (23) controller for the
system (30) is designed as follows.
 21 1 22 sgnn s pu A X A K K      (32)
The below equation Sets armature voltage feedback based
on the derivative of the angular velocity for motor.
   
   
2
1 2 1 2 1
2
2 sgnp s
A s A A A r
U s
A K K
   
  
          
     
(33)
So the sliding mode controller is
   
 
   
2
[
] sgn
g m g m
m
m
g m
p s
Rb K K Rb K KJL b R
JL K JL J LJL
U
K Rb K K b R
r K K
JL J L
  
   
                                         
  
      
                     
(34)
Switching function of sliding mode controller for DC motor
control method according to the relations (34) and (33) are
designed.If the motor parameters like table (1),then the
controller we will numerically designed as follows
 4 6
.0924 *10 .0924*10r   
   (35)
After solving The controller u is given by
    
 
6
.0924*10 3675896.1 3675896.1
7491.256 sgn
r
U
 
 

   
  
   
(36)
Where λ, ks and kp parameters are -100, 1 and 0
respectively.
5.RESULTS
In this thesis work firstly simulink model of sliding
mode controller was introduced and then the SMC is
attached with the real model of dc motor i.e. for dc motor.
The figure below gives the sliding mode controller and
controller equation obtained to control the speed of dc
motor which was designed with help of state space model of
dc motor.
For third order transfer function
The mat lab model and response of the real plant is given
below
Figure1 original system simulink model
The corresponding output is shown in fig2

Figure2 Speed response of DC motor original system
Now for the same DC motor a Adaptive PID with Sliding
mode controller is attached and the corresponding simulink
model and its output for the same reference input of
1000rpm is given below
Figure3 simulink model of dc motor with Adaptive PID
with SMC controller
The speed response of the DC motor with Adaptive PID with
sliding mode controller is shown in figure4
Figure 4 Speed responses of DC motor Original plant and
Adaptive PID with SMC
The control input and switching function in adaptive PID
SMC are given in below figure.
Figure. 5 switching function
Figure. 6 control input
The combined simulation block diagram of DC motor with
PID , SMC , Adaptive PID with SMC controller for the same
reference input of 1000rpm is given below
Figure 7 simulink model of dc motor with PID, SMC and
The speed response of DC motor for above simulation
diagram is shown in below figure 8

Figure8 Speed response of DC motor with all controllers
d its simulink models and corresponding outputs are given
below.
If we observe the outputs of the above figures PID, SMC and
Adaptive PID with SMC controllers, this reveals thatSMCisa
robust controller i.e. irrespective of any disturbances
Adaptive PID SMC produce the same output where as forthe
same motor and same reference speed PID produces
oscillations for which the system parameters are disturbed.
Settling time is also reduced very well in case of Adaptive
PID with SMC when compared withPIDandSMCcontrollers.
Table 2 comparisons between SMC, PID and PIDSMC
controllers
CONTRO
LLER
SETTL
ING
TIME
(SEC)
OVERSHOOT DISTURB
ANCE
REJECTI
ON
RISE
TIME
(SEC)
PID 0.68 moderate poor 0.29
SMC 0.45 nil good 0.23
Adaptive
PID with
SMC
0.12 nil good 0.025
For fifth order transfer function
The mat lab model and response of the real plant is given
below
Figure 9 original system simulink model
The corresponding output is shown in fig 10
Figure10 Speed response of DC motor original system
Now for the same DC motor a Adaptive PID with Sliding
mode controller is attached and the corresponding simulink
model and its output for the same referenceinputof800rpm
is given below
Figure11 simulink model of dc motor with Adaptive PID
with SMC controller
The speed response of the DC motor with Adaptive PID with
sliding mode controller is shown in figure 12
Figure.12 Speed responses of DC motor Original plant and
The control input and switching function in adaptive PID
SMC are given in below figure.

Figure. 13 switching function
Figure.14 control input
The combined simulation block diagram of DC motor with
PID , SMC , Adaptive PID with SMC controller for the same
reference input of 800rpm is given below
Figure15 simulink model of dc motor with PID, SMC and
The speed response of DC motor for above simulation
diagram is shown in below figure 16
Figure16 Speed response of DC motor with all controllers
If we observe the outputs of the above figures PID, SMC and
Adaptive PID with SMC controllers, this reveals thatSMCisa
robust controller i.e. irrespective of any disturbances
Adaptive PID SMC produce the same output where as forthe
same motor and same reference speed PID produces
oscillations for which the system parameters are disturbed.
Settling time is also reduced very well in case of Adaptive
PID with SMC when compared withPIDandSMCcontrollers.
Table 3 comparisons between SMC, PID and PIDSMC
controllers
CONTROL
LER
SETTLI
NG
TIME
(SEC)
OVERSHO
OT
DISTURBA
NCE
REJECTION
RISE
TIME
(SEC)
PID 0.48 moderate poor 0.29
SMC 0.45 nil good 0.23
Adaptive
PID with
SMC
0.22 nil good 0.11
Sliding mode control (SMC) and Adaptive PID with sliding
mode control techniques are used to control the speed of DC
motor. The chattering problem in SMC is avoided by using
Adaptive PID with sliding mode controller and the
performance of the SMC is improved by using an adaptive
PID with sliding mode controller.
6. CONCLUSIONS
After obtaining the entire model of speed control
system, Performance of these controllers has been verified
through simulation results using MATLAB/SIMULINK
software. The simulation results showed that Adaptive PID

with SMC controller was a superior controller than SMC and
PID controllers for speed control of a DC motor. Also, this
controller is very robust and is irrespective of any
disturbances Adaptive PID SMC produce the same output.
7. SCOPE FOR FUTURE STUDY
(1) Besides being simple to construct and to
implement; it has a very fast response and less
sensitive to parameter variation and external
disturbances. But the performance of dc motor
further improved if it is possible to design better
controllers than this controller.
(2) The DC motor is a linear system model, so this
controller is extended to design for nonlinear
systems like Induction motor and robotics.
8. REFERENCES
[1] Utkin.Sliding mode control design principles and
applications to Electric drives, IEEE T
conference on Industrial Electronics, Vol.40, no.1, pp.
23-36, February 1993.
[2] H. Komurcugil, “Non-singular terminal sliding mode
control of DC-DC buck converters”, control engineering
practice, vol.21 no. 3, pp. 321-332,2013.
[3] John Y. Hung, W. Gao, J.C. Hung. Variable Structure
Control: A survey, IEEE Trans. On Industrial Electronics,
Vol.40, no.1, pp.1- 22, February 1993.
[4] J.Huspeka, “Second order sliding mode control oftheDC
motor”, international conference on process control,
pp0 134-139, 2009.
[5] J.Chakravorty, R.Sharma, “Fuzzy logic based method of
speed control of DC motor”, international journal of
emerging technology and advanced engineering, vol. 3,
no. 4, 2013.
[6] K.M.A.Prasad, B.M. Krishna,U.Nair,“Modifiedchattering
free sliding mode control of DC motor”, international
journal of modern engineeringresearch,vol.3,pp.1419-
1423, 2013.
[7] R. Malhotra, T. Kaur, “DC motor control usingfuzzylogic
controller”, international journal of advanced
engineering sciences and technologies, vol.8, no. 2, pp.
291-296, 2011.
[8] Infineon Technologies, Basic DC motor speed PID
control with the Infineon Technologies

Speed Control of Dc Motor using Adaptive PID with SMC Scheme

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