Valve Stiction - Definition, Modeling, Detection, Quantification and Compensation

Transcription

1 Valve Stiction - Definition, Modeling, Detection, Quantification and Compensation Dr. M. A. A. Shoukat Choudhury Department of Chemical Engineering Bangladesh University of Engineering & Technology () Dhaka, BANGLADESH

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3 Control Loop Demographics poor tuning 30% well performing 20% valve problems 30% Excellent, 16% Acceptable, 16% Fair, 22% Poor, 10% design problem 20% Open Loop, 36% (Bialkowski, 1992) (Desborough and Miller, 2002) 3

4 Motivation cause oscillation(s) in process variables poor controller performance shorten the life of control valves may lead to process upsets non-uniform end-products more off-spec products larger rejection rates reduced profitability so on... 4

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6 A CONTROL VALVE 6

7 Control Valve Problems Stiction (Static Friction) Saturation Hysteresis Oversized valve Corroded plug/seat Ruptured diaphragm Deadzone so on. 7

8 ISA Terminology Input Instrument Output 8

9 Input - Output Plot of Instruments 9

10 Where is Valve Stiction? Disturbance SP + - CONTROLLER CO / OP VALVE MV PROCESS PV SP Set Point CO Controller Output (also called OP) MV Valve output or valve positioner signal PV Process Variable (Controlled) 10

11 What is Stiction? Stiction = Static Friction Instrument Society of America (ISA)(ANSI/ISA- S ): ``Stiction is the resistance to the start of motion, usually measured as the difference between the driving values required to overcome static friction upscale and downscale''. The definition was first proposed in 1963 in American National Standard C

12 Inside a Valve Stiction Fluid in out 12

13 Stiction in Real Process Industry In process industries, stiction is measured as a certain % of the valve travel or the span of the control signal. For example: 2% stiction means that when valve gets stuck it will start moving only after the cumulative change of its control signal is greater than or equal to 2%. If the range of the control signal is 4 to 20 ma then 2% stiction means a cumulative change of the control signal less than 0.32 ma in magnitude will not be able to move the valve. 13

14 Stiction in a Level Control Loop valve position, mv controller output, op 14

15 Proposed Input Output Plot for Stiction stickband + deadband valve output (mv) A deadband F G D B C slip jump, j stickband s valve input (op) moving phase E 1. Choudhury, M. A. A. S., Nina F. Thornhill and Sirish L. Shah (2005). Modelling valve stiction, 13,

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17 Stiction Models Mechanistic Models Data Driven Models 17

18 Looking Inside a Valve! Stiction Fluid in out 18

19 Mechanistic Model for a Valve M d2 y dt 2 = F a + F r +F f + F p + F i F a = A Pa F r = - k y Disadvantages: 1. Difficult to simulate 2. Need tailoring for each valve because the model needs mass and force terms. 3. Friction force term is complicated F f = -F c sgn(v) - v F v if v >= 0 -(F a + F r ) if v = 0 and Fa + Fr <= Fs -F s sgn(f a + F r ) if v = 0 and Fa + Fr > Fs 19

20 Other Data-Driven Stiction Models One parameter Model by Hagglund 20

21 Basis of Two-Parameter Stiction Model 21

22 Two-parameter Stiction Model 22

23 Various Types of Stiction valve input and valve output (red) valve output vs. valve input linear deadband stiction (undershoot) stiction (no offset) stiction (overshoot) time/s 23

24 Various Types of Stiction J = 0 J < S J = S J > S Pure Deadband Stiction (Undershoot): Valve output can never reach the valve input Stiction (Stick-Slip): Valve output reaches the valve input Stiction (Overshoot): Valve output crosses the valve input 24

25 Simulation using Two Parameter Stiction Model deadband stiction stiction stiction 25

26 Concentration Loop Obtained from Eborn & Olsson (1995) and Horch & Issakson (1998) Process: G( s) = 3 10 e s 10 s + 1 Controller: 1 C( s) = s 26

27 Comparison of Closed Loop Behavior mv (red) and op (black) mv vs. op mv (red) and op (black) mv vs. op stiction (undershoot) stiction (no offset) stiction (overshoot) time/s Data-driven model time/s Mechanistic model 27

28 Closed Loop PV-OP Plot pv (red) and op (black) pv vs. op stiction (undershoot) stiction (no offset) stiction (overshoot) time/s 28

29 Other Data-Driven Stiction Models Manabu Kano Model same as the two parameter model, notations are different. Peter He Model same as the one parameter model 29

30 Assymetric Stiction Model valve output (mv) kd JD JD ku SD moving phase JU JU slip jump, JU SU valve input (op) Six parameters SU, SD, JU, JD, kd, ku 30

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32 A CHEMICAL PLANT 32

33 Objectives data data matrix Poor performance? diagnosis Why? poor controller tuning oscillatory disturbances nonlinearities Other causes 33

34 Nonlinearities nonlinearities process nonlinearities valve nonlinearities Static Friction stiction corroded valve plug/seat oversized valve saturation deadzone so on. 34

35 What is Nonlinearity? X1 S Y1 X2 S Y2 X1+X2 S Y a X1 S Z If Y=Y1+Y2 and Z=a Y1 S is Nonlinear 35

36 A Simple Example X1 X2 Squaring function Squaring function Y 1 = X 1 2 Y 2 =X 2 2 Squaring X 1 +X 2 Y = X function 12 + X X 1 X 2 Squaring a X 1 Z = a 2 X 2 function 1 Y=Y 1 +Y 2 and Z=a Y 1 S is NON-LINEAR 36

37 Second Order Statistics (SOS) 1 st moment, m 1 = μ = E(x) It represents the mean of the data Number of occurence Histogram X nd moment, m 2 (k)= E {x(n) x(n+k)} It represents the spread of the distribution pdf x std = 22 std std = 1.5 std = 1 37

38 Fourier Transform 38

39 DFT 39

40 Data Representation Time-domain trends Frequency Domain (Power Spectrum) P(f)=DFT {m 2 (k)}= E[X(f) X(f) * ] Z 1 = sin(2*π*0.05*t) + Noise 1 1 Z 2 = cos(2*π*0.3*t) + Noise Z 3 = 0.5*Z *Z M. A. A. Shoukat Choudhury Samples KFUPM, Nov, 2008 Frequency (cycles/time)

41 Why Look at Higher Moments error error signal to controller time 5000 magnitude of error Histogram of error signal no. of occurence Real flow loop data Almost Gaussian distribution Second order statistics are sufficient to describe the distribution error error signal to controller time magnitude of error Histogram of error signal no. of occurence Real flow loop data Skewed distribution Needs higher moments to characterize the distribution for further analysis of this data 41

42 Double Fourier transform F( u, v) = f ( x, y) e i( ux+ vy) dxdy = f ( x, y)cos( ux R(F) + ii(f) + vy) dxdy + i f ( x, y)sin( ux + vy) dxdy = 2 2 often described by magnitude ( R ( F) + I ( F) ) I( F) and phase ( ) arctan( ) R( F) In the discrete case with values f kl of f(x,y) at points (kw,lh) for k= 1..M-1, l= 0..N-1 M 1 N 1 k m l n πi( + ) M N Fmn = fkle k = 0 l= 0 42

43 Stiction Detection Problem Formulation Disturbance SP + - CONTROLLER CO / OP VALVE MV PROCESS PV SP Set Point CO Controller Output (also called OP) MV Valve output or valve positioner signal PV Process Variable (Controlled) 43

44 Data from Industrial Control loops x 10 4 PV and SP PV SP PV and SP PV SP CO CO CO CO sampling instants sampling instants A flow loop in a refinery A level loop in a power plant 44

45 Stiction Detection Methods Horch s cross-corelation method (Horch, 2000) Yamashita (2006) pattern based method Srinivasan et al. (2005 a,b) Qualitative Approach and Hammerstein model method Singhal and Salsbury (2005) - Aria ratio method Rossi & Scali (2005) relay method Surrogate data based method (Nina Thornhill) Choudhury et al. (2006) bicoherence based method Choudhury et al. (2008) Hammerstein model approach Jelali (2008), global search algorithm Scali and Ghelardoni (2008), qualitative shape based valve stiction for flow loops, CEP, 16(12) Chitralekha, Shah, prakash (2010), stiction detection and quantification by the method of unknown input estimation, JPC, 20(2) Zabiri and Ramasamy (2009), NLPCA as diagnostic tool for valve stiction, JPC, 19(8) Ivan and Lakhms (2009), A new unified approach to valve stiction, I&ECR, 48(7) 45

46 It is seldom ONE single problem stiction disturbance tuning nonlinearity 46

47 Time Series Nonlinearity Bispectrum: Δ B(f 1, f 2 ) = E[X(f 1 ) X(f 2 ) X(f 1 + f 2 ) * ] - measures the nonlinear interactions between different frequency components of a signal. Bispectrum is normalized to give a new measure called squared Bicoherence. Its magnitude varies from 0 to 1. bic 2 (f 1,f 2 ) = B(f 1, f 2 ) 2 E X(f 1 ) X(f 2 ) 2 E X(f 1 +f 2 ) 2 47

48 Time Series Nonlinearity (cont d) A discrete stationary time series, x(n), is said to be linear if it can be represented by x( n) = s= 0 h( s) e( n Where, e(s) is a sequence of independent identically distributed random variable with E[e(s)]=0, E[e 2 (s)]= σ e2, and E[e 3 (s)]=μ 3 s) It can be shown that for any linear signal, the squared bicoherence is μ 2 3 bic 2 (f 1, f 2 ) = σ e 6 = constant 48

49 Bicoherence of a linear and nonlinear Signal 49

50 Test of Non-linearity (cont d) Choudhury, M. A. A. S., Sirish L. Shah and Nina F. Thornhill (2004). Diagnosis of poor control loop performance using higher order statistics. NGI = bic 2 - bic 2 crit, NLI = bic 2 max - ( bic σ bic2 ) Automatica, 40(10), Based on the squared bicoherence, Non-Gaussianity Index (NGI) and Nonlinearity Index (NLI) have been developed. Critical Values of bic 2 crit is determined at 95% or 99% confidence interval of the squared bicoherence NGI <= 0 NGI>0, NLI=0 NGI>0, NLI>0 Gaussian Linear Non-Gaussian Linear Non-Gaussian Nonlinear Frequency independent Frequency dependent 50

51 Flow Control Loop in a Refinery (revisited) PV and SP x PV SP CO sampling instants CO NGI = 0.02 and NLI = 0.55 Loop is Nonlinear Assumptions: 1. The process is locally linear in the current operating region 2. Disturbances entering the loop are linear 51

52 Pattern of Stiction in PV-OP Plot apparent stiction = maximum width of the cycles in pv-op plot PV PV OP Hagglund, 1995 Rengaswamy, et. al, OP

53 Flow Control Loop in a Refinery (cont d) x 104 PV-OP plot x PV f PV OP OP f One possible solution is filtering. We have used frequency domain band pass Weiner Filter. The filter boundaries can be obtained from the significant peaks of the bicoherence plot For this example : [f l f h ] = [ ] 54

54 Quantification of Apparent Stiction x PV P a b α Q OP 2a b Apparent Stiction=PQ = ( a sin α + b cos α) = 0.35 %

55 Diagnosis of Poor Control Loop Performance Poorly performing control loop data (SP, PV, OP) no Calculate NGI (use sp-pv) NGI > 0? yes Gaussian, Linear Non-Gaussian Calculate NLI Possible causes: 1. linear external oscillation Non-Gaussian, no yes NLI > 0? 2. tightly tuned controller Linear 3. and so on Nonlinear Filter PV and OP Apparent Stiction % (unit of OP) Fitted Ellipse/ Fuzzy C-means Clustering yes Elliptic loop in PV f OP f plot? no Valve Problems other than Stiction 56

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57 Level Control Loop (revisited) This is a level control loop which controls the level of condensate in the outlet of a turbine in a power plant by manipulating the flow rate of the liquid condensate. PV and SP PV SP CO CO sampling instants NGI = Non-linearity is not a cause for oscillation(s) 58

58 Level Control of Turbine Condensate This is a level control loop which controls valve characteristics the level of condensate in the outlet of a turbine 74 in a power plant by manipulating the flow rate of the liquid condensate. PV and SP valve position OP PV SP sampling 400 instants CO 66 NGI = 0.04 NLI = 0.61 [f f l h ] = [ ] Apparent Stiction 11% PV f OP f 11 % a= 7.75, b= 0.55, α = 4.0 Apparent Stiction 11% controller output 59

59 Industrial Loop Analysis 60

60 Stiction Compensation Repair the valve Use a knocker in the control algorithm (Hagglund, 2002) Increase the proportional controller gain, K Remove the integral time constant, or use a large value of integral time constant Use the derivative component 61

61 Summary Definition of Stiction is discussed Data Driven Model of Stiction has been presented Two indices, NGI and NLI, for detecting nonlinearities in control loop have been developed and applied successfully to simulated as well as industrial data. Filtered pv-op characteristic plots are useful for diagnosis of non-linearities. Ellipse fitting technique has been demonstrated to be successful in automatically quantifying the amount of stiction. Methods for Stiction Compensation are discussed. 62

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63 Questions? 65