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Fault Detection in a Control Loop
Copyright @IFAC Fault Detection, Supervision and Safety for Technical Processes, Espoo, Finland, 1994
FAULT DETECTION IN A CONTROL LOOP I. MAIRET, M. ROBERT, T. CECCHIN and C. HUMBERT Centre de Recherche en Automatique de Nancy, CNRS URA 821, Universite de Nancy I, CRAN-ESSTIN. Rue Jean Lamour. 54500 Vandreuvre France
Abstract. This paper deals with a fault detection method applied to a control loop containing a non-linear actuator. In order to detect failures on the actuator. the sensor or the process itself. only three variables are available: the set-point. the measurement and the controller output. With the use of a static and a dynamical model of the system it is nevertheless possible to detect failures . To improve the quality of detection. a fuzzy Cmean algorithm is proposed to calculate the model parameters. The proposed method has been applied to a flow control loop containing a pneumatic valve. Key Words. Failure detection; sensor failures; closed-loop systems; non-linear systems; actuators; valves; PID control; fuzzy systems
This paper is organised as follows. In section 2. the considered loop and the different kinds of system failures are described and a system model which can be used in a detection framework is achieved. Section 3 deals with the fault detection problem. First. a general strategy for fault detection is presented and some results are shown. Then. a fuzzy C-means algorithm is proposed to emphasise the relevance of parameters used by the model. Finally. the conclusion of the section 4 sums up the advantages of the developed strategy.
1. INTRODUCTION Numerous methods for fault diagnosis using analytical redundancy have been proposed since more than two decades (Willsky, 1976; Isermann, 1984; Frank. 1990). Generally. they use a mathematical model or some relationships. linking inputs and outputs variables of the whole process. This global approach needs a great knowledge of the considered system. So. if this model is not available. it is difficult to detect failures on the basic control loops of the process.
2. THE CONTROL LOOP
In this paper. a local approach limited to the diagnosis of a control loop with the help of the three basic variables: the measurement. the command and the set-point is addressed. The aim is to propose a simple method which can be applied. at an industrial point of view. on a non-linear system. Indeed. in many applications. the open loop system is nonlinear. then it is necessary to consider some related methods. Our purpose consists in developing an algorithm for failure detection that can be implemented in the actuator. in the sensor or in the controller so that they can be considered as "intelligent components" (Bayart et al.. 1992). We consider that fault detection can be a preliminary step of maintenance. That is. if we can detect a very low fault. we can change or repair the defective element before the critical effects appear on the process. An application is given with a flow control loop.
2.1 . Description of the Loop Let us consider a flow control loop (see Fig. 1). where three variables are only available for fault detection: the set point Qsp. the flow measurement Q. the controller output U.
Controller
Qsp ....+------,
Q ....---..., ~----~
Fig. 1. Flow control loop 105
~------------~
To illustrate this inventory, Fig. 2 shows the effect of a sensor drift, without change of the set-point, dn the behaviour of the process variables Q and U. Due to the closed-loop structure, the effect of the fault is compensated and the failure could not be detected by simple ways.
The controller is a PID-controller and the flow sensor is a classical differential pressure sensor. The actuator has two components: an electro-pneumatic converter and a pneumatic valve . The non-linear behaviour comes from the pneumatic valve which presents hysteresis and varying response time , depending of the chosen functioning point. The open-loop system is then composed of the set (actuator + water pipe between actuator and sensor + sensor).
mode\ljn~
2.3. Process
Making a detection supposes the use of a model which represents the normal behaviour of the system. Considering an industrial point of view , this model must be easy to obtain. As far as our application is concerned, the non-linear actuator leads us to consider two kinds of model, a static one and a dynamical one (see Fig 3).
2.2. Failures inventory Normally, the first step before the determination of a specific diagnosis method consists in making a census of failures which are able to append. Table I shows the real faults which have been applied to the control loop: in this table, the sign "+" means that the corresponding fault has been realised. Notice that our study is not concerned by controller faults . Table 1 Census of the realised faults
Bias, gain error Drift
Sensor
Actuator
+ +
+ + +
Pneumatic supply Leak
+
Interference
.:::
.
'1:
'0
0
'"c
11)
en
;2~ 0
ti:
<'
S
:; c.. :;
.. 0
~
ec 0
In a first step, to take into account these characteristics, we use a simple method which consists in determining three areas where the slopes are different. As it will be mentioned in section 3, the accuracy of the calculus of the initial values of these slopes must be improved.
~------------1 lOO
0
::::
Static modeI1in~. According to Fig. 4 we distinguish two kinds of non linearity: - a saturation which involves a complete opening of the valve under a limit value of the controller signal and a non opening of the valve over a limit value, - an hysteresis which implies that for the same controller output signal, the flow will not be necessarily the same and will depend on the sense of variation. Notice also that the slopes of the hysteresis cycle vary.
+ +
+ +
Locking on
Fig. 3. Open loop system modelling
Pipe
400
::~,
600
1000
100
" ,.., , ...
d 4_
lIS
.j
20'
I.,
."
~ I.'
110 0
200
400
600
100
1000
13~-----------------------------
:~~~ 0
200
400
600
100
~ 0
m
ti:
10' IS
., 65
•
,
6
7
•
9 10 11 Il 13 14 15 I' 17 11 19 20
Controller output (mA)
1000
U
Time (Sampling period) Fig. 2. Effect of a sensor drift on variables Q and U
Fig. 4. Hysteresis modelling 106
Dynamical modellinl:. According to our implementation objective. the dynamical of the system is expressed by a first order model with delay. thus the corresponding discrete form is: (1)
Fig. 7. Template geometry
where the coefficient "a" depends on the chosen functioning point caIJed Qi. and of dQ (step of setpoint) as it is shown Fig. 5. 0,9 0,'
'"
3. FAULT DETECTION STRATEGY
+
+ .p-+ +
+
0,1
+
+
0,6 -2,5
·2
-I,S
+
.t+ ++ + -I
-0.5
3.1. Fault detection all:orithm Due to the presence of a non linearity with memory (the hysteresis) classical methods based on, for instance, non-linear observers are not suitable . Moreover, the aim of this work is to provide some simple technique to monitor a control loop. Then, the algorithm for fault detection, taking into account set-point variations is presented Fig. 8.
0,5
0
dQ/Qi
Fig. 5. Coefficient "a" versus dQ
Q.1 The variation of this coefficient "a" has been modeIJed by a two pieces straight line. Another static representation . If we choose to observe the flow measurement versus the controlJer output signal as presented in Fig. 6:
1241
:::
I~L-
12
~
_________________ ___________ ~
12,5
13
13,5
yes ~
Are Meas. into the template?
New template determination
14
Controller output (mA)
yes
no E<
Fig. 6. Measurement flow Q (l/h) versus controlJer output signal U (mA) we notice that: for a given set-point, the controlJer signal varies inside such a "template". the change of set-point is represented by a trajectory linking the two templates corresponding to the two set-points. according to the previous dynamical model.
Emax ?
Fig. 8. The failure detection principle
Two cases are viewed: - during the static phase, if a failure occurs, the functioning point goes out the template. - when a set-point change appears, a test on the prediction error E of the dynamical model , is used to decide if there is fault or not. This test is operational only during dynamical phase, along the trajectory joining the two templates.
The geometry of these templates is defined as folJows (see Fig. 7): - the parameter h represents the acceptable variation of the measurement, around the setpoint value. - the 9 angle and the width I are defined according to the static model characteristics. So, for each set-point value. a particular template must be defined.
107
3.2. Results
order to implement the first step of our procedure (Initial template determination), we try to reproduce the human thought process. The main difficulty consists in choosing the more relevant points, marked with an "x" in Fig. 12, to be considered as templates vertex, in the plane (Q versus U).
To illustrate the previous technique, two examples of failure, namely a sensor bias and an actuator drift are presented Fig. 9 & 10 where continuous lines and the dotted lines respectively represent the template and the evolution due to the fault.
"'I ~I
~:::I be~~ o
tI:
116
12S
liS
end
10S
112~------------------------------J
12
12,S
13
13,5
14
14,5
IS
12
IS,S
13,5
14
14,S
IS
Controller output (mA)
Controller output (mA)
Fig. 12. Templates vertex
Fig. 9. Sensor bias
11.75
11
12,S
12
12.25
12.5
12,75
As proposed by Fitzgerald (1990), a pre-defined sequence of set-point values (see Fig. 13) is applied. It allows to define two areas, surrounding the functioning point. So, three different classes, corresponding to set-point values (110 IIh, 120 lIh, 130 llh), could be pointed up and fuzzy C-means techniques allow to determine if a particular point belongs to one of these classes.
13
Controller output (mA) Fig . 10. Actuator drift
3.3. Fuzzy c-means to improve the performances of detection In order to improve the sensitivity of our method it is very important to determine as good as possible the straight lines representing the non-linearity of the system. The Fig. 11 shows the errors involved by a false computing.
o
" "Real" lines
,, ,
500
1000
ISOO
2000
Time (Sampling period)
Non detection
False alarms Fig. 13. Sequence of opening-closing For each point. the algorithm of fuzzy C-means called also Bezdek's algorithm (Bezdek, 1981) gives us the membership's degree !l of a class as shown Fig . 14.
Computed lines
Fig. 11 . Effects of a false initial positioning
Finally, when the classes are determined, the points which are the extreme values of the classes are considered as templates vertex and a simple linear regression is used to define the needed parameters for static modelling, e, I and h.
The fuzzy logic seems to be a good way to solve this problem because the lines could be positioned with a kind of human sensivity. The human thought process allows to define the vertex of the template, by taking into account a synthetic view of the hysteresis phenomenon . According to Fig. 8, in 108
5. REFERENCES Bayart, M .. Gehin, A.L., Staroswiecki, M. (1992). Fault detection and isolation and mode management in smart actuators. IFAC Symp. on Intelligent Components and Instruments for Control Applications. Malaga. Bezdek. J.c. (1981). Patem recognition with fuzzy objective functions algorithms. Plenum press. Fitzgerald. B. (1990). Control valves: which ones need fixing. Chemical Engineering. Frank, P.M. (1990). Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy - A survey and some new results. Automatica.26. 459-474. Isermann, R. (1984). Process fault detection based on mode ling and estimation methods - A survey. Automatica, 20. 4. 387-404. Willsky, A.S . (1976) . A survey of design methods for failure detection in dynamic systems . Automatica, 12. 601-611.
N
::1.
Time (Sampling period) Fig. 14. Membership's degree Il for the 3 classes (110 lIh, 120 Ilh, 130 lIh)
4. CONCLUSION A very simple and performing way to supervise a control loop has been described. Some experiments have shown that we are able to detect deviations of the order of 1 % of the set point value. Finally we can notice that: - there is no need to add extra sensor or any other equipment which would raise the price of basic elements of a control system, - the running time of the fault detection algorithm allows its setting up in real time. - the method can be adapted to many non-linear process controls. but it is necessary to build a prediction (dynamical) model and to have also idea to model the non-linear part, - the method is available for some functioning points. but the initial positioning of the template must be calculated for each set-point values. This initial calculus step could be compared to a "calibration" phase, in order to adapt our strategy to a particular control loop. At present. the entire fault detection algorithm is set up on a PC. fitted out with an acquisition card, under real-time monitor. The next step of our work consists in implementing all the strategy. including fuzzy C-means calculus on a micro-controller or DSP.
109
FAULT DETECTION IN A CONTROL LOOP I. MAIRET, M. ROBERT, T. CECCHIN and C. HUMBERT Centre de Recherche en Automatique de Nancy, CNRS URA 821, Universite de Nancy I, CRAN-ESSTIN. Rue Jean Lamour. 54500 Vandreuvre France
Abstract. This paper deals with a fault detection method applied to a control loop containing a non-linear actuator. In order to detect failures on the actuator. the sensor or the process itself. only three variables are available: the set-point. the measurement and the controller output. With the use of a static and a dynamical model of the system it is nevertheless possible to detect failures . To improve the quality of detection. a fuzzy Cmean algorithm is proposed to calculate the model parameters. The proposed method has been applied to a flow control loop containing a pneumatic valve. Key Words. Failure detection; sensor failures; closed-loop systems; non-linear systems; actuators; valves; PID control; fuzzy systems
This paper is organised as follows. In section 2. the considered loop and the different kinds of system failures are described and a system model which can be used in a detection framework is achieved. Section 3 deals with the fault detection problem. First. a general strategy for fault detection is presented and some results are shown. Then. a fuzzy C-means algorithm is proposed to emphasise the relevance of parameters used by the model. Finally. the conclusion of the section 4 sums up the advantages of the developed strategy.
1. INTRODUCTION Numerous methods for fault diagnosis using analytical redundancy have been proposed since more than two decades (Willsky, 1976; Isermann, 1984; Frank. 1990). Generally. they use a mathematical model or some relationships. linking inputs and outputs variables of the whole process. This global approach needs a great knowledge of the considered system. So. if this model is not available. it is difficult to detect failures on the basic control loops of the process.
2. THE CONTROL LOOP
In this paper. a local approach limited to the diagnosis of a control loop with the help of the three basic variables: the measurement. the command and the set-point is addressed. The aim is to propose a simple method which can be applied. at an industrial point of view. on a non-linear system. Indeed. in many applications. the open loop system is nonlinear. then it is necessary to consider some related methods. Our purpose consists in developing an algorithm for failure detection that can be implemented in the actuator. in the sensor or in the controller so that they can be considered as "intelligent components" (Bayart et al.. 1992). We consider that fault detection can be a preliminary step of maintenance. That is. if we can detect a very low fault. we can change or repair the defective element before the critical effects appear on the process. An application is given with a flow control loop.
2.1 . Description of the Loop Let us consider a flow control loop (see Fig. 1). where three variables are only available for fault detection: the set point Qsp. the flow measurement Q. the controller output U.
Controller
Qsp ....+------,
Q ....---..., ~----~
Fig. 1. Flow control loop 105
~------------~
To illustrate this inventory, Fig. 2 shows the effect of a sensor drift, without change of the set-point, dn the behaviour of the process variables Q and U. Due to the closed-loop structure, the effect of the fault is compensated and the failure could not be detected by simple ways.
The controller is a PID-controller and the flow sensor is a classical differential pressure sensor. The actuator has two components: an electro-pneumatic converter and a pneumatic valve . The non-linear behaviour comes from the pneumatic valve which presents hysteresis and varying response time , depending of the chosen functioning point. The open-loop system is then composed of the set (actuator + water pipe between actuator and sensor + sensor).
mode\ljn~
2.3. Process
Making a detection supposes the use of a model which represents the normal behaviour of the system. Considering an industrial point of view , this model must be easy to obtain. As far as our application is concerned, the non-linear actuator leads us to consider two kinds of model, a static one and a dynamical one (see Fig 3).
2.2. Failures inventory Normally, the first step before the determination of a specific diagnosis method consists in making a census of failures which are able to append. Table I shows the real faults which have been applied to the control loop: in this table, the sign "+" means that the corresponding fault has been realised. Notice that our study is not concerned by controller faults . Table 1 Census of the realised faults
Bias, gain error Drift
Sensor
Actuator
+ +
+ + +
Pneumatic supply Leak
+
Interference
.:::
.
'1:
'0
0
'"c
11)
en
;2~ 0
ti:
<'
S
:; c.. :;
.. 0
~
ec 0
In a first step, to take into account these characteristics, we use a simple method which consists in determining three areas where the slopes are different. As it will be mentioned in section 3, the accuracy of the calculus of the initial values of these slopes must be improved.
~------------1 lOO
0
::::
Static modeI1in~. According to Fig. 4 we distinguish two kinds of non linearity: - a saturation which involves a complete opening of the valve under a limit value of the controller signal and a non opening of the valve over a limit value, - an hysteresis which implies that for the same controller output signal, the flow will not be necessarily the same and will depend on the sense of variation. Notice also that the slopes of the hysteresis cycle vary.
+ +
+ +
Locking on
Fig. 3. Open loop system modelling
Pipe
400
::~,
600
1000
100
" ,.., , ...
d 4_
lIS
.j
20'
I.,
."
~ I.'
110 0
200
400
600
100
1000
13~-----------------------------
:~~~ 0
200
400
600
100
~ 0
m
ti:
10' IS
., 65
•
,
6
7
•
9 10 11 Il 13 14 15 I' 17 11 19 20
Controller output (mA)
1000
U
Time (Sampling period) Fig. 2. Effect of a sensor drift on variables Q and U
Fig. 4. Hysteresis modelling 106
Dynamical modellinl:. According to our implementation objective. the dynamical of the system is expressed by a first order model with delay. thus the corresponding discrete form is: (1)
Fig. 7. Template geometry
where the coefficient "a" depends on the chosen functioning point caIJed Qi. and of dQ (step of setpoint) as it is shown Fig. 5. 0,9 0,'
'"
3. FAULT DETECTION STRATEGY
+
+ .p-+ +
+
0,1
+
+
0,6 -2,5
·2
-I,S
+
.t+ ++ + -I
-0.5
3.1. Fault detection all:orithm Due to the presence of a non linearity with memory (the hysteresis) classical methods based on, for instance, non-linear observers are not suitable . Moreover, the aim of this work is to provide some simple technique to monitor a control loop. Then, the algorithm for fault detection, taking into account set-point variations is presented Fig. 8.
0,5
0
dQ/Qi
Fig. 5. Coefficient "a" versus dQ
Q.1 The variation of this coefficient "a" has been modeIJed by a two pieces straight line. Another static representation . If we choose to observe the flow measurement versus the controlJer output signal as presented in Fig. 6:
1241
:::
I~L-
12
~
_________________ ___________ ~
12,5
13
13,5
yes ~
Are Meas. into the template?
New template determination
14
Controller output (mA)
yes
no E<
Fig. 6. Measurement flow Q (l/h) versus controlJer output signal U (mA) we notice that: for a given set-point, the controlJer signal varies inside such a "template". the change of set-point is represented by a trajectory linking the two templates corresponding to the two set-points. according to the previous dynamical model.
Emax ?
Fig. 8. The failure detection principle
Two cases are viewed: - during the static phase, if a failure occurs, the functioning point goes out the template. - when a set-point change appears, a test on the prediction error E of the dynamical model , is used to decide if there is fault or not. This test is operational only during dynamical phase, along the trajectory joining the two templates.
The geometry of these templates is defined as folJows (see Fig. 7): - the parameter h represents the acceptable variation of the measurement, around the setpoint value. - the 9 angle and the width I are defined according to the static model characteristics. So, for each set-point value. a particular template must be defined.
107
3.2. Results
order to implement the first step of our procedure (Initial template determination), we try to reproduce the human thought process. The main difficulty consists in choosing the more relevant points, marked with an "x" in Fig. 12, to be considered as templates vertex, in the plane (Q versus U).
To illustrate the previous technique, two examples of failure, namely a sensor bias and an actuator drift are presented Fig. 9 & 10 where continuous lines and the dotted lines respectively represent the template and the evolution due to the fault.
"'I ~I
~:::I be~~ o
tI:
116
12S
liS
end
10S
112~------------------------------J
12
12,S
13
13,5
14
14,5
IS
12
IS,S
13,5
14
14,S
IS
Controller output (mA)
Controller output (mA)
Fig. 12. Templates vertex
Fig. 9. Sensor bias
11.75
11
12,S
12
12.25
12.5
12,75
As proposed by Fitzgerald (1990), a pre-defined sequence of set-point values (see Fig. 13) is applied. It allows to define two areas, surrounding the functioning point. So, three different classes, corresponding to set-point values (110 IIh, 120 lIh, 130 llh), could be pointed up and fuzzy C-means techniques allow to determine if a particular point belongs to one of these classes.
13
Controller output (mA) Fig . 10. Actuator drift
3.3. Fuzzy c-means to improve the performances of detection In order to improve the sensitivity of our method it is very important to determine as good as possible the straight lines representing the non-linearity of the system. The Fig. 11 shows the errors involved by a false computing.
o
" "Real" lines
,, ,
500
1000
ISOO
2000
Time (Sampling period)
Non detection
False alarms Fig. 13. Sequence of opening-closing For each point. the algorithm of fuzzy C-means called also Bezdek's algorithm (Bezdek, 1981) gives us the membership's degree !l of a class as shown Fig . 14.
Computed lines
Fig. 11 . Effects of a false initial positioning
Finally, when the classes are determined, the points which are the extreme values of the classes are considered as templates vertex and a simple linear regression is used to define the needed parameters for static modelling, e, I and h.
The fuzzy logic seems to be a good way to solve this problem because the lines could be positioned with a kind of human sensivity. The human thought process allows to define the vertex of the template, by taking into account a synthetic view of the hysteresis phenomenon . According to Fig. 8, in 108
5. REFERENCES Bayart, M .. Gehin, A.L., Staroswiecki, M. (1992). Fault detection and isolation and mode management in smart actuators. IFAC Symp. on Intelligent Components and Instruments for Control Applications. Malaga. Bezdek. J.c. (1981). Patem recognition with fuzzy objective functions algorithms. Plenum press. Fitzgerald. B. (1990). Control valves: which ones need fixing. Chemical Engineering. Frank, P.M. (1990). Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy - A survey and some new results. Automatica.26. 459-474. Isermann, R. (1984). Process fault detection based on mode ling and estimation methods - A survey. Automatica, 20. 4. 387-404. Willsky, A.S . (1976) . A survey of design methods for failure detection in dynamic systems . Automatica, 12. 601-611.
N
::1.
Time (Sampling period) Fig. 14. Membership's degree Il for the 3 classes (110 lIh, 120 Ilh, 130 lIh)
4. CONCLUSION A very simple and performing way to supervise a control loop has been described. Some experiments have shown that we are able to detect deviations of the order of 1 % of the set point value. Finally we can notice that: - there is no need to add extra sensor or any other equipment which would raise the price of basic elements of a control system, - the running time of the fault detection algorithm allows its setting up in real time. - the method can be adapted to many non-linear process controls. but it is necessary to build a prediction (dynamical) model and to have also idea to model the non-linear part, - the method is available for some functioning points. but the initial positioning of the template must be calculated for each set-point values. This initial calculus step could be compared to a "calibration" phase, in order to adapt our strategy to a particular control loop. At present. the entire fault detection algorithm is set up on a PC. fitted out with an acquisition card, under real-time monitor. The next step of our work consists in implementing all the strategy. including fuzzy C-means calculus on a micro-controller or DSP.
109