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Diagnosis of oscillations in process control loops
16th European Symposium on Computer Aided Process Engineering and 9th International Symposium on Process Systems Engineering W. Marquardt, C. Pantelides (Editors) © 2006 Published by Elsevier B.V.
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Diagnosis of oscillations in process control loops Yoshiyuki Yamashita ^ ^Department of Chemical Engineering, Tohoku University, 6-6-07 Aramaki Aoba, Sendai 980-8579, Japan Abstract Valve stiction is the most common cause of the problem on control loops in process industry. To improve the productivity and quality, industrial engineers demand a tool to facilitate loop monitoring. This paper present a new algorithm to detect valve stiction for diagnosis of oscillation in control loops. The method is for the level control loops and based on a statistical analysis in phase plane by using controller output and level signals, those are available for all the level control loops. The usefulness of the method are successfully demonstrated on a simulation data set and several industrial data sets. Keywords: fault diagnosis, process monitoring, control performance 1. INTRODUCTION Among many control loops in a process plant, quite a few loops have oscillatory behavior. Notwithstanding, it is usually too time consuming and sometimes too difficult to maintain all the control loops in proper working order. Therefore, to improve the productivity and quality, industrial engineers demand a tool to facilitate loop monitoring. These oscillations can be caused by improper controller tuning, external disturbances, and so-called stiction in a control valve. For example, more than 20% of all control loops in paper mills reportedly oscillate because of valve stiction. Detection of oscillations in process control loops have been investigated by many researchers. The next step of the loop monitoring is to indicate likely causes of the oscillations. Several methods have been reported to identify the causes. When the valve position or the corresponding flow rate is available, plot of controller output v.s. valve position or corresponding flow rate represents characteristic pattern for oscillatory loops caused by valve stiction and therefore this pattern can be used for the identification of the cause [1]. Unfortunately the valve position or the corresponding flow rate is not often measured in real plant. Therefore, a method is highly required to detect valve stiction without using this information. Several methods have been proposed for the detection of valve stiction without requiring the valve position. Horch and Isaksson developed a detection method based on the probabiUty density function of the second derivative of the process output [2]. Singhal and Salsbury proposed a simple method to check if the shape of the process output signal is similar to
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Y. Yamashita
Controller Output
(b) Figure 1. IVpical plots for a valve stiction loop
\ -\9
^ (a)
(b)
Figure 2. Typical plots for a non-stiction loop
sinusoidal or not [4] . Rossi and Scali used square sum of the differences between typical oscillatory patterns and the observed data [5]. In this study, a method is proposed to detect stiction in a control loop by using only information of controller input and output. As the result of investigation on the behavior of the controller input and output in polar coordinate, the distribution of the sampling points was found to be lopsided for the oscillation caused by valve stiction, although it is almost symmetrical for the loop with bad tuning. This characteristics can be well displayed in an angle histogram of the controller input and output. Moreover an index to detect stiction is developed based on the skewness of the histogram. The method is illustrated with several level control loops of simulation and industrial plant. 2. Method 2.1. Observation Atfirst,oscillating data in level control loops are visually inspected. If the valve position or correspondingflowrateis available, it is relatively easy to find valve stiction because the plot of controller output and the valve position shows typical parallelogram shape as shown in Fig. 1(a). Automated method for detection of stiction based on these variables is also proposed [1]. Figure 2 shows plots of another oscillatory control loop, which does not include stiction. In this loop, corresponding input-output plots does not show parallelogram shape (Fig 2(b)). However, valve position or correspondingflowrateis not always measured in the industrial plant. Even if the valve position is not available, controller output and controlled measurement variable are always available. Comparing the Figures 1(b) and 2(b), it may be difficult to find typical characteristics for stiction in a plot between controller output and level signal. To find characteristic features for stiction, other plots are investigated. Let the gravity
Diagnosis of Oscillations in Process Control Loops
^
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'•^•^.
Si
- 4 - 3 - 2 - 1 0 1 2 3 4
(a) stiction
(b) non-stiction
Figure 3. Plots converted in polar coordinate
center of the controller-output and the level plots be the new origin, the original plots can be converted into polar coordinate. Figure 3 shows the polar plots of the two loops. By comparing these twofigures,distributions of the sampling points is found to be lopsided for the oscillation caused by valve stiction, although it was almost symmetrical for the loop with bad tuning. This characteristics can be well displayed in an angle histogram of the controller input and output. Fast motion in the slip jump probably causes this uneven distribution of stiction pattern. 2.2. Algorithm Based on the above mentioned observation, a method to identify stiction is developed. The following steps shows the details of the process. 1. Normalization: Let A?i and A^ be each time differences of controller output {u) and tank level {y) during the sampling period. Both of the values are normalized between zero and one by using their mean and standard deviation. 2. Polar conversion: Plots in /S.u v.s. Ay plane are converted in polar coordinate r v.s. 6 as r = v^Au2~+~Ay2, i9 = tan"^(A2//A'?x)
(1) (2)
3. Histogram: To clarify the distribution of the sampling points in polar coordinate, number of samplings are counted for each interval of 6, which is divided into 100 intervals. If the histogram is symmetric, the loop oscillate because of poor tuning. If it is asymmetric, the loop will have stiction. The same information can also be visually shown in rose plot, which is a polar plot showing the distribution of values grouped according to their numeric range. Rose plot is useful to find asymmetrical distribution by human observation. Since the trajectory in polar coordinate is periodic in the 6 direction it is possible to fold into half plane and get 0: if(9>0, e if(9<0.
(3)
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Y. Yamashita
4. Stiction Index: To represent an asymmetrical distribution in the half plane polar histogram, an index based on the skewness is defined:
h=
1
N-l
(4)
where (f)i is the count of each class interval, 0 and a are the mean and the standard deviation of (t)i. If this index shows relatively large value, the loop will have valve stiction. 3. Case Studies 3.1. Simulation Data The method first applied to simulation data sets, which are the closed loop response of a PI controller combined with a stiction model [3]. Two types of simulation data were prepared corresponding to the behavior of the normal and stiction. Input-output behavior of the data are shown in Figure 4. For these two data sets, histogram in polar coordinates were calculated as Figure 5. Although both of the figures may seem similar, by concentrating attention on both sides of the peaks, one can find that the stiction case shows higher asymmetry than the normal case. Calculated stiction index for normal case is 0.195 and that for stiction case is 0.401. This result shows that this index have larger value for stiction case than normal case. It indicates the possibility of the usage of this index for detecting a stiction.
- 2 - 1 0 1 Controller Output
Controller Output
(a) normal (b) stiction Figure 4. Input and output of the controller (simulation data)
(a) normal (b) stiction Figure 5. Histogram in the polar coordinate (simulation data)
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Diagnosis of Oscillations in Process Control Loops
Controller Output
(a) Case 1 (a) Case 2 (a) Case 3 (b) Case 4 Figure 6. Controller output v.s. Level of the industrial data sets
1,0
-0.5
0.0
0.5
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(a) Case 1
1.0
-1.0
-0.5
0,0
9/re
0.5
1.0
-1.0
-0.5
0.0
0.5
1.0
e/jt
(b) Case 2 (c) Case 3 Figure 7. Polar plots of industrial data sets
-1.0
-0.5
0.0
0.5
1.0
e/7c
(d) Case 4
3.2. Industrial Data This section presents an evaluation of the method using four industrial data sets [1], Each of the data sets is of level control loop and has 1440 samples at 1-min intervals. Figure 6 shows plots of controller output and controlled level signals. All the data are normalized divided by its standard deviation, respectively. In this figure, only the Case 1 is of stiction loop. Case 2 and 3 oscillate because of bad tuning. Case 4 is considered to be normal. Figure 7 shows the plots in polar coordinate. Figure 8 shows histogram of the polar plots. This figure is also represented in the angle histogram as shown in Fig 9. These two histograms represent the same information in different forms. Case 1 shows two peaks in this histogram and these shapes are clearly asymmetrical, which is the typical characteristics for valve stiction. Case 2 did not show sharp peaks, which are not for stiction. The histogram for Case 3 data did not show clear characteristics but the corresponding angle histogram shows symmetrical shape and indicates that the loop does not have stiction. The histogram for Case 4 shows relatively clear peaks but their shapes are symmetrical, which are not for typical stiction characteristics. From these results, calculated values of the proposed stiction index are summarised in Table 1. The index showed largest value for the stiction loop. It indicates that this stiction index can be used as an measure to detect stiction. Table 1 Stiction Index for the industrial data sets Data Set Case 1 (Stiction) 0.374 Case 2 (Bad tuning) 0.050 Case 3 (Bad tuning) 0.271 Case 4 (Normal) 0.124
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Y. Yamashita
I •2 10
(a) Case 1
0.01
o
0.00
< -0.01 -0.02 0.00 0.02 AController Output
(a) Case 1
(d) Case 4
(b) Case 2 (c) Case 3 Figure 8. Histograms for industrial data sets
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^
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^ % .
-0.01 0.00 0.01 AController Output
0.00
-0.02 -0.02 0.00 0.02 AController Output
(b) Case 2 (c) Case 3 Figure 9. Angle histograms of industrial data sets
w w
•
•
-0.02 0.00 0.02 AController Output
(d) Case 4
4. Conclusion To identify the root cause of an oscillating level control loop, polar plots of controller output and level signal are investigated. Based on the visual inspection of the plots, a method for diagnosing valve stiction for level control loop was developed. The method is based on a statistical analysis of the polar plots. The proposed index showed good performance in detecting stiction on a simulation data set and several industrial data sets. Acknowledgements The author acknowledge to Mr. Toshio Miura for his help in preparing the manuscript. Mr. H. Kugemoto is acknowledged for providing the industrial data set. Dr. M. Kano and Mr. H. Maruta are acknowledged for the contribution of simulation data.
REFERENCES [1] [2] [3] [4] [5] [6]
Y. Yamashita, Control Engineering Practice, 14 (2006) 503. A. Horch and A.J. Isaksson, European Control Conference, Porto, Portugal (2001) 1327. M. Kano, M. Maruta, K. Shimizu and H. Kugemoto, DYC0PS7, Cambridge, USA (2004). A. Singhal and T.I. Salsbury, J. Process Control, 15 (2005) 371. M. Rossi and C. ScaH, J. Process Control, 15 (2005) 505. M.A.A.S. Choudhury, N.F. Thomhill and S.L. Shah, Control Engineering Practice, 13 (2005)641.
1605
Diagnosis of oscillations in process control loops Yoshiyuki Yamashita ^ ^Department of Chemical Engineering, Tohoku University, 6-6-07 Aramaki Aoba, Sendai 980-8579, Japan Abstract Valve stiction is the most common cause of the problem on control loops in process industry. To improve the productivity and quality, industrial engineers demand a tool to facilitate loop monitoring. This paper present a new algorithm to detect valve stiction for diagnosis of oscillation in control loops. The method is for the level control loops and based on a statistical analysis in phase plane by using controller output and level signals, those are available for all the level control loops. The usefulness of the method are successfully demonstrated on a simulation data set and several industrial data sets. Keywords: fault diagnosis, process monitoring, control performance 1. INTRODUCTION Among many control loops in a process plant, quite a few loops have oscillatory behavior. Notwithstanding, it is usually too time consuming and sometimes too difficult to maintain all the control loops in proper working order. Therefore, to improve the productivity and quality, industrial engineers demand a tool to facilitate loop monitoring. These oscillations can be caused by improper controller tuning, external disturbances, and so-called stiction in a control valve. For example, more than 20% of all control loops in paper mills reportedly oscillate because of valve stiction. Detection of oscillations in process control loops have been investigated by many researchers. The next step of the loop monitoring is to indicate likely causes of the oscillations. Several methods have been reported to identify the causes. When the valve position or the corresponding flow rate is available, plot of controller output v.s. valve position or corresponding flow rate represents characteristic pattern for oscillatory loops caused by valve stiction and therefore this pattern can be used for the identification of the cause [1]. Unfortunately the valve position or the corresponding flow rate is not often measured in real plant. Therefore, a method is highly required to detect valve stiction without using this information. Several methods have been proposed for the detection of valve stiction without requiring the valve position. Horch and Isaksson developed a detection method based on the probabiUty density function of the second derivative of the process output [2]. Singhal and Salsbury proposed a simple method to check if the shape of the process output signal is similar to
1606
Y. Yamashita
Controller Output
(b) Figure 1. IVpical plots for a valve stiction loop
\ -\9
^ (a)
(b)
Figure 2. Typical plots for a non-stiction loop
sinusoidal or not [4] . Rossi and Scali used square sum of the differences between typical oscillatory patterns and the observed data [5]. In this study, a method is proposed to detect stiction in a control loop by using only information of controller input and output. As the result of investigation on the behavior of the controller input and output in polar coordinate, the distribution of the sampling points was found to be lopsided for the oscillation caused by valve stiction, although it is almost symmetrical for the loop with bad tuning. This characteristics can be well displayed in an angle histogram of the controller input and output. Moreover an index to detect stiction is developed based on the skewness of the histogram. The method is illustrated with several level control loops of simulation and industrial plant. 2. Method 2.1. Observation Atfirst,oscillating data in level control loops are visually inspected. If the valve position or correspondingflowrateis available, it is relatively easy to find valve stiction because the plot of controller output and the valve position shows typical parallelogram shape as shown in Fig. 1(a). Automated method for detection of stiction based on these variables is also proposed [1]. Figure 2 shows plots of another oscillatory control loop, which does not include stiction. In this loop, corresponding input-output plots does not show parallelogram shape (Fig 2(b)). However, valve position or correspondingflowrateis not always measured in the industrial plant. Even if the valve position is not available, controller output and controlled measurement variable are always available. Comparing the Figures 1(b) and 2(b), it may be difficult to find typical characteristics for stiction in a plot between controller output and level signal. To find characteristic features for stiction, other plots are investigated. Let the gravity
Diagnosis of Oscillations in Process Control Loops
^
1607
'•^•^.
Si
- 4 - 3 - 2 - 1 0 1 2 3 4
(a) stiction
(b) non-stiction
Figure 3. Plots converted in polar coordinate
center of the controller-output and the level plots be the new origin, the original plots can be converted into polar coordinate. Figure 3 shows the polar plots of the two loops. By comparing these twofigures,distributions of the sampling points is found to be lopsided for the oscillation caused by valve stiction, although it was almost symmetrical for the loop with bad tuning. This characteristics can be well displayed in an angle histogram of the controller input and output. Fast motion in the slip jump probably causes this uneven distribution of stiction pattern. 2.2. Algorithm Based on the above mentioned observation, a method to identify stiction is developed. The following steps shows the details of the process. 1. Normalization: Let A?i and A^ be each time differences of controller output {u) and tank level {y) during the sampling period. Both of the values are normalized between zero and one by using their mean and standard deviation. 2. Polar conversion: Plots in /S.u v.s. Ay plane are converted in polar coordinate r v.s. 6 as r = v^Au2~+~Ay2, i9 = tan"^(A2//A'?x)
(1) (2)
3. Histogram: To clarify the distribution of the sampling points in polar coordinate, number of samplings are counted for each interval of 6, which is divided into 100 intervals. If the histogram is symmetric, the loop oscillate because of poor tuning. If it is asymmetric, the loop will have stiction. The same information can also be visually shown in rose plot, which is a polar plot showing the distribution of values grouped according to their numeric range. Rose plot is useful to find asymmetrical distribution by human observation. Since the trajectory in polar coordinate is periodic in the 6 direction it is possible to fold into half plane and get 0: if(9>0, e if(9<0.
(3)
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Y. Yamashita
4. Stiction Index: To represent an asymmetrical distribution in the half plane polar histogram, an index based on the skewness is defined:
h=
1
N-l
(4)
where (f)i is the count of each class interval, 0 and a are the mean and the standard deviation of (t)i. If this index shows relatively large value, the loop will have valve stiction. 3. Case Studies 3.1. Simulation Data The method first applied to simulation data sets, which are the closed loop response of a PI controller combined with a stiction model [3]. Two types of simulation data were prepared corresponding to the behavior of the normal and stiction. Input-output behavior of the data are shown in Figure 4. For these two data sets, histogram in polar coordinates were calculated as Figure 5. Although both of the figures may seem similar, by concentrating attention on both sides of the peaks, one can find that the stiction case shows higher asymmetry than the normal case. Calculated stiction index for normal case is 0.195 and that for stiction case is 0.401. This result shows that this index have larger value for stiction case than normal case. It indicates the possibility of the usage of this index for detecting a stiction.
- 2 - 1 0 1 Controller Output
Controller Output
(a) normal (b) stiction Figure 4. Input and output of the controller (simulation data)
(a) normal (b) stiction Figure 5. Histogram in the polar coordinate (simulation data)
1609
Diagnosis of Oscillations in Process Control Loops
Controller Output
(a) Case 1 (a) Case 2 (a) Case 3 (b) Case 4 Figure 6. Controller output v.s. Level of the industrial data sets
1,0
-0.5
0.0
0.5
e/7t
(a) Case 1
1.0
-1.0
-0.5
0,0
9/re
0.5
1.0
-1.0
-0.5
0.0
0.5
1.0
e/jt
(b) Case 2 (c) Case 3 Figure 7. Polar plots of industrial data sets
-1.0
-0.5
0.0
0.5
1.0
e/7c
(d) Case 4
3.2. Industrial Data This section presents an evaluation of the method using four industrial data sets [1], Each of the data sets is of level control loop and has 1440 samples at 1-min intervals. Figure 6 shows plots of controller output and controlled level signals. All the data are normalized divided by its standard deviation, respectively. In this figure, only the Case 1 is of stiction loop. Case 2 and 3 oscillate because of bad tuning. Case 4 is considered to be normal. Figure 7 shows the plots in polar coordinate. Figure 8 shows histogram of the polar plots. This figure is also represented in the angle histogram as shown in Fig 9. These two histograms represent the same information in different forms. Case 1 shows two peaks in this histogram and these shapes are clearly asymmetrical, which is the typical characteristics for valve stiction. Case 2 did not show sharp peaks, which are not for stiction. The histogram for Case 3 data did not show clear characteristics but the corresponding angle histogram shows symmetrical shape and indicates that the loop does not have stiction. The histogram for Case 4 shows relatively clear peaks but their shapes are symmetrical, which are not for typical stiction characteristics. From these results, calculated values of the proposed stiction index are summarised in Table 1. The index showed largest value for the stiction loop. It indicates that this stiction index can be used as an measure to detect stiction. Table 1 Stiction Index for the industrial data sets Data Set Case 1 (Stiction) 0.374 Case 2 (Bad tuning) 0.050 Case 3 (Bad tuning) 0.271 Case 4 (Normal) 0.124
1610
Y. Yamashita
I •2 10
(a) Case 1
0.01
o
0.00
< -0.01 -0.02 0.00 0.02 AController Output
(a) Case 1
(d) Case 4
(b) Case 2 (c) Case 3 Figure 8. Histograms for industrial data sets
^
^
'
0.02
Jl# 5
^MK
<
^ % .
-0.01 0.00 0.01 AController Output
0.00
-0.02 -0.02 0.00 0.02 AController Output
(b) Case 2 (c) Case 3 Figure 9. Angle histograms of industrial data sets
w w
•
•
-0.02 0.00 0.02 AController Output
(d) Case 4
4. Conclusion To identify the root cause of an oscillating level control loop, polar plots of controller output and level signal are investigated. Based on the visual inspection of the plots, a method for diagnosing valve stiction for level control loop was developed. The method is based on a statistical analysis of the polar plots. The proposed index showed good performance in detecting stiction on a simulation data set and several industrial data sets. Acknowledgements The author acknowledge to Mr. Toshio Miura for his help in preparing the manuscript. Mr. H. Kugemoto is acknowledged for providing the industrial data set. Dr. M. Kano and Mr. H. Maruta are acknowledged for the contribution of simulation data.
REFERENCES [1] [2] [3] [4] [5] [6]
Y. Yamashita, Control Engineering Practice, 14 (2006) 503. A. Horch and A.J. Isaksson, European Control Conference, Porto, Portugal (2001) 1327. M. Kano, M. Maruta, K. Shimizu and H. Kugemoto, DYC0PS7, Cambridge, USA (2004). A. Singhal and T.I. Salsbury, J. Process Control, 15 (2005) 371. M. Rossi and C. ScaH, J. Process Control, 15 (2005) 505. M.A.A.S. Choudhury, N.F. Thomhill and S.L. Shah, Control Engineering Practice, 13 (2005)641.