PRESENTED BY
ARUMUGASELVAN.D
J.VINOTHKUMAR
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1.Abstract
The concept of Fuzzy Logic (FL) was conceived by Lotfi Zadeh, a professor at the University of California at Berkley, and presented not as a control methodology, but as a way of processing data by allowing partial set membership rather than crisp set membership or non-membership. This approach to set theory was not applied to control systems until the 70's due to insufficientsmall-computer apability prior to that time. Professor Zadeh reasoned that people do not require precise, numerical information input, and yet they are capable of highly adaptive control. If feedback controllers could be programmed to accept noisy, imprecise input, they would be much more effective and perhaps easier to implement.
2.What is Fuzzy Logic?
FL is a problem-solving control system methodology that lends itself to implementation in systems ranging from simple, small, embedded microcontrollers to large, networked, multi-channel PC or workstation-based data acquisition and control systems. It can be implemented in hardware, software, or a combination of both. FL provides a simple way to arrive at a definite conclusion based upon vague, ambiguous, imprecise, noisy, or missing input information. FL's approach to control problems mimics how a person would make decisions, only much faster. Human thinking and decisions are based on ‘yes’/’no’ reasoning, or 1’/ 0” logic. Accordingly Boolean logic was developed, and Expert System principles were formulated based on Boolean logic. It has been argued that human thinking does not always follow crisp “yes”/ no” logic, but is often vague, qualitative, uncertain, imprecise, or fuzzy in nature. For example, an ES rule for speed control in a variable-speed drive may be IF speed of the motor is greater than 1500 rpm AND the machine stator temperature is between 60F and 100F THEN set the stator current I less than 10 amps
The same rule in FL may read as IF speed of the motor is high and stator temperature is medium THEN set the stator current I
low FL can help to supplement an ES, and
it is sometimes hybrided with the latter to solve complex problems. FL has been successfully applied in process control, modeling, estimation, identification, diagnostics, military science, stock market prediction, etc.
Why Fuzzy control?
In general, a control system based on AI is defined as intelligent control. A fuzzy control system essentially embeds the experience and intuition of a human plant operator, and sometimes those of a designer and/or researcher of a plant. The design of a conventional control system is normally based on the mathematical model of a plant. If an accurate model is available with known parameters, it can be analyzed, for example by a bode or Nyquist plot, and a controller can be designed for the specified performance. Such a procedure is tedious and time testing, although CAD programs are available for such design. Unfortunately, for complex process, such a cement plants, nuclear reactors, and the like reasonably good mathematical model is difficult to find. On the other hand, the plant operator may have good experience for controlling the process. Power electronics system models are often ill-defined. Even if a plant model is multi variable, complex, and non-linear, such as the dynamic d-q model of an ac machine. Vector or field-oriented control of a drive can over come this problem, but accurate vector control is nearly impossible, and there may be a wide parameter variation Problem in the system. Fuzzy control, on the other hand, does not strictly need any mathematical model of the plant .It is based on plant operator experience and heuristics, as mentioned Previously, and it is very is to apply. Fuzzy control is basically an adaptive and nonlinear control, which gives robust performance for linear or nonlinear plant with parameter variation.
a. Linguistic Variables :
In 1973, Professor Lotfi Zadeh proposed the concept of linguistic or "fuzzy" variables. Think of them as linguistic objects or words, rather than numbers. The sensor input is a noun, e.g. "temperature", "displacement", "velocity", "flow", "pressure", etc. Since error is just the difference, it can be thought of the same way. The fuzzy variables themselves are adjectives that modify the variable (e.g. "large positive" error, "small positive" error ,"zero" error, "small negative" error, and "large negative" error). As a minimum, one could simply have "positive", "zero", and "negative" variables for each of the parameters. Additional ranges such as "very large" and "very small" could also be added to extend the responsiveness to exceptional or very nonlinear conditions, but aren't necessary in a basic system.
b. Membership functions:
The membership function is a graphical representation of the magnitude of participation of each input. It associates a weighting with each of the inputs that are processed, define functional overlap between inputs, and ultimately determines an output response. The rules use the input membership values as weighting factors to determine their influence on the fuzzy output sets of the final output conclusion. Once the functions are inferred, scaled, and combined, they are defuzzified into a crisp output which drives the system. There are different membership functions associated with each input and output response. Some features to note are: SHAPE - triangular is common, but bell, trapezoidal , haversine and, exponential have been used. More complex functions are possible but require greater computing overhead to impplement.. HEIGHT or magnitude (usually normalized to 1) WIDTH (of the base of function), SHOULDERING (locks height at maximum if an outer function. Shouldered functions evaluate as 1.0 past their center) CENTER points (center of the member function shape) OVERLAP (N&Z, Z&P, typically about 50% of width but can be less).
c. Rule Matrix :
In the last article the concept of linguistic variables was presented. The fuzzy parameters of error (command-feedback) and error-dot (rate-ofchange- of-error) were modified by the adjectives "negative", "zero", and "positive". To picture this, imagine the simplest practical implementation, a 3-by-3 matrix. The columns represent "negative error", "zero error", and "positive error" inputs from left to right. The rows represent "negative", "zero", and "positive" "error-dot" input from top to bottom. This planar construct is called a rule matrix. It has two input conditions, "error" and "error-dot", and one output response conclusion (at the intersection of each row and column). In this case there are nine possible logical product (AND) output response conclusions. Although not absolutely necessary, rule matrices usually have an odd number of rows and columns to accommodate a "zero" center row and column region. This may not be needed as long as the functions on either side of the center overlap somewhat and continuous dithering of the output is acceptable since the "zero" regions correspond to "no change" output responses the lack of this region will cause the system to continually hunt for "zero". It is also possible to have a different number of rows than columns. This occurs when numerous degrees of inputs are needed. The maximum number of possible rules is simply the product of the number of rows and columns, but definition of all of these rules may not be necessary since some input conditions may never occur in practical operation. The primary objective of this construct is to map out the universe of possible inputs while keeping the system sufficiently under control
fig : Example of rule matrix
d. Defuzzyfication :
Combining the results of the inference process and then computing the “fuzzy centroid” of the area accomplish the defuzzification of the data into a crisp output. The weighted strengths of each output their respective output membership function center points multiply member function and summed. Finally, this area is divided by the sum of the weighted member function strengths and the result is taken as the crisp output. One feature to note is that since the zero center is at zero, any zero strength will automatically compute to zero. If the center of the zero function happened to be offset from zero (which is likely in a real system where heating and cooling effects are not perfectly equal), then this factor would have an influence.
(neg_center * neg_strength + zero_center * zero_strength + pos_center *
pos_strength) = OUTPUT
(neg_strength + zero_strength + pos_strength)
(-100 * 0.866 + 0 * 0.500 + 100 * 0.000) = 63.4%
(0.866 + 0.500 + 0.000)
The horizontal coordinate of the centroid of the area marked in Figure 8 is taken as the normalized, crisp output. This value of -63.4% (63.4% Cooling) seems logical since the particular input conditions (Error=-1, Error-dot=+2.5) indicate that the feedback has exceeded the command and is still increasing therefore cooling is the expected and required system response. Following is a system diagram, Figure 3, for a "getting acquainted with fuzzy" project that provides speed control and regulation for a DC motor. The motor maintains "set point" speed, controlled by a stand-alone converter-controller, directed by a BASIC fuzzy logic control program in a personal computer.
3.Speed Control of D.C Motor
The above speed control system is low cost and suitable for learning at home where being rigorously, mathematically correct is not required. It is important to be aware that this speed controller is only an experimental controller to get familiar with the fuzzy logic concept. It is not what engineers call a rigorous, technically correct application of fuzzy logic. The difference is in the fact that this approach does not add triangles to compute center of mass as specified by Dr. Bart Kosko .Adding triangles can be done, but is difficult and time consuming, however that is the way a truly professional application would be designed. There are IC’s that do it all and commercially available fuzzy logic controllers that do everything correctly. This fuzzy logic controller project was done under pressure of very limited money available, resulting in an inexpensive approach. What is needed is an analog to digital converter, which connects to a PC, and a digital to analog output device from the PC to the transistors and DC motor-generator being controlled. Often this is all in one plug-in card that goes inside the PC. Plug in the A to D and D to A converter in the PC and write a program to measure the input and control the output according to fuzzy logic principles. This approach can be somewhat expensive and was not used in this case.
The steps in building our system are:
1. Determine the control system input. Examples: The temperature is the input for
your home air conditioner control system. Speed of the car is the input for your cruise control. In our case, input is the speed in Rpm of the DC motor, for which we are going to regulate the speed. See Figure 3 above. Speed error between the speed measured and the target speed of 2,420 Rpm is determined in the program. Speed error may be positive or negative. We measure the DC output voltage from the generator. This voltage is proportional to speed. This speed-proportional voltage is applied to an analog input channel of our fuzzy logic controller, where the analog to digital converter and the personal computer, including appropriate software, measure it.
2. Determine the control system output. For a home air conditioner, the output is the opening and closing of the switch that turns the fan and compressor on and off. For a car's cruise control, the output is the adjustment of the throttle that causes the car to return to the target speed.In our case, we have just one control output. This is the voltage connected to the input of the transistor controlling the motor.
3. Determine the target set point value, for example 70 degrees F for your home temperature, or 60 Miles per hour for your car. In our case, the target set point is 2,420 Rpm.
4. Choose word descriptions for the status of input and output.For the steam engine project, Professor Mamdani used the following forinput
ositive Big, Positive Medium, Positive Small, Almost No Error, Negative Small, Negative Medium, Negative Big. Our system is much less complicated, so let us select only three conditions for input: Input Status Word Descriptions Too slow, About right, Too fast And, for output: Output Action Word Descriptions Speed up, Not much change needed, Slow down
