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# Fuzzy logic and fuzzy control systems

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### Fuzzy logic and fuzzy control systems

1. 1. F UZZY L OGIC AND F UZZY L OGIC S UN T RACKING C ONTROL RYAN JOHNSON DECEMBER 17, 2002 CALVIN COLLEGE ENGR315AA BSTRACT : Fuzzy logic is a rule-based decision or cold, A-or-not-A. To challenge this type of thinking, consider a half eaten apple. Is it half thereprocess that seeks to solve problems where the system or half gone? Is the glass half full or half empty? Isis difficult to model and where ambiguity or the car going fast or slow? Each of these questionsvagueness is abundant between two extremes. Fuzzy present some shades of gray in this world welogic allows the system to be defined by logic typically describe in black and white.equations rather than complex differential equationsand comes from a thinking that identifies and takes Change is inevitable. There is a danger inadvantage of the grayness between the two extremes. putting definite labels on things. Doing so meansFuzzy logic systems are composed of fuzzy subsets that as changes take place these labels pass fromand fuzzy rules. The fuzzy subsets represent different accurate to inaccurate. Rene Descartes thoughtsubsets of the input and output variables. The fuzzy about change as he pondered a piece of beeswax as itrules relate the input variables to the output variables melted in front of his fireplace. At what point didvia the subsets. Given a set of fuzzy rules, the system the beeswax change from a piece of wax into acan compensate quickly and efficiently. Though the puddle of wax? At some point it had to be both aWestern world did not initially accept fuzzy logic and small puddle and a small piece of wax at the samefuzzy ideas, today fuzzy logic is applied in many time [13]. There is some period between which it issystems. a solid piece and a pure puddle. In this research paper, a solar power sun Grayness is fuzziness. Einstein wonderedtracking system is implemented using fuzzy logic. about the grayness. “So far as the laws ofThe steps of how to create a fuzzy system are mathematics refer to reality, they are not certain.described as well as the description of how the fuzzy And so far as they are certain, they do not refer tosystem works. reality,” he said [13]. Actually, math and science do not fit the world they describe. Math and scienceKeywords: membership function, grayness, fuzzy are neat and organized. They describe the world assubsets, fuzzification, fuzzy rules, defuzzification, neat and organized without any grayness. Math andFuzzy Approximation Theorem (FAT), fuzzy science try to fit every process in the world tonumbers, and fuzzy systems equations and equations are neat and organized. Imagine a world without grayness. It is impossible. The world we live in is very messy and includes I. I NTRODUCTION much grayness. With math and science, we have How do we define the world we live in observed certain tendencies and relationships thattoday? How do we see things around us? Most of us have remained true for a period of time and definedare taught from a very young age to look at the world them as mathematical logic and scientific laws. Thein terms of black and white, A-or-not-A, Boolean 1’s truth of this logic and these laws is only a matter ofand 0’s. Much of science, math, logic, and even degree and could change at any moment [13]. Theyculture assume a world of 1’s and 0’s, true or false, hot could pass from accurate to inaccurate at any time.