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Overview[ edit ] Fuzzy logic is widely used in machine control. The term "fuzzy" refers to the fact that the logic involved can deal with concepts that cannot be expressed as the "true" or "false" but rather as "partially true". Although alternative approaches such as genetic algorithms and neural networks can perform just as well as fuzzy logic in many cases, fuzzy logic has the advantage that the solution to the problem can be cast in terms that human operators can understand, so that their experience can be used in the design of the controller.
This makes it easier to mechanize tasks that are already successfully performed by humans. Zadeh of the University of California at Berkeley in a paper. Fuzzy systems were initially implemented in Japan. Interest in fuzzy systems was sparked by Seiji Yasunobu and Soji Miyamoto of Hitachi , who in provided simulations that demonstrated the feasibility of fuzzy control systems for the Sendai Subway.
Their ideas were adopted, and fuzzy systems were used to control accelerating, braking, and stopping when the Namboku Line opened in In , Takeshi Yamakawa demonstrated the use of fuzzy control, through a set of simple dedicated fuzzy logic chips, in an " inverted pendulum " experiment. This is a classic control problem, in which a vehicle tries to keep a pole mounted on its top by a hinge upright by moving back and forth. Yamakawa subsequently made the demonstration more sophisticated by mounting a wine glass containing water and even a live mouse to the top of the pendulum: the system maintained stability in both cases.
Yamakawa eventually went on to organize his own fuzzy-systems research lab to help exploit his patents in the field. Japanese engineers subsequently developed a wide range of fuzzy systems for both industrial and consumer applications. The automotive company Volkswagen was the only foreign corporate member of LIFE, dispatching a researcher for a duration of three years.
Japanese consumer goods often incorporate fuzzy systems. Matsushita vacuum cleaners use microcontrollers running fuzzy algorithms to interrogate dust sensors and adjust suction power accordingly.
Hitachi washing machines use fuzzy controllers to load-weight, fabric-mix, and dirt sensors and automatically set the wash cycle for the best use of power, water, and detergent. Canon developed an autofocusing camera that uses a charge-coupled device CCD to measure the clarity of the image in six regions of its field of view and use the information provided to determine if the image is in focus.
It also tracks the rate of change of lens movement during focusing, and controls its speed to prevent overshoot.
The output is the position of the lens. The fuzzy control system uses 13 rules and requires 1. An industrial air conditioner designed by Mitsubishi uses 25 heating rules and 25 cooling rules. A temperature sensor provides input, with control outputs fed to an inverter , a compressor valve, and a fan motor.
Other applications investigated or implemented include: character and handwriting recognition; optical fuzzy systems; robots, including one for making Japanese flower arrangements; voice-controlled robot helicopters hovering is a "balancing act" rather similar to the inverted pendulum problem ; rehabilitation robotics to provide patient-specific solutions e.
Work on fuzzy systems is also proceeding in the United States and Europe, although on a less extensive scale than in Japan. The US Environmental Protection Agency has investigated fuzzy control for energy-efficient motors, and NASA has studied fuzzy control for automated space docking: simulations show that a fuzzy control system can greatly reduce fuel consumption.
Firms such as Boeing , General Motors , Allen-Bradley , Chrysler , Eaton , and Whirlpool have worked on fuzzy logic for use in low-power refrigerators, improved automotive transmissions, and energy-efficient electric motors. In Maytag introduced an "intelligent" dishwasher based on a fuzzy controller and a "one-stop sensing module" that combines a thermistor , for temperature measurement; a conductivity sensor, to measure detergent level from the ions present in the wash; a turbidity sensor that measures scattered and transmitted light to measure the soiling of the wash; and a magnetostrictive sensor to read spin rate.
The system determines the optimum wash cycle for any load to obtain the best results with the least amount of energy, detergent, and water. It even adjusts for dried-on foods by tracking the last time the door was opened, and estimates the number of dishes by the number of times the door was opened. Research and development is also continuing on fuzzy applications in software, as opposed to firmware , design, including fuzzy expert systems and integration of fuzzy logic with neural-network and so-called adaptive " genetic " software systems, with the ultimate goal of building "self-learning" fuzzy-control systems.
The process of converting a crisp input value to a fuzzy value is called "fuzzification". A control system may also have various types of switch , or "ON-OFF", inputs along with its analog inputs, and such switch inputs of course will always have a truth value equal to either 1 or 0, but the scheme can deal with them as simplified fuzzy functions that happen to be either one value or another. Given " mappings " of input variables into membership functions and truth values , the microcontroller then makes decisions for what action to take, based on a set of "rules", each of the form: IF brake temperature IS warm AND speed IS not very fast THEN brake pressure IS slightly decreased.
In this example, the two input variables are "brake temperature" and "speed" that have values defined as fuzzy sets. The output variable, "brake pressure" is also defined by a fuzzy set that can have values like "static" or "slightly increased" or "slightly decreased" etc. Fuzzy control in detail[ edit ] Fuzzy controllers are very simple conceptually. They consist of an input stage, a processing stage, and an output stage. The input stage maps sensor or other inputs, such as switches, thumbwheels, and so on, to the appropriate membership functions and truth values.
The processing stage invokes each appropriate rule and generates a result for each, then combines the results of the rules. Finally, the output stage converts the combined result back into a specific control output value. The most common shape of membership functions is triangular, although trapezoidal and bell curves are also used, but the shape is generally less important than the number of curves and their placement. From three to seven curves are generally appropriate to cover the required range of an input value, or the " universe of discourse " in fuzzy jargon.
Typical fuzzy control systems have dozens of rules. Consider a rule for a thermostat: IF temperature is "cold" THEN turn heater is "high" This rule uses the truth value of the "temperature" input, which is some truth value of "cold", to generate a result in the fuzzy set for the "heater" output, which is some value of "high". This result is used with the results of other rules to finally generate the crisp composite output. Obviously, the greater the truth value of "cold", the higher the truth value of "high", though this does not necessarily mean that the output itself will be set to "high" since this is only one rule among many.
In some cases, the membership functions can be modified by "hedges" that are equivalent to adverbs. Common hedges include "about", "near", "close to", "approximately", "very", "slightly", "too", "extremely", and "somewhat". These operations may have precise definitions, though the definitions can vary considerably between different implementations.
In practice, the fuzzy rule sets usually have several antecedents that are combined using fuzzy operators, such as AND, OR, and NOT, though again the definitions tend to vary: AND, in one popular definition, simply uses the minimum weight of all the antecedents, while OR uses the maximum value.
There is also a NOT operator that subtracts a membership function from 1 to give the "complementary" function. There are several ways to define the result of a rule, but one of the most common and simplest is the "max-min" inference method, in which the output membership function is given the truth value generated by the premise. Rules can be solved in parallel in hardware, or sequentially in software. The results of all the rules that have fired are "defuzzified" to a crisp value by one of several methods.
There are dozens, in theory, each with various advantages or drawbacks. The "centroid" method is very popular, in which the "center of mass" of the result provides the crisp value. Another approach is the "height" method, which takes the value of the biggest contributor. The centroid method favors the rule with the output of greatest area, while the height method obviously favors the rule with the greatest output value. The diagram below demonstrates max-min inferencing and centroid defuzzification for a system with input variables "x", "y", and "z" and an output variable "n".
Note that "mu" is standard fuzzy-logic nomenclature for "truth value": Notice how each rule provides a result as a truth value of a particular membership function for the output variable.
Fuzzy control system design is based on empirical methods, basically a methodical approach to trial-and-error. Document the fuzzy sets for the inputs. Document the rule set. Run through test suite to validate system, adjust details as required. Complete document and release to production. As a general example, consider the design of a fuzzy controller for a steam turbine. The block diagram of this control system appears as follows: The input and output variables map into the following fuzzy set: —where: N3: Large negative.
N2: Medium negative. N1: Small negative. Z: Zero. P1: Small positive. P2: Medium positive. P3: Large positive. In practice, the controller accepts the inputs and maps them into their membership functions and truth values.
These mappings are then fed into the rules. If the rule specifies an AND relationship between the mappings of the two input variables, as the examples above do, the minimum of the two is used as the combined truth value; if an OR is specified, the maximum is used.
The appropriate output state is selected and assigned a membership value at the truth level of the premise. The truth values are then defuzzified. For an example, assume the temperature is in the "cool" state, and the pressure is in the "low" and "ok" states. In terms of a centroid calculation, this is the "mass" of this result for this discrete case. That is, in terms of a centroid calculation, the location of the "center of mass" for this individual result.
This value is independent of the value of "mu". It simply identifies the location of ZE along the output range.
Fuzzy control system
Overview[ edit ] Fuzzy logic is widely used in machine control. The term "fuzzy" refers to the fact that the logic involved can deal with concepts that cannot be expressed as the "true" or "false" but rather as "partially true". Although alternative approaches such as genetic algorithms and neural networks can perform just as well as fuzzy logic in many cases, fuzzy logic has the advantage that the solution to the problem can be cast in terms that human operators can understand, so that their experience can be used in the design of the controller. This makes it easier to mechanize tasks that are already successfully performed by humans.
FUZZY CONTROL PASSINO SOLUTION MANUAL PDF
Kevin M. Passino and Stephen Yurkovich To be published by Addison-Wesley, If you have corrections for the above book please send them via email to the first author passino ee. Unsupported Public Domain Code for Intelligent Systems Please feel free to download the following code but understand that we can in no way support its operation including answering simple questions. The authors, all of which are or were OSU students working under the direction of K.