# Introduction to Fuzzy Logic

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### CHAPTER - I

### History of Fuzzy Logic:

The concept of Fuzzy Logic (FL) was introduced by a professor Lotfi Zadeh, at the University of California at Berkley, and handover formally not as a control methodology, but as a way of prepared data by granting the partial set membership rather than clearly determined set membership or non-membership. This began to deal with the set the theory was not applied to control systems until earlier 70s due to lack of small computer capability earlier to that time. Professor Lotfi reasoned that people do not require ideas and the numerical information input, and yet they are capable of high capacity control. If the feedback controllers could be programmed to accept improper input, noisy they would be much more capable and by chance it is easier to implement. Unfortunately, United States manufacturers have not been so quick to practice this technology while the Japanese and Europeans and have been strongly building real products around it.

### Defining Fuzzy Logic:

Fuzzy Logic, is a control system methodology which solves the problems that have the limited time itself to implementation in systems laying out from small, simple, embedded micro controllers to large, multi-channel PC or workstation ,networked based data accomplishment and control systems. It can be implemented in hardware and software or a combination of both hardware and software. And Fuzzy Logic allows us a simple way to arrive at a definite opinion based upon value, imprecise, noisy, ambiguous or missing input information. Fuzzy Logics approach is much faster to control problems as it imitate how a person would make decisions.

The concept of Fuzzy logic has become rapidly one of the most worlds successful of today's technologies for developing advanced control systems. The only one reason for Fuzzy Logic is very simple. And Fuzzy Logic meets the gap between in engineering design methods and left empty by purely numerical advances for example linear control design, and purely logic-based approaches (for example expert systems) in system design. And Fuzzy logic deals much partial applications absolutely as it corresponds human decision making with capacity to generate correct solutions from approximate or certain information.

The fuzzy design and implementation can accommodate the ambiguities of real-worlds human language and logic, where the other application approaches require exact equations to model real-world behaviors. So the Fuzzy Logic provides both no rational method for determining the systems in human terms and automates the conversion of those system specifications into efficient designs.

Numerous popular descriptions given the statements that the fuzzy logic acts as a important shift in outlook, that is a "new way of thinking" about the world, and fuzzy logic this enables a new set of results to problems that have traditionally been handled with old fashioned "unfuzzy" logic. In control theory almost all applications are used the Fuzzy Logic concepts. One actual and most popular practitioner of "fuzzy logic" is OMRON Electronics, and which developes a wide kind of all control systems for industrial and commercial products. And their recognized artists value includes an exposition titled the "Fuzzy Logic, A Twenty first Century Technology: which gives a frank explanation of exactly what they call the "fuzzy logic" and how it's really carried out in a practical control system.

For example given they are three real valued input signals Y(t), X(t),Z(t), and based on these real valued inputs you need to control a real valued output signal O(t). Here first assign to non rational verbal characterization to each of a set of real values for each parameter, such as

-20 , is Very Negative (VN)

-10 , is Somewhat Negative (SN)

0 is, Near Zero (NZ)

+10 is, Somewhat Positive (SP)

+20 is, Very Positive (VP)

As the system operator or control engineer, are very absolve to define the collections for each and every parameter in the conformity with your knowledge of the system and what you believe are the important arrays. The design and implementation process is by all odds fuzzy logic is there. For simple mindedness, let us put on you have selected the all five categories for all three real inputs and for the real output variable. So the "control laws" are determined in the terms of logical if and then statements. For a example, by using control laws we can define like below statements

- IF [A is Very Negative].AND.[B is Slightly Positive]
- IF [A is Sightly Positive].AND.[B is Very Negative]
- IF [A is Near Zero].AND.[B is Near Zero]

THEN [O should be Very Positive]

THEN [O should be Slightly Negative]

THEN [O should be Near Zero]

The main merits of the control laws are, are

- it is more intuitive than several types of principles, and this could alters you to charm your knowledge of how the system should work in everyday linguistic terms.
- And these laws are by nature broken away down into individual if and then arguments that add themselves to multiple processing.

### FL Vs Conventional control methods:

Fuzzy Logic includes a simple, rule based. The Fuzzy Logic model is based relying on the manipulators experience rather than their technical understanding of the system. If A and B Then C approach to a control problem solving quite different than attempting to model a system numerically.

Finally concluded that the Fuzzy Logic is to be very suitable for embedded control applications. And so many manufacture ring business companies related to automotive industry are using fuzzy technology to improve quality and cut down the development time. The fuzzy logic can also applied In aerospace, where it enables very composite real time problems to be tackled using a simple advance. In manufacturing, fuzzy is proven to be invaluable in increasing equipment efficiency and diagnosing malfunctions. And the fuzzy in consumer electronics, used to improves time to market and helps reduce costs.

For a example, dealing with temperature control in terms such as "SP>=500F", "T<=1000F", or "210C<temperature>220C", it is better to use the terms like IF "Process is too cool" AND "Process is getting colder" THEN "add heat to the process" or IF "process is too hot" AND "process is heating rapidly" THEN "cool the process quickly" are used.

These terms are not exactly correct and yet very clear description of what must actually happens. Let us consider what you do in the shower if the temperature is very too cold and you will do the water comfortable very quickly with little bit of trouble. Fuzzy Logic is capable of imitating this type of behavior but at very high rate.

### Functioning of Fuzzy Logic:

Fuzzy Logic requires some numerical parameters in order to operate such as what is considered significant rate-of-change-of-error, but exact value of these numbers are usually not critical unless very responsive performance is required in which case empirical tuning would determine them.

For example, a simple temperature control system could use a single temperature feedback sensor whose data is subtracted from the command signal to compute "error" and then time-differentiated to yield the error slope or rate-of-change-of-error, hereafter called "error-dot". Error might have units of degs F and a small error considered to be 2F while a large error is 5F. The "error-dot" might then have units of degs/min with small error-dot being 5F/min and large one being 15F/min. These values don't have to be symmetrical and can be "tweaked" once the system is operating in order to optimize performance. Generally, Fuzzy Logic is so forgiving that system will properly work the first time without any tweaking.

### CHAPTER - II

### Why use Fuzzy Logic:

Fuzzy Logic offers several unique features that it a particularly good choice for many control problems.

- It is inherently strong enough since it does not require accurate, noise-free inputs and can be programmed to fail safely if a feedback sensor quits or is ruined. The output control is a smooth control function despite a wide range of input variations.
- Since the Fuzzy Logic controller processes user-defined rules responsible for the target control system, it can be modified and adjusted finely easily to improve or drastically after system performance. New sensors can easily be considered into the system simply by generating appropriate governing rules.
- Fuzzy Logic is not limited to few feedback inputs and one or two control outputs, nor is it absolutely essential to measure or compute rate-of-change parameters in order for it to be implemented. Any sensor data that provides some identification of a system's actions and reactions is sufficient. This allows the sensors to be relatively low and imprecise thus keeping the overall system cost and complexity low.
- Because of the rule-based operation, any reasonable number of inputs can be processed (1 to 8 or more) and numerous outputs (1 to 4 or more) generated, although defining the rule base with rapid becomes complex if too many inputs and outputs are chosen for a single implementation since rules defining their reciprocal relation must also be be defined. It would to better to break the control system into smaller pieces and use several smaller Fuzzy Logic controllers distributed on the system, each with more limited activities.
- Fuzzy Logic can control nonlinear systems that would be not easy or impossible to frame mathematically. This opens doors for control systems that would normally be viewed as unfeasible for automation.

### How is Fuzzy Logic used?

- Define control objectives and criteria:
- What am I trying to control?
- What do I have to do control the system?
- What kind of response do I need?
- What are the possible (probable) system failure modes?
- Define the input and output relationships and choose a minimum number of variables for input to the Fuzzy Logic engine (typically error and rate-of-change-of-error).
- Using the rule-based structure of Fuzzy Logic, break the control problem down into a series of IF A AND B THEN C rules that define the desired system output reaction for given system output conditions. The number and complexity of rules depends on the number of input parameters that are to be processed and the number fuzzy variables associated with the each and every parameter. If possible, use at least one variable and its time differential. Although it is possible to use a single, occurring with no delay error parameter without knowing its rate of change, its lames system's power to minimize overshoot for a step inputs.
- Create Fuzzy Logic membership functions that define the meaning of Input/Output terms used in the rules.
- Create the required pre- and post-processing Fuzzy Logic routines if implementing in the software, otherwise program the rules into the Fuzzy Logic hardware engine.
- Test the system, evaluate the results, tune the rules and membership functions, and retest until satisfactory results are obtained.

### LINGUISTIC VARIABLES:

In the year 1973, Professor Lotfi Zadesh suggested the concept of linguistic or "fuzzy" variables. Think of them as linguistic objects or words, rather than numbers. The sensor input in a noun. For a example "temperature", "flow", "displacement", "velocity", pressure" and etc. Since error is just the difference, it can be thought of the same way. The Fuzzy variables themselves are adjectives that modify the variables (for a example "large positive" error, "small positive" error, "zero" error, "small negative" error, and "large negative" error). As minimum, one could simply have "positive", "zero", "negative" variables for each of the parameters. Additional chains such as "very large" and "very small" could also be added cover the responsiveness to particular or very nonlinear conditions, but aren't in a basic system.

### CHAPTER - III

The fuzzy Logic parameters of command-feedback error and error-dot (rate of change of error) were modified by the terms "negative", "zero", and "positive". To give a visual representation of this, imagine the simplest practical implementation, a 3x3 matrix. The vertical columns represent "negative error", "zero error", and "positive error" inputs from left-hand to right-hand. The horizontal rows represent the "negative", "zero", and "positive" "error-dot" input from top to bottom. This two dimensional construct is called a rule matrix. It has two input constrains, "error" and "error-dot", and one output response at the intersection of each row and column conclusion. In this case there are nine possible logical products (AND) output response conclusions.

### Fuzzy Logic Matrix Rule:

The rule matrices usually have an odd number of rows and columns to make a meaningful fit, a "zero" center row and column will be there. This may not be required as long as the functions on any side of the center overlap somewhat and continuous meaningful intermediate values of the output is considered since the "zero" regions parallel process to "no change" output responses the lack of this region will cause the system to continually search for "zero". It is also to have a chance of different number of rows than columns. This occurs when indefinite numbers of inputs are needed. The maximum number of possible rules is simply the multiply the number of rows and columns, but explanation of all of these principles may not be necessary since some input conditions may never occur in real time practical operation. The main importance of this objective is to construct and map out the universe of possible inputs while under constrains of keeping the system sufficiently under control.

### Process of Fuzzy Logic Control System:

In Fuzzy Logic implementation process first important is to identify accurately what we have to control and how we can control.

For above statement see the following example, suppose we want to design and implement a simple temperature controller which is proportional with an electric heating object and having cooling fan with variable-speed. A negative signal output calls for 0-100 percent cooling while a positive signal output calls for 0-100 percent heat. The simple Fuzzy Logic Control is gained with effort through giving equal balance and control of these two active devices.

The above diagram which represents a simple Fuzzy Logic block diagram of the control system.

It is required to establish a meaningful system for making up the linguistic variables in the matrix. For a example, the following will be used:

"Z" -- "zero" error (or) error-dot input level

"P" -- "positive" error or error-dot input level

"H" -- "Heat" output response

"N" -- "negative" error (or) error-dot input level

"-" -- "No Change" to current output

"C" -- "Cool" output response

Determine the minimum number of possible input product compounding and representing output response determinations using these terms. For a three by three (3X3) matrix with heating and cooling output responses and all nine rules will need to be determined. The conclusions to the rules with the linguistic variables linked with the output response for each rule are transferred to the matrix.

Linguistic rules describing the control system comprises into two parts:

- One antecedent block (between the IF and THEN)
- A consequent block (following THEN).

Depending upon the system, it may not be required to estimate every possible input combination (for 5X5 and up matrices) since some may not often or never occurs. By making this type of evaluation, usually done by an experienced operator, fewer rules can be estimated, thus altering the processing logic and possibly even improving the Fuzzy Logic system performance.

After changing the decisions from the nine rules to the matrix there is a detectable balance to the matrix. It suggests (but does not guarantee) a fairly well behaved linear system. This execution may prove to be too simplistic for some control troubles , however it does clarify the process. This will increase the rule-base size and quality but may also increase the quality of the control.

### Fuzzy Logic Membership Functions:

The Fuzzy Logic membership function is represented by graph of the order of magnitude of involvement of each and every input. It is links with weighting of the each input that are processed, determining the functional convergence between each and every input, thus finally it defines an output response. The Fuzzy Logic principles uses the input membership values as weighting components and to determine their influence on the fuzzy output sets of the final output conclusion. There are different membership functions associated with each input and output response. Once the membership functions are scaled, inferred, and combined, they are defuzzified into a clearly defined output which drives the system.

The each and every input parameter, associated with a unique membership function. This weighting factor determines the degree of influence or degree of membership (DOM) each active rule has.The Fuzzy Logic membership functions have logical connection with weighting factor values of each input and the effective rules. By calculating the logical product of the membership weights for each active rule, a set of fuzzy output response magnitudes are produced. All that remains is to combine and defuzzify these output responses.

### Functions of Fuzzy Logic:

The Fuzzy Logic functions are,

whatever

whatever LIST

This function returns one of the nine neo boolean values used in fuzzy logic: what, true, false, sure, whoa, depends, maybe, and elbows. The value returned is determined by standard anti-random vacillation routines.

reconsider

reconsider EXPR

This function useful to, does the program to evaluate an expression until such time as it feels reasonably sure of its determinination. It is totally based on the system and formula; which may take an entire freshman semester or a fraction of a second.

while holdon

while (EXPR) BLOCK holdon (EXPR) BLOCK

This function terms brings like a measure while loop at first, but at some point the function makes it is been bringing personal issues into the rating in an out of keeping manner and begins to evaluate the expression named by holdon instead in an efforts to appear reasonable.

goaway

goaway LABEL

This function is used for , does the program to execute starting at LABEL, while making it clear to the program that you could care less whether it ever returned to the present execution point or not. Use of this function has been generally deprecated since the publication of the landmark essay "'GOAWAY' Considered Thoughtless." Calling the apology function later may cause the program to return to the statement directly after the goaway, but it may also cause the program to exit entirely, depending on how much you've been taking it for granted.

pile

pile LIST

This function used to take a LIST and classifies it until the function makes there are so many items in the "miscellaneous" family and tries to figure out a better sorting system, then it gets drilled and leaves a big pile of unsorted items at the end. Returns a semi-sorted list with a big pile of unsorted items at the end.

grudge

grudge VARIABLE

This function used to, check the program to develop an immediate dislike of the named variable, causing many procedures involving that variable to return false for no evident reason.

pedestal

pedestal VARIABLE

This pedestal function used to, does the program to attach unhealthy significance to VARIABLE. And the function can also check the program will consider the named variable to be a microcosm of its own existence and will fall into a deep depression if the variable is undefined, or treated poorly, ignored, Both grudge and pedestal can be used on the same variable, causing the program to develop a love-hate relationship with the variable in question. This can be fun.

skim

skim FILEHANDLE

This function used to quickly looks over the data contained in FILEHANDLE, trying to get the gist of it and looking for any dirty bits or clever quotations it can use at parties to impress people.

oblique

oblique PLAINTEXT, WIT

The oblique function uses a form of lossy encryption to convert PLAINTEXT into a witty but obscure cultural or social reference which will only make sense to people or processes that share a similar background with the calling program.

With careful application, this function can be used to create entire online humor magazines. WIT is a number between 0 and 7 which determines the cleverness and obscurity of the reference, where 0 will return a catchphrase from a recent television advertisement and 7 will return a reference to The Consolation of Philosophy by Boethius.