International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 6, June 2013
ISSN 2319 - 4847
A Survey on the Application of Fuzzy Logic
Controller on DC Motor
Snehashish Bhattacharjee1, Samarjeet Borah2
1&2
Department of Computer Science and Engineering,
Sikkim Manipal Institute of Technology,
Majitar, Rangpo, Gangtok, East Sikkim-737136, Sikkim, India.
ABSTRACT
The development of fuzzy logic has attracted considerable research interest over the past several decades. Several algorithms
are put forwarded regarding design in controlling DC motor, still due to uncertainty and vagueness of data that are collected in
the implementation phase, fuzzy logic becomes an inseparable area in control system. In this paper a detailed study has been
made in a few applications of control system where fuzzy logic has been incorporated in controlling DC motor. This paper has
been arranged in four phases where in the first phase fuzzy logic and fuzzy logic controller has been studied. The next phase
discusses about the uncontrolled response of second order system. The third phase consists of a study the responses of
conventional controller and fuzzy logic controller and a detail comparison has been discussed among uncontrolled response of
second order system, conventional controller of DC motor and fuzzy logic controller taking settling time as a parameter in the
final phase.
Keywords:fuzzy logic, control system, DC motor, conventional controller.
1. INTRODUCTION
Control system consists of elements arranged in a planned manner where an effect is caused by each element to produce
an output. Mathematically a relation can be made between this cause and effect. The application of control system
includes the control of position, velocity, acceleration, temperature, pressure, voltage and current etc [9]. The data that
are sensed in the various applications of control systems more or less have the characteristics of vagueness and
ambiguity which depends on the devices through which sensors that have been used. Actually the physical factors of the
devices are responsible for the degree of vagueness and ambiguity of data. Because of the presence of characteristics of
ambiguity and vagueness in those data that are collected in various intermediate or final phases of control applications ,
though the degree of presence vary from devices to devices, it sometimes becomes harder to get the desired output .
These problems can be said as fuzzy in nature. To overcome this problem, the application model can be defined
formally in the fuzzy setting in order to take operations that can handle data uncertainty.
2. FUZZY LOGIC AND ITS APPLICATIONS
Fuzzy logic began with the 1965 proposal of fuzzy set theory by Lotfi Al Zadeh. It has been applied to many fields,
from control theory to artificial intelligence. Fuzzy logic also known as many-valued logic or probabilistic logic which
has the property to deal with approximate reasoning rather than fixed and exact [1-5]. In compare with traditional logic
they can have varying values, where binary sets deal with two-valued logic, true or false, fuzzy logic variables extend
that truth value that lies in the interval value between 0 and 1. The extended concept of fuzzy logic to handle the
concept of partial truth, where the truth value may lie between entirely true and entirely false [1]. In addition, when
linguistic variables are applied, these degrees may be controlled by specific functions. Fuzzy logic and the probabilistic
logic are mathematically analogous. Both have truth values ranging between 0 and 1; but conceptually not similar
owing to different elucidations. Fuzzy logic relates to "degrees of truth", while probabilistic logic matches to
"probability, likelihood"; as these differ, fuzzy logic and probabilistic logic yield different models of the same realworld situations. Both degrees of truth and probabilities range between 0 and 1 and hence may seem similar at first. For
example, if “tall” is a set defined as heights equal to or greater than 7 feet, a computer would not recognize an
individual of height 6 feet 11 inch as being the member of the set ‘tall’. But how do we assess the uncertainty in the
following question: is the person nearly 7 feet tall? The uncertainty in this case is due to the vagueness or ambiguity of
the adjective ‘nearly’. A 6 feet 11 inch person could clearly be a member of the set of “nearly 6 feet tall” people. In the
first situation, the uncertainty of whether a person, whose height is unknown, is 6 feet or not is binary; the person either
is or is not, and we can produce a probability assessment of that prospect based on height data from many people. But
the uncertainty of whether a person, whose height is unknown, is 7 feet or not is binary. The degree to which the person
Volume 2, Issue 6, June 2013
Page 84
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 6, June 2013
ISSN 2319 - 4847
approaches a height 7 feet is fuzzy. It is essential to realize that fuzzy logic uses truth degrees as a mathematical model
of the vagueness phenomenon while probability is a mathematical model of ignorance. Fuzzy logic has the greatest
success in control applications [1]. Many of the consumer products that we use today involve fuzzy control. Fuzzy logic
is extensively used in machine control [18]. A fuzzy control system which is based on fuzzy theory—a mathematical
system which scrutinizes analog input values in requisites of logical variables that takes on continuous interval
between 0 and 1, in comparison to digital or classical logic, which controls on discrete parameters of either 1 or 0 (true
or false, respectively). Fuzzy controllers are very straightforward conceptually by nature [4]. These include an input
phase, a processing phase, and an output phase respectively. The input stage illustrates sensor or additional inputs, like
switches, thumbwheels etc., to the suitable membership functions as well as the truth values. Each appropriate rule is
invoked by the processing stage and generates a result for each, then merges the results each of the rules. Eventually,
the output stage renovates the combined outcome back into a precise control output value. The most frequent shape of
membership functions is triangular shape, although trapezoidal shape and bell curves are also worn, but the shape is
usually not so important than the any other number of curves and their assignment. From three to seven curves are
usually appropriate to envelop the essential assortment of an input value, otherwise the "Universe of Discourse" in
fuzzy terminology. As explained earlier, the processing stage is depended on a collection of fuzzy-logic rules in the
form of fuzzy ‘IF-THEN’ statements, where the ‘IF’ part is termed as the "antecedent" and the ‘THEN’ portion is
termed as the "consequent".
2.1 Components of fuzzy systems
A fuzzy system is a computing framework based on the concepts of theory of fuzzy sets, fuzzy rules and fuzzy
inference. Four components of fuzzy systems exist: a knowledge base, a fuzzification interface, an inference engine and
a defuzzification interface.
The knowledge base consist of a rule base defined in terms of fuzzy rules, and a data base that contains the definitions
of the linguistic terms for each input and output linguistic variable.
The fuzzification interface transforms the (crisp) input values into fuzzy values, by computing their membership to all
linguistic terms defined in the corresponding input domain.
The inference engine performs the fuzzy inference process, by computing the activation degree and the output of each
rule.
The defuzzification interface computes the (crisp) output values by combining the output of the rules and performing a
specific transformation.
There are so many approaches in which fuzzy modeling can be done which are described in [6].
2.2 The direct approach to fuzzy modeling
In this approach, the system is first linguistically described, based on the expert‘s a priori knowledge. It is then
translated into the formal structure of a fuzzy model following the steps proposed by Zadeh which have been described
in [6].
Selection of the input, state, and output variables (structural parameters);
Determination of the universes of discourse (structural parameters);
Determination of the linguistic labels into which these variables are partitioned (structural parameters);
Definition of the membership functions corresponding to each linguistic label (operational parameters);
Definition of the rules that describe the model‘s behavior (connective parameters);
Selection of an adequate reasoning mechanism (logic parameters);
Evaluation of the model adequacy.
Besides these a number of approaches has been detailed in [6].
2.3 Approaches based on classic identification algorithms
A fuzzy model is a special type of nonlinear model. In this context, fuzzy modeling may be done applying classic
nonlinear identification methods. These methods deal with an iterative, convergent, estimationof a set of numeric
parameters, which are applied to a, usually pre-defined, model structure in order to approximate an expected behavior.
In these fuzzy modeling approaches, the general structure of the fuzzy system (i.e., logic and structural parameters) is
pre-defined, while the rest of the system (i.e., connective and operational parameters) is estimated.
2.4 Constructive learning approaches
In this approach, the a priori expert knowledge serves to direct the search process instead of being used to directly
construct a part of, or the whole, fuzzy system. After an expert-guided definition of the logic parameters and of some of
the structural parameters (mainly relevant variables and their universes of discourse), a sequence of learning algorithms
is applied so as to progressively construct an adequate final fuzzy model. Most of the methods belonging to this class
Volume 2, Issue 6, June 2013
Page 85
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 6, June 2013
ISSN 2319 - 4847
begin by identifying a large fuzzy system—even systems with one rule for each training case—satisfying certain
performance criteria.
2.5 Bio-inspired approaches: Neuro-fuzzy and evolutionary-fuzzy[6]
Artificial neural networks, evolutionary algorithms, and fuzzy logic belong to the same family of bio-inspired
methodologies. Indeed, they model in different extents natural processes such as evolution, learning, or reasoning. The
dynamic and continuously growing research on these subjects, have allowed identifying the strengths and weaknesses
of each methodology, motivating a relatively recent trend to combine them in order to take advantage of their
complementarities. In fuzzy modeling, such combinations have originated hybrid techniques known as neuro-fuzzy
systems and evolutionary fuzzy modeling.
3. FUZZY LOGIC APPLICATION IN DC MOTOR
Conventional controllers were used to control the speed of DC motor for various industrial processes due to their
simplicity in their operations [7].To control DC motor it is very obvious to know that DC motor is a second order
system. So in this paper we shall first come across a general uncontrolled second order system and we shall calculate
the response time. This response time will then be compared with conventional PID and fuzzy logic controller.
A second order can be defined as follows [11],
Ωm(s)=VT(s)
(1)
Where Ωm(s) is the output and VT(s)is the input step signal.
is the natural frequency of oscillation.
Now when <1, the uncontrolled response can be calculated as follows,
Figure 1 Uncontrolled response when <1
Similarly, when
, the uncontrolled response is shown in the following figure [Figure 2],
Figure 2 Uncontrolled response when
The following figure depicts the second order response when
[Figure 3]
Figure 3 Response of second order system when
The following figure shows the response of a second order control system when
Volume 2, Issue 6, June 2013
, [Figure 4]
Page 86
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 6, June 2013
ISSN 2319 - 4847
Figure 4 Response when
If the curves are observed properly it can be said that the settling time of the curve when
A detailed comparison table has been given of all the second order response.
is the minimum.
Table 1: Second order Un-controlled response time table
Second order response when
<1
Settling time (in secs)(Approximate)
Above 30
Above 100
15
Above 20
PID (proportional integral derivative) is one of those conventional controllers that have been used in earlier to design
DC motor controller. Fuzzy logic based approach has been proposed and it has been proved in many times that motor
parameters are controlled better than conventional approach [7]. The rule based decision approach makes fuzzy logic a
unique domain to control a process that a human can control manually with expertise gained from previous experience.
A good comparison study between conventional PID controller and fuzzy logic controller has been formulated in [7]
where the authors have been successfully differentiated between these two controllers. The architecture of the fuzzy
control [7] consists of four steps: fuzzification, fuzzy reasoning, defuzzification, fuzzy knowledge base and it is shown
in the following figure [Figure 5]
Fuzzification
Fuzzy
reasoning
Error input
Defuzzification
Controller
output
Fuzzy knowledge
base
Figure 5 Architecture model of fuzzy control
The response of the conventional proportional controller and PID controller is shown in the following figure that has
been formulated in [7].
Figure 7 Step response of PID controller.
Volume 2, Issue 6, June 2013
Page 87
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 6, June 2013
ISSN 2319 - 4847
Figure 8 Response of fuzzy logic controller.
The comparison of settling time and maximum overshoot for the above two controllers are also calculated in [8]
Table 2: Comparison of maximum overshoot and settling time
Controller
Maximum overshoot(%)
Settling time(sec)
PID controller
44.6
11.42
Fuzzy logic controller
7.21
7.78
Another method PID like FLC [8] proposed where the performance between conventional PID and PID like FLC are
compared which is shown in the following figure. The dotted line represents response of PID like FLC and solid line
represents conventional PID.
Figure 9 Step response of armatured controlled DC motor using conventional and PID like FLC controllers.
The rise time and the settling time for both the controllers which have been calculated in [8] are shown in below table.
Table 3: the rise time and the settling time for conventional PID and PID like FLC
Controller
Rise time(sec)
Settling time(sec)
Conventional PID
7
12
PID like FLC
4
5
Finally, the results based on the analysis carried out among all the techniques to control DC motor are consolidated in
table 4. It depicts the comparison of all the responses in terms of settling time.
Table 4: Comparison table of all the responses
Responses
Uncontrolled second order response(
Volume 2, Issue 6, June 2013
Settling time (approximate in secs)
)
15
Page 88
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 6, June 2013
ISSN 2319 - 4847
Conventional PID by D Sharma
11.42
Fuzzy logic controller by D Sharmah
7.78
Conventional PID by Natshaeh et al
12
PID like FLC
5
4. CONCLUSION
In this paper, a comparative analysis has been carried out between PID controller and fuzzy logic controller. Although
it has been studied that conventional controller gives a very efficient result, but the time taken by the motor to become
steady is very high. The analysis also shows that PID like FLC is better than conventional PID. So both the result
suggests that fuzzy logic controller is better than conventional controllers. But in future it will be more desirable that
the response time taken by the motor should be less than 5 seconds.
References
[1.] Timothy J. Ross, ‘Fuzzy Logic with Engineering and Application’, 3rd Ed, India, Wiley India Pvt. Ltd, ch 13,
pp-408-433, 2010.
[2.] He Yikang, ‘Computer Simulation of AC Motor Vuying Speeds System’, Zhejiang UniversityPress, 1993
[3.] J.M. Mendel, ‘Fuzzy Logicsystems for engineering A tutorial,Proceedings’, IEEE, 83 3, 1995, pp. 345–377.
[4.] R Jager, ‘Fuzzy logic in control’, PhD Thesis, Delft university, Holland, 1995.
[5.] K.J. Astrom, ‘Computer controlled systems’, Prentice-Hall, UK, 1990.
[6.] Sharma,’Designing and Modeling Fuzzy Control Systems’,International Journal of Computer
Applications,Volume 16– No.1, February 2011,pp.46-53
[7.] R.Malhotra,T Kaur,G.S.Deol, ’Dc Motor Control Using Fuzzy Logic Controller’, International Journal Of
Advanced Engineering Sciences And Technologies Vol No. 8, Issue No. 2, pp.291 – 296.
[8.] E. Natsheh, K.A. Buragga ‘Comparison between Conventional and Fuzzy Logic PID Controllers for Controlling
DC Motors’, IJCSI International Journal of Computer Science, Vol. 7, Issue 5,pp.128-134 September 2010.
[9.] Shakowat Zaman Sarkar, “A proposed Air–conditioning System using Fuzzy Algorithm for Industrial
Application” ICSEIEEE Proc. (2006) 832-834
[10.] M.Y. Hassan and F. Waleed Sharif, “Design of FPGA Based PID-like Fuzzy Controller for Industrial
Applications”, IAENG, IJCS.34:2 (2005)
[11.] B.S Manke, ‘Linear Control Systems’ Khanna Publishers,Eleventh edition,2012,pp-131-140
[12.] P. C. Sen, ‘Principles of Electric Machines and PowerElectronics’. 2nd Ed,India Wiley India Pvt. Ltd, ch 04,
2009, pp.-121-200.
[13.] Kevin Warwick, ‘Introduction To Control Systems’,2nd Ed,World Scientific Publishing Co. Pvt. Ltd, Ch 09,
1996, pp.-274-305.
[14.] C. C. Lee, ‘FuzzyLogic In Control Systems : Fuzzy Logic Controller’,IEEE transactions on systems ,Man and
Cybernatics vol-20 no-2 1990, pp.-404-418,.
[15.] W. Leonard, ‘Control of electrical drives’, Springer-Verlag, Berlin Heidelberg, New York, 1985.
[16.] Cavallo, R. Setola, F. Vasca, ‘Using Matlab, Simulink and control system toolbox: A practical approach’, Prentice
Hall, Europe, UK, 1995.
[17.] J.L. Afonso, J. Fonseca, J.S. Martins, C. Couto, ‘Fuzzy logic techniques applied to the control of a three-phase
induction motor’, ISIE’97- IEEE International symposium on Industrial Electronics, Guimara˜es, Portugal, July 711, 1997, IEEE, pp. 1179–1184.
[18.] Guanrong
Chen,
Young
Hoon
Joo,
“Introduction
to
Fuzzy
Control
Systems”,
raic.kunsan.ac.kr/paper/BOOK/book-2000-3.pdf, 2001.
AUTHORS
Snahashish Bhattacharjee received the B.Sc (Hons.) in Mathamatics from Gauhati University in 2008,
MCA from Sikkim Manipal Institute of Technology in 2011 and pursuing student of M. Tech in
Computer Science and Engineering from Sikkim Manipal Institute of Technology during 2011-2013. His
numerous publications are in several domains like, Digital Image Processing, Communications and
Volume 2, Issue 6, June 2013
Page 89
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 6, June 2013
ISSN 2319 - 4847
Networking etc. He has been doing the research-based project in Fuzzy-logic based motor controllers.
Dr. Samarjeet Borah is currently working as Associate Professor in the Department of Computer Science &
Engineering in Sikkim Manipal Institute of Technology, Sikkim, India. He has obtained his Ph. D. (Engg)
from Sikkim Manipal University in 2010 and M. Tech. degree in Information Technology from Tezpur
University, Assam, India in the year 2006. His major field of study is Data Mining and Bioinformatics. He
has published around forty research papers in various journals and conference proceedings. Dr. Borah is a member of
various national and international organizations like ACM (CSTA), International Association of Engineers (IAENG),
Hong Kong and International Association of Computer Science & Information Technology (IACSIT), Singapore.
Volume 2, Issue 6, June 2013
Page 90