Introduction to Fuzzy Control Background Fuzzy control enables noncontrol-specialists to design control system. A fuzzy controller works with verbal rules rather than mathematical relationships. knowledge based control rule based control expert control Traditionally computer decision is based on two -valued boolean logic (true/false, yes/no, 0/1), but not all real world problems lend themselves to a strict yes/no or true/false formulation. Approaches Fuzzy logic To make computers cope with imprecise statements 1
Introduce a gradual transition from true to false (or yes to no, 0 to 1). e.g. temperature warm/cold, warm slightly warm slightly cold cold, Applications robots, machinery, electrical systems, consumer products, e.g. video cameras, washing machine, TV, etc. Characteristics of fuzzy control Usually nonlinear, More complex than PID, More tuning parameters, Smooth operation, robust. Easier to cope for a non-control-specialist (IF-THEN rules are no theoretical difficulty).
0 scale 1 fuzzy nonfuzzy 0 10 20 30 40 fuzzy and nonfuzzy interpretation of a room temperature A fuzzy controller is driven by a collection of verbal rules, often in IF-THEN format. A fuzzy controller uses fuzzy logic to simulate human thinking. Fuzzy logic is a logic based on truth value in [0,1], rather than just true/false. A fuzzy controller consists of a user interface, a rule base and an inference engine. 2
controller user ref condition rule base action process output inference engine A fuzzy controller
User interface designed for process operators. Often it is given as a diagram on a graphical screen showing overall architecture of the control system. Or it can be given as a matrix. It is possible to see the fuzzy set definitions by means of graphs. Rule base a collection of stored control rules. R i : If x is A i and y is B i, Then z is C i. where x and y, the inputs, are measured variables, and z is the controller output or the control action; A i, B i, C i are linguistic terms, such as low, medium, or high. The IF part of the rule is called the premise or condition, The THEN part is called the consequence or action. 3
An IF-THEN rule is mathematically speaking an implication. Inference engine a program that draws the actual conclusions from the actual inputs to the controller. Rule: If an apple is red, then it is ripe Fact: My apple is red Consequence: My apple is ripe
Fuzzy sets Nonfuzzy set A (nonfuzzy) set is any collection of objects which can be treated as a whole. An item from a given universe is either a member of the set or not. set/collection/class (item/element/member). (a) The set of nonnegative integers less than 4. finite set (0,1,2,3). (b) The set of live dinosaurs. empty set. (c) The set of measurements greater than 3. an infinite set, but there is no difficulty in determining where a given measurement is a member. A set can be specified by stating when an item is in the set. 4
Fuzzy set Many sets do not have a precise criterion for membership. (a) people at 20, 30, or 40 years? (b) high temperature, strong winds, nice days? Zadeh proposed a degree of membership, such that the transition from member to nonmember of a set is gradual rather than abrupt. The grade of membership for all its members thus describes a fuzzy set. An item s grade of membership is normally a real number between 0 and 1. Universe Elements of a fuzzy set are taken from a universe of discourse or just universe. The universe contains all elements that come into consideration.
membership function each element in the universe of discourse has an associated grade of membership with regard to the fuzzy set. The function that ties a number to each element of the unverse is called the membership function. (a) The set of young people could be all human beings in the world. Or numbers between 0 and 100. (b) The set x 10 could have a universe all positive measurements. 1 membership 0 0 2 4 6 8 Membership function of the set around 4.
Example: Set of fast speed 1 Grade of membership 0 30 60 90 120 speed For a different car/driver the set might look like: 1 Grade of membership 0 30 60 90 120 speed Fuzzy logic control is application dependent, subjective, inexact. 5
Ref + error FLC control input System output error Fuzzification Fuzzy control defuzzification control input Fuzzy value Real value Standard feedback loop of a fuzzy controller Fuzzy Logic Controller (FLC) Fuzzification Measured variables are real world signal, e.g. 63mph, Fuzzy systems interpret them as fast speed associated with a degree of membership (fuzzification) 6
63mph 0.8 fast, or 0.3 medium, or 0.0 slow. Fuzzy control Fuzzy controller acts upon these values, its derivatives, integrals, etc.. Defuzzification Inference from the fuzzy controller to the real values of system control action. Problems exponential growth of number of rules. Exercises: 1. Given an example of a fuzzy set on outdoor temperature of January in Reading. 2. Draw a diagram of a fuzzy control system.