what is fuzzy logic

CS 561, Sessions 22-23 1 What is fuzzy logic? • A super set of Boolean logic • Builds upon fuzzy set theory • Graded truth. Truth values between True and False. Not everything is either/or, true/false, black/white, on/off etc. • Grades of membership. Class of tall men, class of far cities, class of expensive things, etc. • Lotfi Zadeh, UC/Berkely 1965. Introduced FL to model uncertainty in natural language. Tall, far, nice, large, hot, … • Reasoning using linguistic terms. Natural to express expert knowledge. If the weather is cold then wear warm clothing CS 561, Sessions 22-23 2 Why use fuzzy logic? Pros: • Conceptually easy to understand w/ “natural” maths • Tolerant of imprecise data • Universal approximation: can model arbitrary nonlinear functions • Intuitive • Based on linguistic terms • Convenient way to express expert and common sense knowledge Cons: • Not a cure-all • Crisp/precise models can be more efficient and even convenient • Other approaches might be formally verified to work Issues of Fuzzy logic Control • Requires tuning of membership functions • Fuzzy Logic control may not scale well to large or complex problems • Deals with imprecision, and vagueness, but not uncertainty CS 561, Sessions 22-23 4 Limitations of fuzzy logic • How to determine the membership functions? Usually requires fine-tuning of parameters • Defuzzification can produce undesired results Application (2) Fuzzy Logic Control Topics of Today 1. Fuzzy logic control (FLC): concepts and system structure 2. Example of FLC 3. Fuzzy PID control Conventional Control System The dynamic filter compute all the system dynamics: x (state variables) consists of selected elements of e = r – y, de/dt, or ∫edτ. . Plant Conventional PID Controller Architecture y u Dynamic Filter r x PID Controller Algorithm Mathematical Model Fuzzy Logic Control • Fuzzy Logic Control (FLC) or sometimes known as Fuzzy Linguistic Control is a knowledge based control strategy that can be used - when either a sufficient accurate and yet not unreasonably complex model of the plant is unavailable, or - when a (single) precise measure of performance is not meaningful or practical. • FLC design is based on empirically acquired knowledge regarding the operation of the process. • This knowledge, cast into linguistic, or rule-based form, is the core of the FLC system. • FLC is particularly useful when the plant model is unknown or difficult to develop. FLC Architecture The rule base (knowledge base) provides nonlinear transformations without any built-in dynamics. Decoder (Defuzzifier) Knowledge Base Encoder (Fuzzifier) PlantInference Engine Fuzzy Logic Controller Architecture y u Dynamic Filter r x Fuzzification Fuzzy quantization of the state variables. For example, the state variable "Angle" may be quantified into a set of linguistic variables, with two parameters, polarity and size: Fuzzification converts a crisp sensor reading (value of state variable), x = xo, into the membership to these linguistic variables: [ µ NL (x o ), µ NS (x o ), µ ZO (x o ), µ PS (x o ), µ PL (x o ) ] NL NS ZO PS PL –180 0 180 NL – Negative, Large; NS – Negative, Small; ZO – Zero; PS – Positive, Small; PL – Positive, Large. x 0 [...]... fuzzy logic operations, e.g union, intersection, and complement • For rules which has a non-zero activation value, the output fuzzy variables will be combined (fuzzy union) yielding a resultant fuzzy set 1 1 A3 1 B1 0.1 0.0 0 x1 0 X Rule 1: IF x is A3 (0.0) OR 1 y1 y is B1 (0.1) 1 A2 0 x1 y1 Rule 2: IF x is A2 (0.2) AND y is B2 (0.7) 1 0 A1 THEN C3 Z z is C1 (0.1) AND (min) Y 0.2 C1 C2 C3 0 Z 1 z is. .. distance between cars Adjust Speed? distance Current speed Example: automotive driving Keep distance between cars: Step 1: construction of control rules: Rule 1: IF distance between cars is short AND speed is slow THEN hold the gas pedal steady (maintain the speed) Rule 2: IF distance between cars is short AND speed is fast THEN step on the brake (reduce the speed) Rule 3: IF distance between cars is. .. \ ∆ e ( k ) Fuzzy Rules • Example: “If our distance to the car in front is small, and the distance is decreasing slowly, then decelerate quite hard” – Fuzzy variables in blue – Fuzzy sets in red • QUESTION: Given the distance and the change in the distance, what acceleration should we select? CS 561, Sessions 22-23 25 Fuzzification: Set Definitions v small small perfect big v big brake distance 0.75 delta IF change in distance is = THEN Keep the speed CS 561, Sessions... and ∆u PI Fuzzy Logic Control Fuzzy reasoning r e + - ∆e Ge G∆e Fuzzy reasoning Ti Kp PI Controller u plant y • PI controller: H( z) = K p + K i z 1 z = K p (1 + ) z −1 Ti z − 1 • The proportional gain K p and integral time constant Ti are adjusted on-line by fuzzy reasoning PI Fuzzy Logic Control • Fuzzy rules for computation of Kp: • Fuzzy rules for computation of Ti: N ZE P N B B B ZE S B S P B . Rule 2: IF x is A3 (0.0) y is B1 (0.1) z is C1 (0.1) IF x is A2 (0.2) y is B2 (0.7) z is C2 (0.2) IF x is A1 (0.5) z is C3 (0.5) Defuzzification • The resultant fuzzy set needs. 561, Sessions 22-23 1 What is fuzzy logic? • A super set of Boolean logic • Builds upon fuzzy set theory • Graded truth. Truth values between True and False. Not everything is either/or, true/false,. cure-all • Crisp/precise models can be more efficient and even convenient • Other approaches might be formally verified to work Issues of Fuzzy logic Control • Requires tuning of membership functions • Fuzzy