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**Dipl.Ing (FH) Mario Sader**

FachHochschule Lausitz University of Applied Sciences THE SEMINAR OF MASTER PROJECT “The Implementation of Feedforward-Feedback Fuzzy Logic Algorithm for Level Control System at Process Mini-Plant Measurement Laboratory FH-Lausitz “ by R.Danu Setyo Nugroho (Matrikel.Nr ) Supervisor Prof.Dr.Ing. E.Stein Co-Supervisor Dipl.Ing (FH) Mario Sader Senftenberg, 7th July 2004

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**3. Fuzzy Logic Algorithm Theory**

FachHochschule Lausitz University of Applied Sciences Topic Discussion : 1. Introduction 2. Basic Control Theory 3. Fuzzy Logic Algorithm Theory 4. Fuzzy Logic Control Design 5. Validation 6. Summary

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**INTRODUCTION Background FachHochschule Lausitz ON/OFF Control Mode**

University of Applied Sciences INTRODUCTION Background ON/OFF Control Mode Set Point Process Mini-Plant at Measurement Laboratory

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**To keep the set point : qin = qout**

FachHochschule Lausitz University of Applied Sciences INTRODUCTION The Goal CONTINUOUS CONTROL qin Set Point qout To keep the set point : qin = qout

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**? ? INTRODUCTION Problems Lack of Parameter Systems Information Gc Gm**

FachHochschule Lausitz University of Applied Sciences INTRODUCTION Problems Lack of Parameter Systems Information ? ∑ Gc Gm Gt Process SP + - e controller control valve level transmitter mini plant Block Diagram of Close Loop Systems ?

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**qin should be increased qin should be reduced qin > qout**

FachHochschule Lausitz University of Applied Sciences INTRODUCTION Problems Set point Changing Load Change Error New Set Point Set Point Load Change Normal Load qin should be increased qin should be reduced qin > qout

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**Feedforward – Feedback**

FachHochschule Lausitz University of Applied Sciences INTRODUCTION SOLUTION Feedforward – Feedback Fuzzy Logic Control

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**process characteristics**

FachHochschule Lausitz University of Applied Sciences BASIC CONTROL SYSTEMS process characteristics dead time τd time constant τc response time τr Step Response 95% τr 63% τc actual level τd time

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**criteria of good control**

FachHochschule Lausitz University of Applied Sciences BASIC CONTROL SYSTEMS criteria of good control minimum absolute error quarter amplitude decay critical damping minimum absolute error SP1 CV1 time SP2 t0 a a/4 CV2 ∫|E|dt= minimum

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**criteria of good control**

FachHochschule Lausitz University of Applied Sciences BASIC CONTROL SYSTEMS criteria of good control critical damping SP2 CV2 SP1 CV1 time t0 under damping over damping critical damping

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**feedforward control systems**

FachHochschule Lausitz University of Applied Sciences BASIC CONTROL SYSTEMS control systems feedforward control systems feedback control systems disturbance controller process sp valve sprayed 90o 180o 270o 5m 10m 15m calibration set

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**free of mathematic modeling systems **

FachHochschule Lausitz University of Applied Sciences FUZZY LOGIC ALGORITHM advantages history free of mathematic modeling systems The concept of Fuzzy Logic (FL) was conceived by Lotfi Zadeh, a professor at the University of California at Berkley, and presented not as a control methodology, but as a way of processing data by allowing fuzzy set membership rather than crisp set membership or non-membership. ( e.g Laplace transform, transfer function systems are not required) empirically-based on operator’s experience rather than technical understanding of control systems ( The advance knowledge of control theory is not required) flexible and easy in design (e.g MIMO,MISO,SISO, rule base determination, simple aritmethic) fun

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**Upss , it is warm !, it isn’t hot at all !**

FachHochschule Lausitz University of Applied Sciences FUZZY LOGIC ALGORITHM Fuzzy Set Vs Crisps Set 700C warm hot Fs : X [0,1] [1] [0] Crisps Set (FS ) Fuzzy Set (μf) How about T = 69oC ? warm 250C 750C 650C 850C hot Upss , it is warm !, it isn’t hot at all ! Are you happy with that ? μf : X |0,1|

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**The Properties of Fuzzy Set**

FachHochschule Lausitz University of Applied Sciences FUZZY LOGIC ALGORITHM The Properties of Fuzzy Set Label 1 0.5 μf(x) 50 30 70 100 cold warm hot oC membership function degre of fuzzy universal of discorse scope domain crisps input

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**The most common used operation logic**

FachHochschule Lausitz University of Applied Sciences FUZZY LOGIC ALGORITHM Operation Logic Boolean Logical Fuzzy The most common used operation logic

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**Fuzzy Inference Engine**

FachHochschule Lausitz University of Applied Sciences FUZZY LOGIC ALGORITHM Fuzzy Inference Engine fuzzyfication defuzzyfication rule evaluation rule base crisps inputs outputs controller

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**Simple Fuzzy Logic Application Home sprinkler system**

FachHochschule Lausitz University of Applied Sciences FUZZY LOGIC ALGORITHM Simple Fuzzy Logic Application Home sprinkler system How long the watering duration should take? It depends on the air temperature and soil moisture Air temperature Soil moisture ..FUZZY duration

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**Fuzzification for air temperature**

FachHochschule Lausitz University of Applied Sciences FUZZY LOGIC ALGORITHM Fuzzification for air temperature cool warm hot 1 μ 30 50 80 Temp/C fuzzification C W H T_in 60 0.66 0.66 30 0.33 0.33 -30 60 μw = (temp_in – 80) / gradient μh = (temp_in – 50) / gradient μh = (60 – 50) / 30 μw = (60 – 80) / -30 μh = 0.33 μw = 0.66

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**Fuzzification for soil moisture**

FachHochschule Lausitz University of Applied Sciences FUZZY LOGIC ALGORITHM Fuzzification for soil moisture 0.43 0.56 dry moist wet 1 μ 15 25 Moist% fuzzification D M W T_in 8 % 8 30 -30

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**Which knowledge base should be used ? operator’s experiences**

FachHochschule Lausitz University of Applied Sciences FUZZY LOGIC ALGORITHM Rule Evaluation Which knowledge base should be used ? operator’s experiences If temperature is hot AND moister is wet THEN watering duration is short If temperature is hot AND moister is moist THEN watering duration is medium If temperature is hot AND moister is dry THEN watering duration is long If temperature is warm AND moister is wet THEN watering duration is short If temperature is warm AND moister is moist THEN watering duration is medium If temperature is warm AND moister is dry THEN watering duration is long If temperature is cool AND moister is wet THEN watering duration is short If temperature is cool AND moister is moist THEN watering duration is medium If temperature is cool AND moister is dry THEN watering duration is long If “antecedence 1” AND “antecedence 2 “ THEN “consequent”

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**Mamdani Min-Max Operation**

FachHochschule Lausitz University of Applied Sciences FUZZY LOGIC ALGORITHM Rule Evaluation Mamdani Min-Max Operation temp cool warm hot rule strength 0.66 0.33 moisture wet 0.56 0.43 S M L = S M L 0.43 0.33 moist 0.56 0.56 0.43 dry 0.33 If temperature is warm (0.66) AND moisture is moist (0.56) THEN watering duration is medium (0.56) Y = Max (a,b) If temperature is hot (0.33) AND moisture is dry (0.43) THEN watering duration is long (0.33) Y = Min (a,b)

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**Center Of Gravity = 0 x 20 + 0.56 x 40 + 0.43 x 60**

FachHochschule Lausitz University of Applied Sciences FUZZY LOGIC ALGORITHM Singleton Defuzzification watering duration (min) 1 μ short medium long S M L time defuzzification 0.56 0.43 0.56 0.43 COG 20 40 60 Center Of Gravity = 0 x x x 60 (COG) = 48.2 minute

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**Strategy of Control Design**

FachHochschule Lausitz University of Applied Sciences Strategy of Control Design ∑ Process SP + - e Feedback Fuzzy Controller Feedforward diagram block system

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**Strategy of Control Design**

FachHochschule Lausitz University of Applied Sciences Strategy of Control Design fuzzification of feedforward systems Level Membership Function μ(f) 19,30 29,35 37,90 50,35 very low low medium high very high h(cm) 1 12,60 The degree of membership function |1,0| very low low medium high very high 18 0,21 0,782 20 0,949 0,05 25 0,543 0,45 28 0,137 0,86 36 0,22 0,77 Level (cm)

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**Strategy of Control Design**

FachHochschule Lausitz University of Applied Sciences Strategy of Control Design rule evaluation of feedforward systems 1. IF the level is “very high” THEN the opening of valve is “very big” 2. IF the level is “high” THEN the opening of valve is “big” 3. IF the level is “medium” THEN the opening of valve is “medium” 4. IF the level is “low” THEN the opening of valve is “small” 5. IF the level is “very low” THEN the opening of valve is “very small” THEN level 1 1/2 “high” IF 1 1/2 opening of valve “big” 1/2 “big” 1 opening of valve fuzzification.vi defuzzification.vi 5 rule

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**The degree of membership function [1,0]**

FachHochschule Lausitz University of Applied Sciences Strategy of Control Design defuzzification of feedforward system Set Point The degree of membership function [1,0] Control Signal very low low medium high very high 18 0,938 0,06 5,78 V 20 0,54 0,36 6,05 V 25 0,4 0,6 6,55 V 28 6,86 V 30 0,1 0,9 7,77 V 8 9 very small small medium big very big 6 7 volt 1 5 μ(f) Opening Valve Membership Function Level (cm)

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**The degree of membership function [1,0]**

FachHochschule Lausitz University of Applied Sciences Strategy of Control Design fuzzification of feedback system NB NS ZE PS PB e 1 Error membership function μ(f) LNB PVB XLNB -0,5 0.5 1,5 -1,5 -1 -2 The degree of membership function [1,0] XLNB LNB NB NS ZE PS PB LPB -2 1 -0,9 0,8 0,2 -0,2 0.4 0.6 0.5 1,2 0,4 0,6 1,5 error (cm)

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**Strategy of Control Design**

FachHochschule Lausitz University of Applied Sciences Strategy of Control Design rule evaluation of feedback system Based on P Controller IF error is “XL Negative Big” THEN corrective valve is “XL Negative Big” IF error is “Large Neg. Big” THEN correction valve is “Large Neg. Big “ IF error is “Negative Big” THEN correction valve is “Negative Big” IF error is “Negative Small” THEN correction valve is “ Negative Small” IF error is “Zero Error” THEN correction valve is “Zero” IF error is “Positive Small” THEN correction valve is “Positive Small” IF error is “Positive Big” THEN correction valve is “Positive Big” If error is “Large Pos Big” THEN correction valve is “Large Pos Big”

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**The degree of membership function [1,0]**

FachHochschule Lausitz University of Applied Sciences Strategy of Control Design defuzzification of feedback system NB NS ZE PS PB volt 1 Defuzzification of Corrective Valve μ(f) LNB LPB XLNB -1,5 0.1 3 -2,2 1.0 -2 -3 The degree of membership function [1,0] XLNB LNB NB NS ZE PS PB LPB -2 1 -3 -0,9 0,8 0,2 -1,34 -0,2 0.4 0.6 -0.28 0.5 0,5 1,2 0,4 0,6 1,8 1,5 3 Error (cm) correcting signal (v)

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**FachHochschule Lausitz**

University of Applied Sciences

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**Note : Parameter PI Controller are P = 1,33 and I = 120/s.**

FachHochschule Lausitz University of Applied Sciences VALIDATION THE COMPARISON OF PERFOMANCE CONTROLLER τs 95% of 25 FUZZY LOGIC Vs PI CONTROLLER STEP RESPONS TESTING SET POINT CHANGING LOAD CHANGE Note : Parameter PI Controller are P = 1,33 and I = 120/s.

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**25 cm level is the normal level without load change **

FachHochschule Lausitz University of Applied Sciences VALIDATION LOAD CHANGE TESTING error Note : 25 cm level is the normal level without load change Error open loop in 450% load change is 7 cm

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**SET POINT CHANGE TESTING**

FachHochschule Lausitz University of Applied Sciences VALIDATION SET POINT CHANGE TESTING

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**in steady state response**

FachHochschule Lausitz University of Applied Sciences SUMMARY The performance of Fuzzy Logic Control here is better then PI Controller in transient response. The performance of PI Controller here is better then Fuzzy Logic Control in steady state response The number of fuzzy membership’s label that is used influence the smoothness of the controller’s reaction. Fuzzy Logic Control is able to avoid both of overshoot and undershoot condition Even plant has two tank, it is catagorized as first order systems. Because the second tank doesn’t act as capacitive element during normal process.

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**THANK YOU FOR YOUR ATTENTION**

FachHochschule Lausitz University of Applied Sciences SUMMARY RECOMMENDED FUTURE RESEARCH TOPICS Fuzzy Logic Control based on the PI controller THANK YOU FOR YOUR ATTENTION Adaptive Neuro-Fuzzy Logic Control Self Tuning or Gain Scheduling PI Controller using Fuzzy Logic Algorithm

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