Fuzzy ANFIS

t
1s IEEE International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES-2016)
Fuzzy & ANFIS based Temperature
Control ofWater Bath System
Bharat Bhushanl, Ajit Kumar Sharma2 and Deepti Singh3
1,2,3Electrical Engineering Department, Delhi Technological University, Delhi, India
E-mail: [email protected]. [email protected][email protected]. in
the conventional methods for its analysis [10]. The concept
of soft computing began to materialize near about the time
when Lotfi Zadeh was working on soft analysis of data and
fuzzy logic [12]. This gave birth to the intelligent systems.
Nearly four decades later, the intelligent system became a
reality [13]. However, initially the technology needed for
building systems that possess Artificial intelligence (AI) was
not available. Instead only predicate logic and symbol
manipulation techniques formed the core of the traditional
AI [14]. These techniques could not be used for building
machines which could be called intelligent from the point of
view of real world application [15]. But today the requisite
hardware, software and sensor technology are available for
building intelligent systems [16]. Morever, computational
tools are available now which are far more effective for
conception and design of intelligent systems [17]. The Fuzzy
logic gives a simple way to reach definite conclusion even
when the input is based on vague, noisy, imprecise,
ambiguous or missing information [18]. For stable direct
adaptive control of nonlinear system Lyapunov function
with fuzzy approach is used[19].The effectiveness of the
proposed method, simulation results on a temperature
control system are analyzed and compared with another very
popular intelligent technique which is Multi-objective [20].
This paper is organized as folIows. Section 2 presents
the different control techniques such as fuzzy logic
controller and ANFIS controller. System modeling of
water bath with fuzzy and ANFIS is detailed in section 3.
Section 4 describes the result and discussion of water bath
system. Finally, some concluding remarks are drawn in
Section 5 followed by references.
Abstract-Conventional controllers usually require a
prior knowledge of mathematical modeling of the process.
The inaccuracy of mathematical modeling degrades the
performance of the process, especially for non-linear and
complex control problem. To overcome above difficulties
intelligent controllers like Fuzzy Logic (FL) and Adaptive
Neuro-Fuzzy Inference System (ANFIS), are implemented.
The Fuzzy controller is designed to work with knowledge in
the form of linguistic control rules. But the translation of
these linguistic rules into the framework of fuzzy set theory
depends on the choice of certain parameters, for which no
formal method is known. It is analyzed that ANFIS is best
suitable for adaptive temperature control of above system.
As compared to FLC, ANFIS produces a stable control
signal. It has much better temperature tracking capability
with almost zero overshoot and minimum absolute error.
I.
INTRODUCTION
Now a day systems are large and complex in nature.
Electrical power, chemical, water treatment and similar
large-scale industrial plants are all complex in nature.
System outputs may be measurable or immeasurable [1].
They may consist of many interconnected systems, sub­
processes or components. The processes involved in the
complex systems may possess widely varying properties.
Modelling of complex systems is of fundamental importance
in almost all fields [2]. This is because models facilitate
better understanding of the system and so help in system
analysis. The design, optimization and supervision of
controllers, fault detection and fuulty component diagnosis
are all based on the system mode [3]. Modeling of large
scale, complex [4], systems has been a special topic of
interest among the researchers of various disciplines
worldwide. Most of the real world systems are ill defined in
nature and hence difficult to model. Generally the
performance of the system is dependent on the accuracy of
the model [5]. Therefore it is of utmost importance to build a
model which correctly retlects the behavior of the system
under consideration [6]. The functioning of complex large­
scale systems also involves numerous trades off problems
like cost and accuracy [7]. Hence, there is a strong demand
for developing advanced methods of system modeling and
identification techniques [8]. The conventional methods that
have been used for system modeling rely heavily on the
mathematical tools which require precise knowledge about
the involved physical processes [9]. In systems where the
mathematical model is not available, it is not possible to use
978-1-4673-8587-9/16/$31.00 ©2016 IEEE
11.
CONTROL TECHNIQUE
To attain desired temperature within a specified
period of time for water bath system, different control
techniques are used.
A.
Fuzzy Logic Controller
The fuzzy logic is methodology for computing with
imprecision and granularity. Fuzzy set theory provides a
systematic approach to deal with such information
linguistically, also perform Numerical computation by
using membership function for the stipulated linguistic
labels. The Fuzzy inference system (FIS) is based on the
concepts of fuzzy set theory, fuzzy if-then rules and fuzzy
[1]
t
1s IEEE International Conference on Power Electronics. Intelligent Control and Energy Systems (ICPEICES-2016)
y(k + 1)
reasoning. The framing of the fuzzy if-then rules forms the
key component in FIS. FIS is a very popular technique and
has been widely applied in different fields like data
c1assification, automatic control, expert system, decision
making, robotics,
time series analysis,
pattern
c1assification, system Identification etc. The basic
structure of a fuzzy inference system consists of three
principal components viz a rule base comprising of the
selected fuzzy rules, a database defining the membership
functions of the fuzzy rules, and a reasoning mechanism
which performs a fuzzy reasoning inference with respect
to the rules so as to derive a reasonable output or
conclusion.
B.
Where
L:oycr4
ß(l
e(-aT)
= :..._-­
....:..
-
a
Fuuy CCIII U'Qlkr
WIll
1
Fig. 2: Fuzzy Control Model for Water-Bath System
B.
Water Bath Temperature Control using ANFIS
The learning is required in order to fine-tune the
parameters of the membership function as weil as the
parameters of defuzzification. Figure (2) has shown the
learning phase of ANFIS, where water bath temperature
system is to be controlled. And that the learning of ANFIS
is based on error back propagation as weIl.
One of the major features of Neural Network (NN) is
its learning capability.
'fIild2
x y
t t
Fig. I: Architecture of ANFIS Controller
SYSTEM MODELLING
Water-Bath temperature control is one of the most
important and widely used applications of non-linear
control system in process control industry.
A.
e(-aT)
The parameters of the plant are sets as a= IxlO-4,
ß=8.7xlO-3, 1ZI=40 and YO = 250 C. The plant input u (k)
is lirnited to between 0 and 5 volts. The sampling period,
T, is set as 25 seconds. The goal is to design a fuzzy
controller that will control the water temperature to follow
a reference profile as c10sely as possible. This reference
profile is 350 C for 0�t�I20 minutes and 800 C for
120�t�I80 minutes.
The input variables for this controller are chosen as e
(k), de (k) where e (k) is the performance error indicating the
error between the desire output and the actually output. The
de (k) is the change of the error. The output of the controller
is the voltage that lirnited to between 0 to 5 volts.
A s shown in fig (1) system used two input variables
error 'E' change of error 'DE' and one output variable
'U' . The computational structure of fuzzy logic control
scheme is composed of fuzzification, inference engine and
defuzzification. The input to the fuzzy controller is error
'Ek' and the change in error 'DEk' is computed from the
reference output 'Uk' based on error and change in error.
f
III.
=
(1)
La�rS
1
1
a(T)
b(T)
ANFIS is a hybrid system of fuzzy inference and
neural network architecture. A neuro-fuzzy system
describes a fuzzy-rule based model using an N N-like
structure (i.e. involving nodes and links). A neuro-fuzzy
system differs from an NN in four major ways. Firstly, the
nodes and link in a neuro-fuzzy system usually are
comprehensible because they each correspond to a specific
component in fuzzy system. Secondly connection between
nodes in a neuro-fuzzy system retlects the rule structure of
the system. Thirdly second layer node are connected to
only two nodes from the first layer, each one of which
describes a condition about an input variable. The nodes in
the second layer thus perform the "AND" (conjunction)
operator in fuzzy rules third. Finally the nodes in different
layer of neuro-fuzzy system typically perform different
operations. So a neuro-fuzzy system typically has more
layers than neural networks.
Layer3
b(T)u(k)
a(T)y(k) + l+exp (O.5y(k)-y) + (1 - a(T))Yo
and
ANFIS Controller
l..a)'crl
=
yLk)
Water Bath Temperature Control using Fuzzy Logic
Control
In this demonstration, water bath plant for
temperature control of fuzzy logic controller is described
by:
Fig. 3: Learning Phase of ANFIS
[2]
z'
t
1s IEEE International Conference on Power Electronics. Intelligent Control and Energy Systems (ICPEICES-2016)
A fter the learning phase is finished, the trained
ANFIS is then to be used as a controller for the plant,
shown in Fig. (3)
�(k)
3
.
..
u
u
..
.
.
u . .
'
�
i'!. · ·
........:
.
..
�
. . . .. . ..
�
.
10
60
sampling
To design an ANFIS controller for the temperature
control of described module. It is implemented by using
the direct inverse control strategy, and training data is
obtained by imposing random input voltages to the water
bath system and record corresponding temperature.
The ANFIS is then trained to identify the inverse
model of the water bath system using the gathered training
data to start the ANFIS training, where FIS matrix is
required that specifies the structure and initial parameters
of the FIS for learning the given number and types of
membership functions.
80
time step
100
120
Kr T=25 seconds
140
160
180
Fig. 6: Controlled Output ofFuzzy Logic Gaussian Membership
Function
B.
Gaussian Membership Function (ANFIS)
(2)
A ES= sum (abs (ref-y))
=367.3556
SIMULATION REsULTS & DISCUSSION
Water-Bath temperature control is widely used
applications of non-linear control system in process
control industry. The main objective is to develop a
Water-Bath system, to attain desired temperature within a
specified period of time to avoid the overshoot and
absolute error, with better temperature tracking capability,
To overcome above difficulties intelligent controllers,
Fuzzy Logic (FL) and A daptive Neuro-Fuzzy Inference
System (ANFIS) based temperature control of water bath
system is simulated for different membership functions.
Results of Water bath Temperature Control using
Fuzzy Logic Control & ANFIS for different membership:
Sampling Time Step KT T=25 seconds
Fig. 7: Controlled Output of ANFIS for Gauss Membership Function
In figure (7) the graph shows the output of the
controller is the voltage that lirnited to between 0 to 5 volts.
c.
Trapezoidal Membership Function (Fuzzy Logic)
1 ,.. I IA) 'iiiiiif2i
Ty,..
Tv.,..
P.. ,.......
.....p ...
R..n_
Gaussian Membership Function (Fuzzy Logic)
1" '1
I�
I···
.._m ... . ..
In the figure (6) the graph shows the actual output is
reach approximate to the reference signal. The output of
the controller is the voltage that lirnited to between 0 to 5
volts. Sampling time t is for 25 seconds.
I!J
'"
.. .
0
20
t/' T
u
'---"
u
----._
.-;
:' ,
r
" "
:�.11"! '----,.
1 .,'/".-!_-"'
.. . . . :
Fig. 4: Controller for the Plant
A.
...
,.
i 50
� 40
x., (k+l)
'
60
�(k+l)
L/
reference
signal--actual output.control S i gn .'_
u
��
,
u ,
u u '
-,-_
-,
70
,------,
IV.
u
80
U
_
e...
-----.J
I
Fig. 8: Trapezoidal Membership Function ofFuzzy Logic
80
.. .. . ., .. ..
..
,
60
_utt"
i=
l,/
_t
3
0
.' '
.;
.
.
....
......ct)
G:::::::::;::::!
u
/<_
.. u
....... J
. ; . . . . . . . . . . . . . . . . . .�
20
10
,
.
,---,
. . .. .......F-
reference signal--actual output.contro! signa!_
................. , . .
.. . .
.
.. ..
.
...
.. .
.
70
M .. rn �rshi p Function Editor: fis2
Curn.nt M"rnb."$hip Function (click on MF 10
".........
(_0_.5_0.0 ........ 0_0 .....70_ · "1
-----.J
H..
.
.
:
..
60
samp!ing
:
.
u
80
time step
100
120
KT T=25 $econds
..
:
..
j
.. . ... .. . . .. . . . . .
- ..,
: ..
.. u h : ....F----\
.
..
140
u
:
]
:
. .. ..
. .;
..
160
..
180
Fig. 9: Controlled Output ofFuzzy Logic Controller for Trapezoidal
Membership Function
Fig. 5: Gaussian Membership Function ofFuzzy Logic
[3]
t
1s IEEE International Conference on Power Electronics. Intelligent Control and Energy Systems (ICPEICES-2016)
In the figure (9) the graph shows the absolute error
sum for the trapezoidal function is coming much larger
than that for Gaussian membership function.
smaller than trapezoidal fimction (501.72) but coming
much larger than that for Gaussian membership function
(429.07).
D.
F.
Trapezoidal Membership Function (ANFIS)
Gbell Membership Function (ANFIS)
A ES= sum (abs (ref-y))
=368. 9700
A ES= sum (abs (ref-y))
=370. 2979
(3)
Reference Signat-- Actual Output. Control SignaL
Reference Signal-- Actual Output. Control SignaL
80
c----�
70
Sampling Time Step
Kr
T=25 seconds
Sampling Time Step
Fig. 10: Controlled Output of ANFIS Controller for Trapezoidal
Membership Function
m
Gbellmf (Fuzzy Logic)
M""
.... ber" h i p
I
Function Editor: gbell 1
N
NS
NM
ZR
PS
�
In figure (13) the graph shows the absolute error sum
for the Anfis, gbellmf (370.9652) is coming bit larger than
Gaussian membership function (367.3556), trapezoidal
membership function(368.9700).
I 13 !5f'E/
.....
T=25 seconds
Fig. 13: Controlled Output of AN FIS Controller for Gbell
Membership Function
In the figure (10) the graph shows the absolute error
sum for the Anfis trapmf (368.9700) is coming bit larger
than the Gaussian membership function (367.3556).
E.
Kr
G.
111
P
Triangular Membership Function (Fuzzy Logic)
M
.. ..., bersh ' p
Function Editor: trirnfl
Member$hip
1'"--'-" rx:x:x:x55J
1 '----'--'"----""'l
OB
0.4
02
0
0.2
0..
HefTle
N __
0 '"
0.8
g.,.. .......
r=-----,
Curren. Membership Function (eliek on MF
d
v
10
select)
Ty_
Fig. 11: Gbell Membership Function ofFuzzy Logic
../.
1-...---..1.'
�
,
1'_' "
..
... ,
plot point
'NS
Type
"'­
Reng_
08
tunction PlOts
[_1 . 333_1 -0_6666)
·....
I�
H1)
I1
Fig. 14: Triangular Membership Function ofFuzzy Logic
/
reference
90
signal-aclual output.control signal_
80
...
70
--
.,.60
'"
�50
�
�
E
"
00
40
'" 30
..
""
S�I_I!.pKl'·25wcorwk
20
10
Fig. 12: Controlled Output ofFuzzy Logic Controller for Gbell
Membership Function
I----._--v
-.
J
.'
_ . . . . .. _ . _ . . . .
. .. . .. . . 20
__
,
.. . . . . . . i
: .... , .... � .... .
0.60
40
sampling time step
In the figure (12) the graph shows the absolute error
sum for the G bell function (476.26) is coming much
.
. � ..
Kr T=25
seconds
Fig. 15: Controlled Output ofFuzzy Logic Controller for Triangular
Membership Function
[4]
t
1s IEEE International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES-2016)
REFERENCES
In Fig. 15 the graph shows the absolute error sum for
the Triangular function (430.72) is coming much smaller
than G bell function (476. 26) and trapezoidal function
(501.72) but coming much larger than that for Gaussian
membership function (429.07).
H
[I]
using Wavelet Network", Journal of Computer Science and
Information Systems, Vol. 6, No. 2, pp.141-163.
[2]
Control and Engineering Process Control", Journal of Quality
[3]
Reference Signal-- Actual Output. Contral Signal_
Analysis of Conventional, P, PI, PID and Fuzzy Logic Controllers
Journal of Computer Applications, Vo1.17, No.6, pp.12-16.
70
[4]
50
40
30
K. S. Tang, Kim Fung Man, Guanrong Chen, Sam Kwong, August
2001 -An Optimal Fuzzy PID Controller ll. IEEE Transactions on
Industrial Electronics, Vol.48, No.4, pp.757-765.
60
'"
E
FarhadAslam and GagandeepKaur, March 2011 "Comparative
for the Efficient Control of Concentration in CSTR", International
80
�
(5)
Technology, Vo1.26, NO.2.
90
1�
Douglas C, Montgomery and Ber! Keats J, George C. Runger and
William S. Messina, April 1994 "Integrating Statistical Process
Triangular Membership Function (ANFIS)
A ES= sum (abs (ref-y))
=381. 2979
Q)
Ibrahiem M. M. EI Emary, WalidEmar, and Musbah J. Aqel,
December 2009 "The Adaptive Fuzzy Designed PID Controller
[5]
I---,,--�--V
P. Berk, D. Stajnko and P. Vindis, B. Mursec and M. Lakota, April
20II"Synthesis water level control by fuzzy logic", Journal of
Achievements
20
in
Materials
and
Manufacturing
Engineering,
Vo1.45, NO.2.
10
[6]
Sampling Time Step
Kr
T=25 seconds
Vo1.14, pp.635-650.
Fig. 16: Controlled Output of ANFIS for Triangular Membership
Function
[7]
Computer Applications, Vol.8, No.6, pp.22-27.
[8]
Membership
Trapmf
501.72
368.97
Function
Gbellmf
476.26
370.96
Journal of Computer Science Engineering and Technology, Vol.1,
No.6, pp.315-319.
[9]
NishaJha and Udaibir Singh, T.K.Saxena and AvinashiKapoor,
20II"Optimal Design of Neural fuzzy interference network for
temperature controller 11, Journal of Applied Sciences, Vol.1l,
No.15, Pp.2754-2763.
Trimf
430.72
381.95
[10] Truong Nguyen Luan Vu, Jietae Lee and Moonyong Lee, April
2007 "Design of Multi-Ioop PID Controllers Based on the
Generalized IMC-PID Method with Mp Criterion", International
From the Table 1 it is c1ear that ANFIS system gives
lowest absolute error for Gaussian membership function.
V.
Rahul Malhotral and RajinderSodhi, July 20II"Boiler Flow
Control Using PID and Fuzzy Logic Controller", International
TABLE I: ABSOLUTE ERROR OF CONTROLLER AT DIFFERENT
MEMBERSHIP FUNCTION
Gaussmf
429.07
367.35
YuvrajBhushanKhare and Yaduvir Singh, October 2010"PID
Control of Heat Exchanger System", International Journal of
In Fig.(16) the graph shows the absolute error sum for
the Anfis trimf (381.9652) is coming much bit larger than
the gbell membership function (370.9652), Gaussian
membership function (367.3556), trapezoidal membership
function(368.9700).
Absolute Error of
Controller
Fuzzy Logic
ANFIS
KJ.Astrom and T. Hagglund, 2004 "Revisiting the Ziegler-Nichols
step response method for PID control", Journal of Process Control,
Journal of Control, Automation, and Systems, Vo1.5, No.2,
pp.212-217.
[lI] Jie Zhang, 2007 -Modelling and Multi-objective optimal control of
CONCLUSION
Batch
process
using
recurrent
Neuro-Fuzzy
Networks 11 ,
International Journal of Automation and Computing, Vol.l, pp.17.
The designed fuzzy controller has a good temperature
capability, and control signal has a big change rate in the
region of high temperature.
It is observe that for different membership function;
Gaussian function has good temperature tracking
capability in comparison with Trapezoidal, Triangular,
and Gbell membership function.
The ANFIS controller has a perfect temperature
tracking capability. It produces a stable control signal to
the plant
It is also c1ear that ANFIS controller gives better
results in comparison with fuzzy logic controller and also
have smaller performance index than of fuzzy controller.
[12] Nancy G. Leveson, Mats Per Erik Heimdahl, Holly Hildreth, and
Jon Damon Reese, September 1994 "Requirements Specitication
for Process-Control Systems", IEEE Transactions on software
Engineering, Vol.20, No.9, pp.684-707.
[13] G.T.Thampi, D.R.Kalbande and NileshDeotale, PriyankSinghal and
Sumiran Shah, 2011"An Advanced Technology Selection Model
using Neuro Fuzzy A1gorithm for Electronic Toll Collection
System", International Journal of Advanced Computer Science and
Applications, Vo1.2, No.4.
[14] Mahesh Kr. Nandwanal and NirojPokhrel, S. N. Singh and
J.Kumar, July 2010 -Fuzzy logic control implementation in a PVC
extruderfor temperature control in a cable manufacturing industry ll,
Indian
Journal
pp.798-801.
[5]
of
Science
and
Technology,
Vo1.3,
No.7,
t
1s IEEE International Conference on Power Electronics. Intelligent Control and Energy Systems (ICPEICES-2016)
[15] Rahul Malhotra, Narinder Singh and Yaduvir Singh, December
[18] Bharat Bhushan, October 2013 "Indirect Adaptive Control of
2010 -Fuzzy Logic Modelling, Simulation and Control: A Review,
Nonlinear Systems", In!. J. of Advanced Research in Computer
International Journal of Computer Science and Technology, Vol.1,
Science and Software Engg, vol. 3, issue 10, pp: 1359-1365.
No.2, pp.183-188.
[19] Bharat Bhushan, S.K.Valluru, Madhusudan Singh, April 2013
"Takagi-Sugeno Fuzzy System based Stable Direct Adaptive
[16] Bharat Bhushan, Madhusudan Singh, 2006 "Fuzzy and Neural
Controllers: An Overview", Proc. of 3'" International Conference
Control of Nonlinear Systems", Int. J. of Computer Applications
(0975-8887), vol. 68, no. 15, PP: 30-36.
on Quality, Reliability and Infocom Technology, Indian National
Science Academy, New Delhi, pp. 1-9, 02-04 December.
[20] Ruchi Bansal, Mohit Jain, Bharat Bhushan, "Designing of MuIti­
objective Simulated Annealing Algorithm Tuned PlD Controller
[17] B. Bhushan, M. Singh and Y. Hage, February 2012 "Identification
and Control Using MLP, Elman, NARXSP and Radial Basis
for a Temperature Control System", 2014 IEEE Sixth Power India
Function
Conference.
Networks:
A
Comparative
Analysis,
"
Artificial
Intelligence Review, Springer Journal, vol. 37, issue 2, pp.133-156.
[6]