Fuzzy Logic Samson Okoh Engr 315 Fall 2002

Introduction  Brief History  How it Works –Basics of Fuzzy Logic  Rules –Step by Step Approach of Fuzzy Logic  Fuzzification  Rule Evaluation  Defuzzification –Example Application  Inverted Pendulum  Other applications of Fuzzy Logic  Conclusion

Brief History  Fuzzy logic can be defined as a superset of conventional (Boolean) logic that has been extended to handle the concept of partial truth - truth values between “completely true” and “completely false”  Brought up by Lofti Zedah in the 1960s  Professor at University of California at Beckley

How it Works  Basics of Fuzzy Logic (Rules) –Operates similar to humans  Humans base their decisions on conditions –Operates on a bunch of IF-THEN statements –An example is A then B, if C then D where B and D are all set of A and C.

Steps by Step Approach  Step One –Define the control objectives and criteria.  Consider question like –What is trying to be controlled? –What has to be done to control the system? –What kind of response is needed? –What are the possible (probable) system failure modes?  Step Two –Determine input and output relationships –Determine the least number of variables for inputs to the fuzzy logic system

Steps by Step Approach  Step Three –Break down the control problem into a series of IF X AND Y, THEN Z rules based on the fuzzy logic rules. –These IF X AND Y, THEN Z rules should define the desired system output response for the given systems input conditions.  Step Four –Create a fuzzy logic membership function that defines the meaning or values of the input and output terms used in the rules

Steps by Step Approach  Step Five –After the membership functions are created, program everything then into the fuzzy logic system  Step Six –Finally, test the system, evaluate results and make the necessary adjustments until a desired result is obtain

Steps by Step Approach  The above steps are summarized into three main stages –Fuzzification  Membership functions used to graphically describe a situation –Evaluation of Rules  Application of the fuzzy logic rules –Diffuzification  Obtaining the crisp results

Steps by Step Approach

Inverted Pendulum  Task: –To balance a pole on a mobile platform that can move in only two directions, either to the left or to the right.

Inverted Pendulum  The input and output relationships of the variables of the fuzzy system are then determined. –Inputs:  Angle between the platform and the pendulum  Angular velocity of this angle. –Outputs:  Speed of platform

Inverted Pendulum  Use membership functions to graphically describe the situation (Fuzzification)  The output which is speed can be high speed, medium speed, low speed, etc. These different levels of output of the platform are defined by specifying the membership functions for the fuzzy-sets

Inverted Pendulum

 Define Fuzzy Rules –Examples  If angle is zero and angular velocity is zero, then speed is also zero  If angle is zero and angular velocity is negative low, the speed is negative low  If angle is positive low and angular velocity is zero, then speed is positive low  If angle is positive low and angular velocity is negative low, then speed is zero

Inverted Pendulum

 Finally, the Defuzzification stage is implemented.  Two ways of defuzzification is by –Finding the center of Gravity and –Finding the average mean.

Inverted Pendulum  Example Application a/pend/pendjava.htm a/pend/pendjava.htm

Other Applications  Coal Power Plant  Refuse Incineration Plant  Water Treatment Systems  AC Induction Motor  Fraud Detection  Customer Targeting  Quality Control  Speech Recognition  Nuclear Fusion  Truck Speed Limiter  Sonar Systems  Toasters  Photocopiers  Creditworthiness Assessment  Stock Prognosis  Mortgage Application  Hi-Fi Systems  Humidifiers  Domestic Goods - Washing Machines/Dryers  Microwave Ovens  Consumer Electronics – Television  Still and Video Cameras - Auto focus, Exposure and Anti-Shake  Vacuum Cleaners

Questions?