Fuzzy Logic control system Report

1. [1]
ABSTRACT
Automobiles have become an integrated part of our daily life. The development of
technology has improved the automobile industry in both cost & efficiency. Still, accidents
prove as challenge to technology. Man is intelligent with reasoning power and can respond
to any critical situation. But under stress and tension he falls as a prey to accidents. The
manual control of speed & braking of a car fails during anxiety. Thus automated speed
control & braking system is required to prevent accidents. This automation is possible only
with the help of Artificial Intelligence (Fuzzy Logic). Fuzzy Logic control system is used to
control the speed of the car based on the obstacle sensed, the angle of the obstacle is sensed
and the speed is controlled according to the angle subtended by the obstacle. If the obstacle
cannot be crossed by the car, then the brakes are applied and the car comes to rest before
colliding with the obstacle. Thus, this automated fuzzy control unit can provide an accident
free journey.

2. [2]
1. INTRODUCTION
Fuzzy logic is best suited for control applications, such as temperature control, traffic
control or process control. Fuzzy logic seems to be most successful in two kinds of
situations:
i) Very complex models where understanding is strictly limited, in fact, quite judgmental.
ii) Processes where human reasoning, human perception, or human decision making are
inextricably involved.
Our understanding of physical processes is based largely on imprecise human reasoning.
This imprecision (when compared to the precise quantities required by computers) is
nonetheless a form of information that can be quite useful to humans. The ability
to embed such reasoning and complex problem is the criterion by which the efficacy
of fuzzy logic is judged.
Undoubtedly this ability cannot solve problems that require precision problems such
as shooting precision laser beam over tens of kilometres in space; milling machine
components to accuracies of parts per billion; or focusing a microscopic electron beam
on a specimen of size of a nanometre. The impact of fuzzy logic in these areas might
be years away if ever. But not many human problems require such precision -problems
such as parking a car, navigating a car among others on a freeway, washing clothes,
controlling traffic at intersections & so on. Fuzzy logic is best suited for these problems
which do not require high degree of precision.
Alternatively, fuzzy systems theory can have utility in assessing some of our more
conventional, less complex systems. For example, for some problems exact solutions are
not always necessary. An approximate, but fast, solution can be useful in making
preliminary design decisions, or as an initial estimate in a more accurate numerical
technique to save computational costs, or in the myriad of situations where the inputs to a
problem are vague, ambiguous, or not known at all. For example, suppose we need a
controller to bring an aircraft out of a vertical dive. Conventional controllers cannot handle
this scenario as they are restricted to linear ranges of variables; a dive situation is highly
nonlinear. In this case, we could use a fuzzy controller, which is adept at handling nonlinear
situations albeit in an imprecise fashion, to bring the plane out of the dive into a more linear

3. [3]
range, then handoff the control of the aircraft to a conventional, linear, highly accurate
controller
2. CLASSICAL SETS AND FUZZY SETS
A classical set is defined by crisp boundaries, i.e., there is no uncertainty in the prescription
or location of the boundaries of the set, as shown in Fig.1a where the boundary of crisp set
A is an unambiguous line. A fuzzy set, on the other hand, is prescribed by vague or
ambiguous properties; hence its boundaries are ambiguously specified, as shown by the
fuzzy boundary for set in Fig. 1.b.
Figure-1
Outside the boundary region of the fuzzy set, point b is clearly not a member of the fuzzy set.
However, the membership of point c, which is on the boundary region, is ambiguous. If
complete membership in a set (such as point a in Fig. 2.1b) is represented by the number 1,
and no-membership in a set (such as point b in Fig. 2.1b) is represented by 0, then point c in
Fig. 2.1bmust have some intermediate value of membership (partial membership in fuzzy set
) on the interval [0,1]. Presumably the membership of point c in A approaches a value of 1
as it moves closer to the central (unshaded) region in Fig. 2.1b of A and the membership of
point c in A approaches a value of 0 as it moves closer to leaving the boundary region of .A

4. [4]
2.1. Fuzzy sets:
In classical, or crisp, sets the transition for an element in the universe between
membership and non-membership in a given set is abrupt and well-defined (said to be
‘‘crisp’’). For an element in a universe that contains fuzzy sets, this transition can be
gradual. This transition among various degrees of membership can be thought of as
conforming to the fact that the boundaries of the fuzzy sets are vague and ambiguous.
Hence, membership of an element from the universe in this set is measured by a function
that attempts to describe vagueness and ambiguity.
A fuzzy set, then, is a set containing elements that have varying degrees of membership in
the set. This idea is in contrast with classical, or crisp, sets because members of a crisp set
would not be members unless their membership was full, or complete, in that set (i.e.,
their membership is assigned a value of 1). Elements in a fuzzy set, because their
membership need not be complete, can also be members of other fuzzy sets on the same
universe .Elements of a fuzzy set are mapped to a universe of membership values using a
Function-theoretic form. As
Fuzzy sets are denoted in this text by a set symbol with a tilde under strike; so, for
example, A would be the fuzzy set A. This function maps elements of a fuzzy set A to a
real numbered value on the interval 0 to 1.If an element in the universe, say x, is a
member of fuzzy set A, then this mapping is given by µA(x)∈[0,1]. This mapping is
shown in Fig. 2.14 for a typical fuzzy set .A notation convention for fuzzy sets when the
universe of discourse, X, is discrete and finite, is as follows for a fuzzy set A
When the universe, X, is continuous and infinite, the fuzzy set A is denoted by

5. [5]
Membership function for fuzzy set A
Figure-2
2.2.FuzzyVs. Probability:
Fuzziness describes the ambiguity of an event, whereas randomness (probability)
describes the uncertainty in the occurrence of the event. An example involves personal
choice. Suppose a person seated at a table on which rest two glasses of liquid. The
liquid in the first glass is described to you as a 95 percent change of being healthful and good.
The liquid in the second glass is described as having a 0.95 membership in the class of
“healthful & good” liquids. Which glass would the person select, keeping in mind first
glass has a 5 percent chance of being filled with non-healthful liquids including poisons.
What philosophical distinction be made regarding these two forms of information? Suppose
that person allowed to test the in the glasses. The prior probability of 0.95 in each case
becomes a posterior probability of 1.0 or 0; i.e., the liquid is either benign not. However,
value of 0.95, which measures the drinkability of the liquid is “healthful & good”,
remains 0.95 after measuring & testing. These examples illustrate very clearly the
difference in the information content between change & ambiguous events.

6. [6]
3. MEMBERSHIP FUNCTION:
Membership function characterize the fuzziness in a fuzzy set, whether the elements in
the set are discrete or continuous - in a graphical form for eventual use in the
mathematical formalisms of fuzzy set theory. Just as there is infinite number of ways
to characterize fuzziness, there are an infinite number of ways to graphically depict the
membership functions that describe fuzziness.
3.1 Features ofthe membership function:
Since all information contained in a fuzzy set is described by its membership function, it is
use full to develop a lexicon of terms to describe various special features of this function. For
purposes of simplicity, the functions shown in the following figures will all be continuous,
but the terms apply equally for both discrete and continuous fuzzy sets. Figure below assists
in this description. The core of a membership function for some fuzzy set A is defined as that
region of the universe that is characterized by complete and full membership in the set A
.That is, the core comprises those elements x of the universe such that µA (x)=1. The support
of a membership function for some fuzzy set A is defined as that region of the universe that is
characterized by nonzero membership in the set A .That is, the support comprises those
elements x of the universe such that µA(x) >0.
Figure-3

7. [7]
The boundaries of a membership function for some fuzzy set A are defined as that region of
the universe containing elements that have a nonzero membership but not complete
membership. That is, the boundaries comprise those elements x of the universe n such that
0<µA(x) <1. These elements of the universe are those with some degree of fuzziness, or only
partial membership in the fuzzy set A. Figure below illustrates the regions in the universe
comprising the core, support, and boundaries of a typical fuzzy set. A normal fuzzy set is one
whose membership function has at least one element x in the universe whose membership
value is unity. For fuzzy sets where one and only one element has a membership equal to one,
this element is typically referred to as the prototype of the set, or the prototypical element.
Figure 4 illustrates typical normal and subnormal fuzzy sets.
(Normal) (Sub normal)
Figure-4
4.FUZZIFICATION:
Fuzzification is the process of making a crisp quantity fuzzy. We do this by simply
recognizing that many of the quantities that we consider to be crisp & deterministic are
actually not deterministic at all. They carry considerable uncertainty. If the form of
uncertainty happens to arise because of imprecision, ambiguity, or fuzzy and can be
represented by a membership function.

8. [8]
5.DEFUZZIFICATION:
Defuzzification is the conversion of a fuzzy quantity to a precise quantity, just as
fuzzification is the conversion of precise quantity to a fuzzy quantity. Some of the
defuzzification techniques are:
5.1. Max - Membership Principle:
Also known as the height method, this scheme is limited to peaked output
junctions. This method is given by the algebraic expression
5.2. Centroid Method:
This procedure (also called centre of area, centre of gravity) is the most prevalent &
physically appealing of all the defuzzification methods; it is given by the algebraic
expression:
5.3. WeightedAverage Method:
This method is only valid for symmetrical output membership function. It is given by the
algebraic expression:

9. [9]
5.4. Means-MaxMembership:
This method (also called middle-of maxima) is closely related to the first method,
except that the locations of the maximum membership can be non-unique
(i.e., the maximum membership can be a plateau rather than a single point. This method is
given by the expression:
6.FUZZY LOGIC CONTROLSYSTEM:
A control system for a physical system is an arrangement of hardware components designed
to alter, to regulate, or to command, through a control action, another physical system so that
it exhibits certain desired characteristics or behaviour. Control systems are typically of two
types: open-loop control systems, in which the control action is independent of the physical
system output, and closed-loop control systems (also known as feedback control systems), in
which the control action depends on the physical system output.
The general problem of feedback control system design is defined as obtaining a generally
nonlinear vector-valued function h ( ), defined for some time, t, as follows
U(t)=h[t ,x(t),r(t)]
Where u(t)is the control input to the plant or process ,r(t)is the system reference
(desired)input, and x(t) is the system state vector; the state vector might contain quantities
like the system position, velocity, or acceleration. The feedback control law his supposed to
stabilize the feedback control system and result in a satisfactory performance. In the case of a
time-invariant system with a regulatory type of controller, where the reference input is a
constant set point,

10. [10]
7.AUTOMATED AUTOMOBILES
7.1. Obstacle Sensor Unit:
The car consists of a sensor in the front panel to sense the presence of the obstacle.
7.2. Sensing Distance:
The sensing distance depends upon the speed of the car. As the speed increases the sensing
distance also gets increased, the obstacle can be sensed at a large distance for higher
speed and the speed can be controlled by gradual anti-skid braking system. The speed of
the car is taken as the input and the distance sensed by the sensor is controlled.
7.3. Mechanism:-
A fuzzy system with two inputs and one output, the best way to represent it is a nXm matrix,
where n and m are the numbers of linguistics terms for each of the two inputs, and each cell
of the matrix contains the desired output for the combination of input values. Suppose a Car
breaking control system with two inputs: distance and velocity. The output is the range to be
applied in the break. The distance goes from 0 to 100meters and can be describe as: very near
(VN), near (N), far (F) and very far (VF). The velocity goes from 0 km/h to 100 km/h and can
be described as: none (N), very slow (VS), slow (S), fast (F) and very fast (VF). The range to
be applied to the brake goes from 0% to 100% and can be described as: none (N), weak (W),
strong (S), very strong (VS). One single rule among the many possible would be:
IF velocity. is fast AND distance is near THEN strength is very strong. A reasonable set of
rules, with the rule in grey background, would be described as in Table

11. [11]
The linguistic terms “near” and “far”, the meaning are described by the membership
functions of these terms. “Distance”, “Velocity” and “Range” are linguistic variables, taking
on values in the real domain. “Near”, “far”, etc. are linguistic terms and describe fuzzy sets.
The rules say that if a value has membership greater than zero to a pair of fuzzy sets, then a
specific output is necessary.
Input membership function for distance
Figure-5
Input membership function for velocity
Figure-6

12. [12]
Output membership function
Or control action
Figure-7
The functions of Figure are used for the fuzzification, the first step of any fuzzy system. The
functions of Figure, relative to the output, are used for the reasoning and defuzzification.
Since the linguistic terms are fuzzy sets, and their support intersect, it is expected that, given
a distance and a velocity value, one or more rules will fire.
7.4. Speed Control:
The speed of the car is controlled according to the angle subtended by the obstacle.
The angle subtended by the obstacle is sensed at every instant. Obstacles which the car can
overcome: At any instant, if the obstacle subtends an angle less than 60 degree then the
car can overcome the obstacles and the speed of the car reduces according to the angle.

13. [13]
7.5. Obstacles which the car cannot overcome:
At any instant, if the angle subtended by the obstacle is greater than 60 degree, then the
car comes to rest before colliding with the obstacle as the car cannot overcome the
obstacle
8. Conclusion:
In this world of stress and tension where the drivers concentration is distracted in many
ways, an automated accident prevention system is necessary to prevent accidents. The
fuzzy logic control system can relieve the driver from tension and can prevent accidents.
This fuzzy control unit when fitted in all the cars can result in an accident free world.
9. Reference:
[1] Timothy J. Ross “Fuzzy logic for Engineering Applications”, 2nd
edition, Pearson education
[2] http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?reload=true&punumber=91