Fuzzy Control –Configuration –Design choices –Takagi-Sugeno controller

Direct Control Deviations Actions Outputs Ref Controller End-user Inference engine Rule base Plant

Building Blocks Fuzzy controller Inference engine Rule base Defuzzi -fication Postpro - cessing Fuzzi- fication Prepro- cessing

Nonlinear Input Scaling measured input scaled input

If-Then Rule Base 1. If error is Neg and change in error is Neg then output is NB 2. If error is Neg and change in error is Zero then output is NM 3. If error is Neg and change in error is Pos then output is Zero 4. If error is Zero and change in error is Neg then output is NM 5. If error is Zero and change in error is Zero then output is Zero 6. If error is Zero and change in error is Pos then output is PM 7. If error is Pos and change in error is Neg then output is Zero 8. If error is Pos and change in error is Zero then output is PM 9. If error is Pos and change in error is Pos then output is PB

Relational Rule Format ErrorChange in errorControl Pos PB PosZeroPM PosNegZero PosPM Zero NegNM NegPosZero NegZeroNM Neg NB

Tabular Rule Format Change in error NegZeroPos NegNBNMZero ErrorZeroNMZeroPM PosZeroPMPB

Connectives minimum maximum algebraic product probabilistic sum

FLS I/O Families Input Membership Output Membership Neg Zero Pos

Examples Of Primary Sets

Inference And Terminology AND Aggregation Accumulation Defuzzification Activation  4  5

Defuzzification RM BOA COG MOM LM

Rule Based Controllers 1.If error is Neg then control is Neg 2.If error is Zero then control is Zero 3.If error is Pos then control is Pos

Mamdani Inference

FLS Inference

Sugeno Inference

Singleton Output 1. If error is Pos then control is If error is Zero then control is 0 3. If error is Neg then control is -10

First Order Output 1. If error is Pos then control is a 2 *error + b 2 2. If error is Neg then control is a 1 *error + b 1

Interpolation (Takagi-Sugeno) (a) output (b) membership

Rule Base To Table

Look-Up Table Change in error Error

Control Surface E CE u input family membership

Linear Controller E CE u input family membership

Linear Rule Base

Conditions For Linearity Triangular sets, crossing at  = 0.5 Rules: complete  -combination Define  as * Use conclusion singletons, positioned at sum of input peak positions Use sum-accumulation and COGS defuzzification

Simplification of 4 rules 1. If error is Neg and change in error is Neg then control is NB 3. If error is Neg and change in error is Pos then control is Zero 7. If error is Pos and change in error is Neg then control is Zero 9. If error is Pos and change in error is Pos then control is PB is

Simplification of 9 rules 1. If error is Neg and change in error is Neg then output is NB 2. If error is Neg and change in error is Zero then output is NM 3. If error is Neg and change in error is Pos then output is Zero 4. If error is Zero and change in error is Neg then output is NM 5. If error is Zero and change in error is Zero then output is Zero 6. If error is Zero and change in error is Pos then output is PM 7. If error is Pos and change in error is Neg then output is Zero 8. If error is Pos and change in error is Zero then output is PM 9. If error is Pos and change in error is Pos then output is PB is

Summary Of Choices Rule-base related choices: # of inputs and outputs, rules, universes, continuous or discrete, # of membership functions, their overlap and width, singleton conclusions Inference engine choices: Connectives, modifiers, activation operation, aggregation operation, accumulation operation Defuzzification method: COG, COGS, BOA, MOM, LM, RM Pre- and postprocessing: Scaling, quantization, sampling time