Fuzzy Logic and Sun Tracking Systems Ryan Johnson December 9, 2002 Calvin College ENGR315A

Overview Introduction Introduction History and Explanation of Fuzzy Logic History and Explanation of Fuzzy Logic Fuzzy Logic Applied Fuzzy Logic Applied Conclusion Conclusion Questions Questions

Introduction The world we live in: How do we describe it? The world we live in: How do we describe it? –Defined in 1’s and 0’s, true and false, A or not-A, black and white –How do we define a half eaten apple? Half there or half gone? Half there or half gone? –Is the glass half full or half empty? What is a house? What is a house?

Grayness Grayness in a world of black and white… Grayness in a world of black and white… –Math and science do not fit the world they describe. We have taken tendencies and relationships that have remained true for a period of time… We have taken tendencies and relationships that have remained true for a period of time… –The world we live in is filled with much grayness that can not be accurately described in black and white. This grayness can be described as “Fuzziness.” This grayness can be described as “Fuzziness.”

Grayness Example Scientific model showing either adult or not adult… Scientific model showing either adult or not adult…

Grayness model showing a gray area where someone could have both non-adult and adult characteristics. To a degree they are an adult and to a degree they are a non-adult… Grayness model showing a gray area where someone could have both non-adult and adult characteristics. To a degree they are an adult and to a degree they are a non-adult… Grayness is a key principle in Fuzzy Logic… Grayness is a key principle in Fuzzy Logic…

What is Fuzzy Logic? Fuzzy logic is a rule-based decision process. Fuzzy logic is a rule-based decision process. It seeks to solve problems where the system is difficult to model and where ambiguity or vagueness (grayness) is abundant between extremes. It seeks to solve problems where the system is difficult to model and where ambiguity or vagueness (grayness) is abundant between extremes. It allows the system to be defined by logic equations rather than complex differential equations. It allows the system to be defined by logic equations rather than complex differential equations.

History Originator-Lotfi Zadeh, UC Berkeley, Dept. of Electrical Engineering and Computer Sciences Originator-Lotfi Zadeh, UC Berkeley, Dept. of Electrical Engineering and Computer Sciences –Began with a paper in 1965 on fuzzy sets. –He named it “fuzzy” because “it ties to common sense.” U.S. History U.S. History –Took much criticism from probability schools, people who wanted to see fuzzy logic applied, and people who couldn’t see the grayness that he was speaking about. –The Western world had a hard time accepting Fuzzy Logic because it challenged their scientific ideas and thought. Eastern World Eastern World –Accepted and embraced fuzzy thinking. –In 1980, Japan pursued fuzzy logic for their controls and by 1990 had over 100 real fuzzy control applications. Today… Today…

Fuzzy Sets Fuzzy thinking and fuzzy logic occurs in sets. Fuzzy thinking and fuzzy logic occurs in sets. Example: Example: –Vehicle: What is a vehicle to you? –Vehicle represents a fuzzy set and things belong to this fuzzy set to some degree. Fuzzy sets are the building blocks of fuzzy systems. Fuzzy sets are the building blocks of fuzzy systems. –They can be broken down further into subsets such as an off road vehicle. An off road vehicle is a subset of vehicle.

Fuzzy Rules Human knowledge builds fuzzy rules. Human knowledge builds fuzzy rules. –Consider the decision to bring an umbrella to work under the following circumstances: 70% chance of rain. 70% chance of rain. An umbrella keeps you dry. An umbrella keeps you dry. If it rains you will get wet. If it rains you will get wet. If you get wet, you will be uncomfortable at work. If you get wet, you will be uncomfortable at work. If you have an umbrella you will be dry. If you have an umbrella you will be dry. –Through this knowledge, you reason to bring an umbrella to work. –The knowledge of the percentage of rain and what an umbrella is used for led you to make rules that guided you through your reasoning.

Fuzzy Rules as Fuzzy “Patches” The fuzzy rules define fuzzy “patches.” The fuzzy rules define fuzzy “patches.” Patches and grayness are the two key ideas of fuzzy logic. They create a link between common sense and geometry. Patches and grayness are the two key ideas of fuzzy logic. They create a link between common sense and geometry. –Patches can be large or small. The larger the patches, the more uncertain the rules. The larger the patches, the more uncertain the rules. The less fuzzy the rules, the smaller the patches. The less fuzzy the rules, the smaller the patches. If the rules are so precise that they are not fuzzy, then they are really points and don’t cover much. If the rules are so precise that they are not fuzzy, then they are really points and don’t cover much.

Fuzzy System The fuzzy sets and fuzzy rules combine to form a fuzzy system. The fuzzy sets and fuzzy rules combine to form a fuzzy system. Consider a sun tracking system for a standalone photovoltaic system… Consider a sun tracking system for a standalone photovoltaic system…

Building the Fuzzy System Details and Background Details and Background –Single Axis tracking system –Pole mount system that rotates with the sun throughout the day –Fixed tilt angle with the season –Two light intensity sensors, one on the right side of the panel, one on the left side of the panel. –At night, the panel automatically moves back to the morning position. MATLAB VS. Mathematica MATLAB VS. Mathematica –Mathematica only has fuzzy tools in version 2.2 (Very old school)

MATLAB Fuzzy Toolbox Type in “fuzzy” in at the MATLAB prompt. Type in “fuzzy” in at the MATLAB prompt. Included in MATLAB 6.1. Included in MATLAB 6.1.

System Sketch and Setup

Step 1: Choose variables The variables become the input (X) and output (Y) The variables become the input (X) and output (Y) –In this case, X is b oth of the light intensity sensors. There is a logic device that compares each sensor measurement to see which side has more intensity making this a single input system. –Y, the output is the amount (degrees) to move the panel clockwise or counter-clockwise. –If X, then Y –If the sun is more intense in the right sensor, rotate the panel toward the right some degrees.

Step 2: Pick the Fuzzy Sets Pick subsets of the inputs and outputs. Pick subsets of the inputs and outputs. Draw these as curves or triangles. Draw these as curves or triangles.

Input Subsets Engineering judgment and common sense define how these triangles are shaped. Engineering judgment and common sense define how these triangles are shaped. The widest sets are least important and give rough control. The widest sets are least important and give rough control. Thin sets give fine control and bring quick adjustment. Thin sets give fine control and bring quick adjustment.

Output Subsets

Step 3: Pick the fuzzy rules

Curve of Rules

Results: Facing the sun

More intensity in the right sensor

Cloud Lift

Defuzzification The triangles are usually added… The triangles are usually added… –Then the average of the addition is found as the defuzzified value. If Ai, then Bi If A1, then B1 If A2, then B2 B’1 B’2 B’i X+ B Defuzzification Y A....

Conclusion Fuzzy logic allows control with little math. Fuzzy logic allows control with little math. –It is very difficult and often impossible to represent a natural process with an accurate equation Fuzzy Logic is another way to look at the world. Fuzzy Logic is another way to look at the world. Step back and consider the problem. It doesn’t always involve huge, difficult solutions. Step back and consider the problem. It doesn’t always involve huge, difficult solutions.

Questions?