Universal Fuzzy Logic Controller

Universal Fuzzy Logic Controller Sourabh Kaushal, Raghav Sharma

Department of electronics & Communication

Institute of science & Technology Klawad, Haryana,India

Email: [email protected], [email protected]

ABSTRACT – This research paper emphasis on the

universal controller implemented by us. Fuzzy logic is a

powerful problem-solving methodology with wide range

of application in industrial control, consumer

electronics, management, medicine, expert system and

information technology. It provides a simple way to

draw definite conclusion from vague information and is

very close to the way the human being think and make

decision even under highly uncertain environment.

Fuzzy logic has rapidly become one of the most

successful of today's technologies for developing control

systems. The reason for which is very simple. Fuzzy

logic addresses such applications perfectly as it

resembles human decision making with an ability to

generate precise solutions from certain or approximate

information. It fills an important gap in engineering

design methods left vacant by purely mathematical

approaches (e.g. linear control design), and purely logic-

based approaches (e.g. expert systems) in system design.

In our research we implemented the mamdani type

fuzzy logic controller using MATLAB software. In

addition, we also implemented the algorithm for

universal implementation of Mamdani type fuzzy logic

controller.

Keywords: Fuzzy, Controller, Mamdani Model, MATLAB

I. INTRODUCTION

The research work deals with a Fuzzy Logic

Controller using MATLAB. An example system i.e.

battery charger is being implemented using

MATLAB for testing purpose. The response of the

system will be simulated by using Fuzzy Logic

Toolbox in MATLAB. The aim of this project is to

design a fuzzy logic based rapid battery charger that

has two inputs, temperature and temperature gradient,

and charging current as output. The battery

temperature can vary between 0 and 50 degree

centigrade. The battery is likely to get damaged

beyond this temperature. Let us assume that the

temperature sensor gives 0-5 volts as output,

corresponding to the variation in temperature in range

0 to 50 degree centigrade which is divided into 50

equal parts, each part representing one-degree

temperature. The temperature gradient obtained from

sensor is in mv/10 seconds.

II. METHODOLOGY

A. Using MATLAB along with FIS editor

For implementation of Mamdani type fuzzy logic

system we are using MATLAB so here we are giving

a brief introduction to MATLAB along with FIS

editor which has been used for verifying the

implemented system.

MATLAB is a product of The Math works, Inc.

and is an advanced interactive software package

specially designed for scientific and engineering

computation. The Matlab environment integrates

graphic illustrations with precise numerical

calculations, and is a powerful, easy-to-use, and

comprehensive tool for performing all kinds of

computations and scientific data visualization.

Matlab has proven to be a very flexible and usable

tool for solving problems in many areas. Matlab is a

high-performance language for technical computing.

It integrates computation, visualization, and

programming in an easy-to-use environment where

problems and solutions are expressed in familiar

mathematical notation [7].

B. FIS Editor window in MATLAB

The FIS Editor displays general information about

a fuzzy inference system. There is a simple diagram

at the top that shows the names of each input variable

on the left, and those of each output variable on the

right[7].

mailto:[email protected]

mailto:[email protected]

Figure1

FIS Editor Window

The sample membership functions shown in the

boxes are just icons and do not depict the actual

shapes of the membership functions:

Above the diagram is the name of the

system and the type of inference used. The

default, Mamdani-type inference, is what is

described so far and what you continue to

use for this example. Another slightly

different type of inference, called Sugeno-

type inference, is also available. This

method is explained in Sugeno-Type Fuzzy

Inference.

Above the name of the fuzzy inference

system, on the left side of the figure, are the

pop-up menus that allow you to modify the

various pieces of the inference process.

On the right side at the bottom of the figure

2 is the area that displays the name of either

an input or output variable, its associated

membership function type, and its range.

The latter two fields are specified only after

the membership functions have been.

Above that region are the Help and Close

buttons that call up online help and close the

window, respectively. At the bottom is a

status line that relays information about the

system.

Figure 2

Membership Function Window

The Membership Function Editor is the tool that

lets you display and edit all of the membership

functions associated with all of the input and output

variables for the entire fuzzy inference system. When

you open the Membership Function Editor to work

on a fuzzy inference system that does not already

exist in the workspace, there are no membership

functions associated with the variables that you

defined with the FIS Editor. On the upper-left side of

the graph area in the Membership Function Editor is

a "Variable Palette" that lets you set the membership

functions for a given variable [1]. To set up the

membership functions associated with an input or an

output variable for the FIS, select a FIS variable in

this region by clicking it.

Figure3

Rule Viewer Window

The Rule Viewer displays a roadmap of the whole

fuzzy inference process. It is based on the fuzzy

inference diagram described in the previous section.

You see a single figure window with 19 plots nested

in it. The six plots across the top of the figure

represent the antecedent and consequent of the first

rule. Each rule is a row of plots, and each column is a

variable. The rule numbers are displayed on the left

of each row. You can click on a rule number to view

the rule in the status line.

The first two columns of plots (the twelve

yellow plots) show the membership

functions referenced by the antecedent, or

the if-part of each rule.

The third column of plots (the six blue plots)

shows the membership functions referenced

by the consequent, or the then-part of each

rule.

The seventh plot in the third column of plots

represents the aggregate weighted decision

for the given inference system. This decision

will depend on the input values for the

system. The defuzzified output is displayed

as a bold vertical line on this plot.

III. WORKING OF FUZZY SYSTEM

We refer to figure 4 to illustrate the working of

fuzzy system. We consider here a compositional

inferencing system. Other kinds of inferencing

mechanism are not discussed here. A fuzzy system

working under the frame work of compositional

inference mechanism performs its computing in the

following 5 steps.

Figure4

Flow Chart of Fuzzy System

STEP 1:- FUZZIFICATION OF THE INPUTS

Fuzzification is a process of transforming the crisp

input value to the corresponding value in fuzzy

domain. In this step fuzzifier take the input and

determine the degree which they belong to each of

the appropriate fuzzy set via membership functions.

The input is always crisp numerical value.

STEP 2:- APPLY FUZZY OPERATORS

Usually the antecedent of a given rule has more

than one part hence; the fuzzy operators are applied

to obtain one number that represents the result of the

antecedent for that rule. This will then be applied to

obtain one number that represents the result of the

antecedent for that rule. This number will then apply

to the output function. The input to a fuzzy operator

is two or more membership value from fuzzified

input variables. The output is single truth value. We

mention only two commonly used fuzzy operators

here namely “MIN” corresponding to “and”

connective and “MAX” operator corresponding to

“or” connective. For example if we have the

following rule regarding rating of a university

department: IF (RESEARCH is GOOD) and

(STUDENT_EMPLOYMENT is HIGH) then

(Department Rating is Excellent) And let us further

assume that crisp input value of variables

RESEARCH and STUDENT_EMPLOYMENT

Fuzzify Inputs

Apply Composition Operators

Apply Implication Operators

Aggregate All Outputs

Defuzzify

are such that these have a membership grade of 0.8

and 0.4 in fuzzy set GOOD and HIGH respectively,

then our and operation will result into

Min (0.8, 0.4) =0.4

This is graphically represented in figure

Figure5

Research Data

Figure6

STUDENT_EMPLOYMENT

STEP 3:- APPLY IMPLICATION METHODS The shaping of the consequent based on the

composed value of antecedent is termed as

implication. The input for the implication process is a

single number obtained from the composition process

and the output is a fuzzy set. Implication is applied

for each rule. Two commonly used implication

operators are MIN and PRODUCT.

STEP 4:- AGGREGATE ALL OUTPUTS

Aggregation is a process by which several fuzzy

sets are combined into a desirable way to produce a

single fuzzy set. Aggregation is performed by

combining all the fuzzy sets that represent the output

of each rule into a single fuzzy set. Aggregation only

occurs once for each output variable. For our model

the input of the aggregation process is the list of

truncated output function returned by implication

process for each rule. The output of the aggregation

process is one fuzzy set for output variable.

STEP 5:- DEFUZZIFY

Defuzzification means the fuzzy to crisp

conversions. The fuzzy results generated cannot be

used as such to the applications, hence it is necessary

to convert the fuzzy quantities into crisp quantities

for further processing. This can be achieved by using

defuzzification process. The defuzzification has the

capability to reduce a fuzzy to a crisp single-valued

quantity or as a set, or converting to the form in

which fuzzy quantity is present. Defuzzification can

also be called as “rounding off” method.

Defuzzification reduces the collection of membership

function values in to a single sealer quantity.

Defuzzification transforms the fuzzy value to crisp

values. The input for the defuzzification process is a

fuzzy set and the output is a corresponding single

crisp number. The process of defuzzification in fuzzy

system is not a standard one. There are numerous

defuzzification methods available. In this research

work we used Mamdani style interference.

IV. INTEFERENCE STYLE

Mamdani type inference, as defined it for the

Fuzzy Logic Toolbox, expects the output

membership functions to be fuzzy sets. After the

aggregation process, there is a fuzzy set for each

output variable that needs defuzzification. It is

possible, and in many cases much more efficient, to

use a single spike as the output membership function

rather than a distributed fuzzy set[2]. This is

sometimes known as a singleton output membership

function, and it can be thought of as a pre-defuzzified

fuzzy set. It enhances the efficiency of the

defuzzification process because it greatly simplifies

the computation required by the more general

Mamdani method, which finds the centroid of a two-

dimensional function. Rather than integrating across

the two-dimensional function to find the centroid, the

weighted average of a few data points. Sugeno type

systems support this type of model. In general,

Sugeno type systems can be used to model any

inference system in which the output membership

functions are either linear or constant[3].

Figure 7

A two input, two rule Mamdani FIS with crisp inputs

The usual method of designing a control system

based on of fuzzy logic result from obtaining the

knowledge of the process and then encoding this

knowledge in term of rule. To design a fuzzy logic

control one has to describe the operation

linguistically[4]. Generally, the design steps involved

are

Determining a set of fuzzy rules.

Fuzzifying the inputs using the input

membership functions.

Combining the fuzzified inputs according to

the fuzzy rules to establish a rule strength.

Finding the consequence of the rule by

combining the rule strength and the output

membership function.

Combining the consequences to get an

output distribution.

Defuzzifying the output distribution (this

step is only if a crisp output(class) is

needed).

The input and output variable, membership

function and rule based come from the complete

knowledge of process. Generally, it is not possible to

define this parameter in one attempt and consequent

tuning of membership function and rule is

continuously done until an acceptable response is

obtained.

V. DESIGNING BATTERY CHARGER

In this section, we have described how to design a

battery charger using fuzzy inference system editor in

MATLAB[7]. The charger design can be represented

as shown in figure below:

Figure8

Fuzzy Designing System

Figure 9

Input Variable Temperature Membership Function

The figure 9 is represents the membership

function of first input variable i.e. temperature. In the

above figure there are different types of membership

function i.e. z-function. Triangular function, sigma

function, It specify the parameters of all the

membership functions of temperature. The value of

temperature can vary between 0 to 50.

Figure10

Input Variable Temperature Gradient Membership

Function

The figure 10 represents the membership function

of second input variable i.e. temperature gradient. It

specify the parameters of all the membership

functions of temperature gradient. The value of

temperature gradient can vary between 0 to 1.

Figure 11

Output Variable Charging Current Membership

Function

The figure 11 represents the membership function

of output variable i.e. charging current. The value of

charging current vary between 0 to 4.

VI. RULE BASE

Rules form the basis for the fuzzy logic to obtain

the fuzzy output. The rulebased system is different

from the expert system in the manner that the rules

comprising the rule-based system originates from

sources other than that of human experts and hence

are different from expert systems[5]. The rule-based

form uses linguistic variables as its antecedents and

consequents. The antecedents express an inference or

the inequality, which should be satisfied. The

consequents are those, which we can infer, and is the

output if the antecedent inequality is satisfied. The

fuzzy rule-based system uses IF–THEN rule-based

system, given by, IF antecedent, THEN consequent.

Figure12

Rule Base Window in FIS Editor

1. If Temperature is Low & Temperature

Gradient is Low then Charging is Ultra Fast.

2. If Temperature is Low & Temperature

Gradient is High then Charging is Ultra Fast.

3. If Temperature is Medium & Temperature

Gradient is Low then Charging is Medium.

4. If Temperature is Medium & Temperature

Gradient is High then Charging is Low.

5. If Temperature is High & Temperature

Gradient is Low then Charging is Low.

6. If Temperature is High & Temperature

Gradient is High then Charging is Trickle.

These six rules form the rule base for the charger

system. The block diagram for the design can be

constructed as given below in figure.

Figure13

Working of Fuzzy System

VII. FUZZY ASSOCIATED MEMORY

The fuzzy rule base for is the system can be

represented in the form of a table as shown below.

This is also called FAM.

Table1 Fuzzy Rule Base

Temperature

Temp Grad

Low Medium High

Low UltraFast Medium Low

High UltraFast Low Trickle

Now, let us consider the control action if the

temperature is 37 degree Celsius and temperature

gradient is 0.4.

A temperature 37 degree Celsius has a membership

of 0.6 in low, 0.4 in medium, 0 in high i.e.

μlow (37) = 0.60

μmed (37) = 0.40

μhigh(37) = 0

A temperature gradient 0.4 has a membership of

0.6667 in low, 0.3333 in high i.e.

μlow (0.4) = 0.6667

μhigh (0.4) = 0.3333

Figure14

Rule Viewer Windows Output

VIII. IMPLEMENTATION

A. Implemention using Mamdani Style

In this project we are implementing the Mamdani

type Fuzzy logic Temperature controller using

MATLAB[6]. Also, we developed an algorithm

which can be implemented on other processor. There

are different algorithms used in this project.

Flow Chart 1

Steps in Fuzzy Logic Controller

B. Algorithm of Fuzzy Logic System

1) Define the linguistic variables and terms

(initialization)

2) Construct the membership functions of an

antecedents & consequent.(initialization)

3) Construct the rule base (initialization)

4) Convert crisp input data to fuzzy values

using the membership functions

(fuzzification)

5) Compose the rules in the rule base

(inference)

6) Implicate the results of each rule (inference)

7) Convert the aggregated output to crisp

values(non-fuzzy values) (defuzzification)

C. Algorithm of Fuzzification

1) Description of the problem in an acceptable

mathematical form.

2) Definition of the threshold for the variables

i.e. point of discontinuity, specifically the

two extremes of the greatest and least degree

of satisfaction.

3) Based on the above threshold values a

proper membership function is selected

among those available e.g. linear, piece-wise

linear, trapezoidal, parabolic etc.

4) Selection of the fuzzy operations so that the

results obtained are similar to those obtained

by experts.

Flow Chart 2

Flow chart of Fuzzification

D. Trapezoidal Membership Function

Flowchart of Trapezoidal Membership Function

Flow Chart3

Flowchart for Trapezoidal Membership Function

E. Output of Membership Function

We are calculating the membership function for

the following input variable which are shown below

Figure15

Membership Functions Output Screenshot

F. Algorithm of the Composition method

The algorithm for the composition method is

shown below.

1. Compare the 1st membership function of 1

st

input variable with the 1st membership

function of the 2nd

input variable and find

the minimum value then stored in W1.

2. Compare the 1st membership function of 1

st

input variable with the 2nd

membership

function of the 2nd



3. Compare the 2nd

membership function of 1st


function of the 2nd



4. Compare the 2nd membership function of 1st

input variable with the 2nd

membership

function of the 2nd



5. Compare the 3rd



function of the 2nd



6. Compare the 3rd



function of the 2nd



Usually the antecedent of the given rule has more

than one part; hence, the fuzzy operator are applied to

obtain one number that represents the result of the

antecedent for that rule. This number will then be

applied to the output function. The input to a fuzzy

operator is two or more membership values from

fuzzified input variables. The output is a single truth

values.

Output of Min operator

Figure16

Min Output Screen

G. Algorithm of the Implication Method

The shaping of the consequent based on the

composed value of antecedent is termed as

implication[8]. The input for the implication process

is a single number obtain from the composition

process and the output is the fuzzy set. Implication is

applied for each rule.

1. Compare the same consequent and find the

maximum composed values among these

then stored this value in MCVi.

2. Repeat the step 1 until all the four MCV’s

are calculated.

Output of Implication Method

Figure17

Implication Output Screen

H. Algorithm of the Aggregation Method

Aggregation is the process by which several fuzzy

sets are combined into a desirable way to produce a

single fuzzy set[9]. Aggregation is performed by

combining all the fuzzy sets that represents the output

of each rule into a single fuzzy set. Aggregation only

occurs once for each output variable

There are two steps in this methods which are :

To calculate point of intersection

PICx(n),PICy(n).

To calculate point of discontinuities PD(n).

For the calculation of PICx(n),PICy(n)

The PICx(n) (where n=1 to 3) can be

calculated using the formulaes

PICx(1)=((a(2)*diff1)+(d(1)*diff2))/(diff1+

diff2)

PICy(1)=(d(1)-PICx(1))/diff1

PICx(2)=((gap2*a(3))+(gap3*d(2)))/(gap2+

gap3)

PICy(2)=(d(2)-PICx(2))/gap2

PICx(3)=((d(3)*diff4)+(a(4)*diff3))/(diff3+

diff4)

PICy(3)=(d(3)-PICx(3))/diff3

Where the values

diff1=d(1)-c(1)

diff2=b(2)-a(2)

gap2=d(2)-c(2)

gap3=b(3)-a(3)

diff3=d(3)-c(3)

diff4=b(4)-a(4)

Figure18

Output Variable Screenshot

Figure19

PICx,PICy Output Screenshot

Flowchart 4

Flowchart for PD Calculation

Figure20

Xcord and Ycord output values screenshot

Figure21

Aggregated Output

I. Algorithm of Defuzzification

1. Calculate the area of decomposed portion

i.e. triangular, rectangular, trapezoidal etc.

and stored the values in A.

2. Calculate the centroid of each portion and

stored in C

3. Multiplication of area & centroid of each

decomposed portion and stored in AC.

4. Summation of the area A and stored in

SUMAREA.

5. Summation of all the AC values and stored

in SUM.

6. Divide the SUM by SUMAREA.

7. Stored the results in output

Figure22

Defuzzification output value screenshot

IX. CONCLUSION

The output of our program code and the FIS editor

window are approximately same. This work is not

only basically a simple literature or file for us, indeed

it’s a file agenda prepared by us. On account of our

own hand work throughout the semester, we got

overview of learning being put to practical work.

Besides it taught us how to work as team and gain

knowledge from each other faithfully.

Figure23

Rule Viewer Output Screenshot

Figure24

Crisp Output of program screenshot

References [1] Shakti Kumar,”Introduction to Fuzzy Logic; Based System’, Proceedings Workshop on Intelligent System

Engineering (WISE-2010), Institute of Science &

Technology Klawad, pp.23-40. [2] John Yen, Reza Langari,”Fuzzy Logic Intelligence,

Control, and Information’,pp 10-55.

[3] Timothy J.Ross,”Fuzzy Logic with Engineering Applications”.pp-150-183.

[4] S. N. Sivanandam, S. Sumathi and S. N.

Deepa,”Introduction to Fuzzy Logic Using MATLAB”,pp 11-17,73-80,113-127.

[5] Novák, Vilém, Adam Hilger,” Fuzzy Sets and Their

Applications” [6]http://www.cs.princeton.edu/courses/archive/fall07/cos436

/HIDDEN/Knapp/fuzzy004.ht

[7] http://www.scribd.com/doc/33412283/Solving-Fuzzy-Logic-Problems-With-MATLAB

[8]

http://enpub.fulton.asu.edu/PowerZone/FuzzyLogic/chapter%201/frame1.htm

[9] www.seattlerobotics.org/encoder/mar98/fuz/flindex.html

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