- Overview of Dyeing Processes - Current Status of Dyeing Process Control DARG Approach to Dyeing Process Control

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3 Outline * Introduction - Overview of Dyeing Processes - Current Status of Dyeing Process Control DARG Approach to Dyeing Process Control 9. * Classical Fuzzy Logic Control - Basics of Fuzzy Logic Control - Structure of a Fuzzy Logic Controller * Adaptive Fuzzy Logic Control - Self-scaling Factor Tuning Scheme - Self-Learning Scheme * Fuzzy Logic Control for Multi-Input, Multi-Output Systems - The Optimization Method - - Simulation Results * Concluding Remarks and Future Activities

4 Introduction Overview of Dyeing Processes Description of Dyeing Processes Influence Factors - Controllable: Temperature, Time, ph, Salt, Liquor Ratio... - Uncontrollable: Fiber Shape and Properties, Concentration of Dye Sites, Merge, Maturity... Current Market Trend - Small Lots, High Quality, Quick Response... Process Control - Optimize Production EfFiciency, Improve Product Quality, Detect Mistaken Operations...

5 Current Art of Dyeing Process Control Open-Loop Control: Dyeing processes follow prede- termined standard procedures in order to produce consist en t resu Its. Problems - Different Process Requirements - Uncontrollable Factors - Mistaken Parameter Settings -eeeeee

6 DARG Approach to Dyeing Process Contro! Closed-Loop Control: Dyeing processes are moni- tored and process parameters are adjusted on-line in such a way to arrive at the desired end results. Control Methods - Parametric Methods: PID, LQR... - Nonparametric Methods: FL, ANN, ES... Reasons for Fuzzy Logic Control - Lack of General Reliable Models - Lack of Accurate On-Line Measurements

7 GOAL DEVELOP A NON-MODEL (OR PARTIAL MODEL) BASED ADAPTIVE CONTROLLER FOR DYEING PRQCESSES. APPROACH EMPLOY FUZZY LOGIC CONTROL WITH * SELF-LEARNING RULE BASE * ON-LINE SCALING FACTOR TUNING * APPLY METHOD TO DYEING PROCESS

8 * Issues For Discussion Purpose of Control: Improve performance of system. Control Strategies: * model-based vs. non-model based * what information is known before start process with control? Why Fuzzy Logic Control? What are some of the important parameters in FLC? How is FLC implemented in dyeing process? What is the current state of FLC research that is applicable to the dyeing industry?

9 Classical Fuzzy Logic Control Basics of Fuzzy Logic Control e Literature Review - Theory of Fuzzy Sets and Fuzzy Logic(Zadeh,L.A., 1965, 1968) - Fuzzy Logic Control(Zadeh,L.A., 1973; Mamdani,E.H., ) e A Fuzzy Logic Controller: A knowledge-based controller that attempts to simulate the human control decision making using the theory of fuzzy logic and fuzzy sets. Advantage of Fuzzy Logic Control - Reject Disturbance - Cope with Nonlinearities - Adapt to New Situations

10 Fuzzy Logic Control * Rule-Based An Individual Rule is constructed using IF <...qualitative terms... > THEN <...q ua/itative terms > Examples of qualitative terms are: big, small, hot, cold, fast, slow... A linguistic rule (for balancing a stick): IF the stick is inclined moderately to the left THEN move the hand quickly to the left. These linguistic terms come from and are converted to numeric values Rules are somewhat vague (resembling how humans think) Fuzzy Set Theory allows a linguistic term to take on a range of values through a membership function.

11 Classical Fuzzy Logic Controller Algorithm: 1) Compute the current error (E) and rate of change of error (CE) 2) Convert numerical E and CE into fuzzy E and CE 3) Evaluate the control rules using the fuzzy logic operations 4) Compute the deterministic input required to control the process * Fuzzifier: scaling, membership function * Rule base: control surface ~ -- * Defuzzifier: scalar function

12 Structure of a Fuzzy Logic Controller E CE Fuzzifier 3- Control Rule Base

13 Structure of a Fuzzifier hmerical E Fuzzy E I I Numerical C Fuzzy C< - Scaling Factors Membership Functions Figure 2: Structure of a Fuzzifier

14 SCALING FACTOR: TRANSFORMS RANGE OF INPUT VALUES TO RANGE OF SCALED NUMERICAL VALUES 8.O 6.0 { 4.0 { 2.0 { / { : I 6d.O Error (degrees) PURPOSE: LIMIT THE RANGE OF VALUES TO BE INVESTIGATED INPUT: ACTUAL VALUE OF ERROR AND CHANGE OF ERROR OUTPUT: -- SCALED VALUE OF ERROR AND CHANGE OF ERROR

15 SHIP MEMBERSHIP FUNCTION: TAKES SCALED VALUES AND ASSIGNS MEMBER- SHIP VALUES FOR EACH FUZZY CLASS 5'0" 5'4" 5'9" 62" 6'6" Universe of Discourse (U) PURPOSE: FUZZIFY THE NUMERICAL VALUES INTO LINGUISTIC VALUES INPUT: SCALED NUMERICAL VALUES OUTPUT: FUZZY VALUES ACCORDING TO MEMBER- CLASS AND MEMBERSHIP VALUE -- ~

16 MANY DIFFERENT TYPES OF MEMBERSHIP FUNCTIONS CAN BE USED: Bell Shaped Trapezoidal Triangular Sinusoidal a b C d * CAN CHOOSE DIFFERENT FUNCTIONS FOR DIFFERENT RANGE OF VALUES * MUST SELECT HOW MEMBERSHIP CLASSES OVERLAP (COVER) RANGES OF VALUES * FOR CONTROL PURPOSE, LINGUISTIC RULES USE MEMBERSHIP CLASSES LIKE LARGE POSITlVE OR SMALL NEGATIVE

17 Large Positive y = sin [K/4*(X4) J 1 Medium Positive 1 y = sin [K/4*(X-2)] -' I I I I Small Positve y = sin [K/4*(X)] Zero y = Sin [K/4*(X+2)] I I I I I I Small Negative y = sin [7t/4*(x+4)] I I I I I I Medium Negative y = sin [rr/4*(x+6)) 1 -' I I I I I I Large Negative 1 -- * y = sin [1~/4*(x+8)] -, I I I I I I 2 4 6

18 LN MN S PI SP Mp LP 1 < U \ ANTECEDENT BLOCKS Logic product example

19 Structure of a Rulebase 1) If E is LP, and CE is LP, then Ctrl is LN. 2) If E is LP, and CE is SP, then Ctrl is MN. Fuzzy Process Control Input Fuzzy CE 0 0 Structure of a Rulebase Rule Surface -3 Control Rule Surface with (-3:LN) (-2:MN) (-1:SN) (05%) (1:SP) (2:MP) (3:LP)

20 CONTROL RULE BASE: * THIS IS THE ESSENTIAL COMPONENT OF THE FLC PURPOSE: DEFINE CONTROL ACTION FROM FUZZY SET OF RULES AND FUZZY INPUT VALUES INPUT: FUZZY SET OF VALUES OF INPUT OUTPUT: FUZZY SET OF CONTROL ACTIONS * MADE UP OF: IF <mmmqualitative TERMS="> THEN <mmmmmqualitative TERMS".> * EACH RULE MAY HAVE MANY CONDITIONS = NEED WAY OF RESOLVING ONE RESULT: USE LOGICAL AND *MAY HAVE MANY RULES, EACH OF WHICH DEFINES A CONTROL ACTION = NEED WAY OF RESOLVING -- ONE ACTION: USE LOGICAL OR

21 F F 2 w E. (P i; id id P w L U L x z i! Z 3 Z il Z b m U & b U 0 i U b a U L L m c L

22 Structure of a Defuzzifier Fuzzy Process Control Input Numerical Process Structure of a Defuzzifier

23 DEFUZZIFIER: * TAKES FUZZY CONTROL ACTION AND PRODUCES A NUMERICAL CONTROL COMMAND * MUST TAKE CONTROL ACTIONS FROM MULTIPLE MEMBERSHIP CLASSES AND PRODUCE ONE VALUE: USE METHOD OF CENTER OF GRAVITY LN h4n SN SP MP LP U PURPOSE: PRODUCE A NUMERICAL CONTROL COMMAND INPUT: FUZZY CONTROL VALUE ~ -- OUTPUT: NUMERICAL CONTROL VALUE

24 Results loo 1hI"min) a w loo li~.(llll") I -- - Process Response with and without Control(solid line : desired exhaustion) (dashed line : actual exhaustion) (dashed-point line : controlled temperature)

25 Results s D"C-PROCESS(~OUr-CONTROL) -.; Process Response with and without Control(solid line : desired exhaustion) (dashed line : actual exhaustion) (dashed-point line : controlled temperature)

26 Adaptive fizzy Logic Control Self-scaling Factor Tuning Scheme Phase Portrait

27 Self-Scaling Factor Tuning Scheme Else K,E+l = K, Else K,c+E1= KZE

28 Self-scaling Factor Tuning Scheme IC:: scaling factor for E at time ti K?~: scaling factor for CE at time ti LUP: length of universe of discourse for E LUDCE: length of universe of discourse for CE 6 and A: convergence coefficients (1 > 6, X > 0) The sign(x) function is defined as 1 if x>o sign(x) = O if x = O -1 if x<o

29 Results I.... I. *.. (.... I T"(min) Process(With_Self_Tuning) Xme(min) Process Response with and without Self-tuning (solid line : desired exhaustion) (dashkd line : actual exhaustion) (dashed-point line : controlled temperature)

30 Self-Learning Scheme Control Rule Identification Vy Fuzzy/ output * Copfroller > Process > Structure of a self-learning Fuzzy Logic Controller If X i, And Yi, Then Zi = XinYi'Zi u(xi nyi) + z = f (P, E, CE)

31 Results Rule Surface -- The Initial -3 Process 0 z I 1 I I 1 The Initial Run Control Rule Surface with (-3:LN) (-2:MN) (-1:SN) (0:ZE) (1:SP) (2:MP) (3:LP) and Process Response (solid line : desired exhaustion) (dashed line : actual exhaustion) (dashed-point line : controlled temperature)

32 Results Rule Surface -- The First Run -3 fime(min). The First Run Control Rule Surface with (-3:LN) (-2:MN) (-1:SN) (0:ZE) (1:SP) (2:MP) (3:LP) and Process Response (solid line : desired exhaustion) (dashed line : actual exhaustion) (dashed-point line : controlled temperature)

33 Results Rule Surface -- The Second Run -3 Process? / x Time(min) The Second Run Control Rule Surface with (-3:LN) (-2:MN) (-1:SN) (0:ZE) (1:WI (2:MP) (3:LP) and Process Response (solid line : desired exhaustion) (dashed line : actual exhaustion) (dashed-point line : controlled temperature)

34 Results Rule Surface -- The Third Run -3 Process Tirne(min). The Third Run Control Rule Surface with (-3:LN) (-2:MN) (-1:SN) (0:ZE) (1:SP) (2:MP) (3:LP) and Process Response (solid line : desired exhaustion) (dashed line : actual exhaustion) (dashed-point line : controlled temperature)

35 Results Rule Surface -- The Tenth Run 3-3 Timc(min) ' The Tenth Run Control Rule Surface with (-3:LN) (-2:MN)(-1:SN) (0:ZE) (1:SP) (2:~) (3:LP) and Process Response (solid line : desired exhaustion) (dashed line : actual exhaustion) (dashed-point line : controlled temperature)

36 Results Rule Surface -- Tho Fifteenth Run -3 Process 0 E- I l I I 1 I c-- _---- * - -. L._._._._._._._._. Jed I I I I I I Timc(min) The Fifteen Run Control Rule Surface with (-3:LN) (-2:MN) (-1:SN) (0:ZE) (1:SP) (2:MP) (3:LP) and Process Response (solid line : desired exhaustion) (dashed line : actual exhaustion) (dashed-point line : controlled temperature)

37 fizzy Logic Control for MIMO Systems Rij: Rulebase between ith Input and jth Output ej,aej: Error and Error Change of jth Output

38 Fuzzy Logic Control for MIMO Systems where Min Subject to : L < I(tn) < H - fl F= f2 I= L, H are Constraints of Control Inputs P, Q: Weighting Matrices

39 Results Process I I I I CO 0 0 I Q) n N Tim e( min) Process Response (solid line : dye component one) (dashed line : dye component two) (dashed-point line : dye component three) ~ --

40 Results Process Response

41 Results 0 7 \ Control-Of-Temperature I I I I o m W f! 3 Y t- e P) P 0 Fl Tim e( min) Temperature Control

42 Results Con trol-ocdye-dosing 7 I I I I I I 1 I Time( min) Dye Dosing Control

43 Results Process I I I I I 4 f I I I I Time(min) Process Response (solid line : dye component one) (dashed line : dye component two) (dashed-point line : dye component three) -- -

44 Results Process Response

45 Results 0 - Con trol-of-tempera ture I I I I 0 a3 0 cu Time(min) Temperature Control

46 Results Control-Of-Dye-Dosing I I I I 1 0 J 1 I, I I I I Tim e( min) 200 Dye Dosing Control

47 Concluding Remarks: * Fuzzy Logic Control uses humanistic approach to define control rule base * Fuzzy logic control does not require complete knowledge of the process being controlled * Several parameters can be used to improve performance of FLC: scaling factor, adaptive control rule base, extension to MlMO case, selection of membership function, selection of membership ranges, defuzzifier function * Have sho-wn through simulation results that adaptive FLC can be applied to the qeing process Future Activities: * Experimental Implementation * FLC Analysis relationship to other control strategies - stability -- and convergence analysis

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