Ratio Control

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ABNORMAL SITUATION CORRECTION BASED ON CASCADFJRATIO CONTROL

Takashi Hamagchi·. Yoshihiro Hashimoto... Toshiaki Itob··. Akihiko Yoneya· and Yoshitaka Togari·

• Dept. of Systems Engineering, Nagoya Institute of Technology Gokiso-cho, Showa-ku, Nagoya 466-8555,JAPAN

•• Dept. of Systems Management, Nagoya Institute of Technology Goldso-cho, Showa-ku, Nagoya 466-8555,JAPAN E-mail : [email protected]

Abstract: In this paper, the countenneasure planning based on cascade andIor ratio control is proposed. The algorithm to configure multi-loop controllers and the one to plan correction actions based on it were already proposed by Hamaguchi, et al. However, for some abnonnal situations, the operator actions similar to cascade control or ratio control are necessary. The controller configuration algorithm for cascade andIor ratio control is developed based on the extended Cause-Effect matrices. This algorithm is useful for not only abnonnal situation correction but also plant wide controller design. Copyright 0200]

]FAC

Keywords: Fault-tolerant systems, Operators, Qualitative simulation, Computer -aided instruction, Knowledge representation

planning. Hamaguchi, et al.(l999, 2000a, b) already proposed an algorithm for abnormal situation correction. It was based on the single loop To manipulate an controllers configuration. actuator based on a sensed value is a basic concept for operator actions. However, the set-points of some single loop controllers are decided based on ratios. For example, the oxygen supply flow rate is decided to keep the ratio to the fuel flow rate in boiler control. For abnormal situation correction, ratios sometimes become very important.

1. INTRODUCTION

most chemical plants, distributed control systems(DCS) are used to simultaneously control thousands of process variables such as temperature and pressure. The master human role in this control is to supervise these highly automated systems. The master activities of plant operators are fault detecting and diagnosing; planning countermeasures; compensating and correcting abnormal situations, although the frequency of the abnormal situations is very low. In

If the number of actuators are short and some

Operators must be faced with these complex decision making in managing abnormal situations. While monitoring and fault diagnosis have very fertile grounds for theoretical and industrial development, there are a few papers discussing countermeasure

controlled variables have allowable ranges for their set-points, their set-points can be utilized for other control objects. In such a case, the set-point can be regarded as a manipulated variable with the upper and lower limits. This action to manipUlate a

209

set-point is similar to cascade control.

the solvent. In this example, the concentration of the product is not measured. The ratio of the feed flow rates, F21F3, is considered as the controlled variable. The controlled variables of this plant are the level of the feed tank, Ll, the level of the mixer, L2, the product flow rate, F4, and the ratio of the feed flow rates, F21F3. Four valves, VI, V2, V3 and V4, can be utilized as the manipulated variables.

In this paper, the algorithm to propose the abnormal situation correction similar to ratio control and/or cascade control is developed. In Section 2, a control problem, for which ratio control is necessary, is illustrated. The plant has a mixer and a feed tank. In Section 3, the controller configuration method, which can deal with ratio control and/or cascade control, is proposed. In order to consider ratio control, the Cause-Effect matrix (CE-matrix) for the plant is extended from the CE-matrix for single loop controllers. In Section 4, a scenario of an abnormal situation is adopted to explain the relationships between controller configuration and abnormal situation correction. Sticking of the valve on the line from the feed tank to the mixer had occurred. The command to increase the flow rate was given to the product flow rate controller. Even though the ratio control tried to increase the feed flow rate, the flow rate did not change because the valve is stuck. In order to continue the safe operation, the controllers of the plant must be changed.

--v-""",,

F4 C4

Fig. 1 Example plant for abnormal situation correction Figure 1 shows the controller configuration of this plant. The set-point value of the ratio, F21F3, are multiplied by the sensed flow rate, F3. The product, F2, is sent to the flow rate controller of F2 as its set-point.

It is shown that the cascade controller design algorithm can suggest to manipulate the set-point of the feed tank level instead of the stuck valve. If the magnitude of the product flow rate set-point change was too large, the ratio control could not be accomplished even if the set-point of the feed tank level was moved to the upper control limit. In this case, the ratio controller should be re-arranged and the product flow rate control should be abandoned. The countermeasure for this situation can be designed based on the ration controller design algorithm.

3. DESIGN PROCEDURE OF RATIO AND CASCADE CONTROL In this section, the design procedure of the controller configuration including cascade controllers and ratio controllers is explained. At first, the basic procedure to design single loop controllers is illustrated.

3.1. Cause-Effect Matrices In Conclusion, the usefulness of this method is explained. The proposed controller configurations show the points to be focused for abnormal situation correction. Even though it does not give any quantitative information, it is useful for plant operators. They can manipulate one actuator adequately in focusing their attention to one controlled variable, although many problems cannot be considered simultaneously.

Hamaguchi, et aI.(999) already proposed a controller configuration algorithm based on Cause-Effect matrices (CE-matrices). It is illustrated by using tank level control problem shown in figure 2. The table in figure 3 shows the CE-matrix of the plant. ....................

~F1 $

~l

2. EXAMPLE PLANr FOR RATIO CONTROL Consider control problem of a very simple plant, which consists of a mixer and a feed tank. The flow, F2, is the concentrated material and the flow, F3, is

Fig. 2 Tank level control

210

G Lt

Fl

Lt

Fl F2

If the diagonal elements corresponding to the controlled variables are "1 " 5, the control loops can work. Otherwise, the controller configuration expressed by C is not available.

F2 VI V2

1

1 1

1

1

Fig. 3 CE-matrix of the plant L1

C

Fl

3.2. Cascade Controller Design

F2

L1

1

Fl F2 VI V2

Here, the cascade control design procedure is explained. Cascade controllers have master control The set-point of the slave and slave control. controller is the manipulated variables of the master controller. The controller in figure 7 is simple single loop controller. Figure 8 shows the cascade control structure. The manipulated variables of the both of the controllers are the inlet flow valve, VI. In figure 7, Fl is the state variable. However, Fl is the manipulated variable and controlled variable in figure 8. The CE-matrix of the cascade controller in figure 8 is shown in figure 9.

1 1

Fig. 4. CE-matrix of controllers Each column Its elements are "0" or "1". corresponds to a cause and each row to an effect. When the ( i, j ) element of the CE-matrix is "1", the j-th column variable affects the i-th row variable. The "I" at the (2,4) element of figure 3 shows that the valve, VI, affects the flow rate, Fl. Because Fl affects Ll, the (1,2) element is "I". Figure 4 shows the CE-matrix to express the controller configuration of the tank control. The valve opening, VI, is the manipulated variable of the controller for the tank level, L1. The (4,1) element of the controller CE-matrix is "I". The flow rate, Fl, is not controlled in this configuration. The variables, which are not controlled variables or manipulated variables, are called state variables in this paper. The diagonal elements of the controller CE-matrix corresponding to the state variables are "1"s. Each column of the controller CE-matrix has only one "1" element. GC

L1

Fl F2

p

ffi :. . . . . . . .-: Y@Fl $ ~!

F2

Fig. 7 Single loop controller

Fl F2 1

L1

VI is determined by F1. Fl is determined by L1. The reachability matrix of the cascade control is shown in figure 10.

1

1

Fig. 5. Propagation of set-point change F2

R L1

L1

WiJ{

Fl F2

Fl

F2

1

Fig. 8 Cascade controller

1

C L1 Fl F2

Fig. 6. Reachability matrix

L1

F2

F1

1 1 1

P

V1

Figure 5 shows the propagation of the set-point signals. The signal of the Ll set-point change is sent to V 1. The change of V 1 causes the change of L1. Then the signal of Ll set-point arrives at the L1. This The feedback control of Ll can work. propagation can be illustrated by Boolean multiplication of the CE-matrices. The reachability matrix R is defmed as shown in eq. (1);

R=

I:=t (GC)k

P

1

Fig. 9 Cotroller matrix R L1

Fl

L1

Fl

1 1

1 1

F2 1 1

P 1

F2

P

Fig. lO Reachability matrix The availability of the control configuration is judged by the diagonal elements corresponding to the controlled variables. The "l"s in the (1,1) and (2,2)

(1)

where n is the dimension of GC.

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of R in figure 10 shows that the cascade control is available. One of the benefits of cascade controllers is rejection of disturbances using slave controllers. Ps in figures 7, 8, 9 and 10 are the pressure of the source. P affects F1 . If the single loop controller in figure 7 is utilized, the effect of P is detected by Ll sensor. VI is manipulated by Ll controller. The cascade controller in figure 8 can detects the effect of P on F1 . F1 is much more sensitive to the change of P than Ll. The slave controller manipulates VI based on Fl. Therefore, the effect of the disturbance of P is rejected before Ll changes. This phenomena can be illustrated by using the product of Rand G shown in figures 11 and 12. While the element from P to L 1 in figure 11 is "1", the one in figure 12 is not "1". It is shown that the effect of P on L1 is rejected.

controlled variable. The set-point of F2 is the manipulated variable to realize the ratio. F2 is controlled by using V2. F3 is a state variable. L2 is controlled by using V3 . The product flow rate F4 is controlled by using V4. L1 G L1 L2 F4 1 F2 F3 F1 F21FJ F2+FJ C2 C3 C2IC3

L2 F4 F2 FJ Fl F2 / FJ F2+FJ C2 C3 C2/ C3 C4 V1 V2 V3 V4 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1

C4

1

1 1

Fig. 13 CE-matrix of the plant in fig. 1 c

°

1F3 1F1 1112l1'31 F2+F3 C2 C3 C2IC3

C4

L1

RG

11

11

1 1

Fl F2

Fl F2 1 1

1 1

P

Vl

F4

1 1

1 1

F3

1

'2/ F3 F2+F3 C2

P

Fig. 11 Propagation matrix of single loop controller R'G '

11

11

1

Fl F2

1

F1

Fl F2 1

P

Vl

1

1

1

03 IC2 / 03

1

1

Fig. 14 CE-matrix of the controller in fig. 1.

B" . . . ,." '" '"

P

Fig. 12Propagation matrix of cascade controller

~

When the controlled variable, which is available as the manipulated variable for another control, is decided, the controller matrices of the available cascade controllers can be found automatically.

F3 F

:m s F2+F3 C2 C3 C2IC3 C4

3.3 Ratio Controller Design Here, the design procedure of the ratio controller is explained. When the two feed flow rates of the mixer in figure 1 change in keeping the ratio of them constant, the concentration of the product is kept constant. When the feed flow rates change in keeping the sum of them constant, the liquid level of the mixer is not affected by the flow rate changes.

1 1

1 1 1 1

1

1

t NlI'ki 1

cv", '"

1 1 1 _1

1 1

1 1

1

Fig. 15 Reachability matrix of the controller in fig. 1 The reachability matrix of the controller configuration is shown in figure 15. It can be understood that the controller configuration is available, because the all diagonal elements corresponding to the controlled variables are "1"s.

In order to describe the effect of the ratio and the sum, the CE-matrix of the mixer contains them as shown in figure 13. C2, C3 and C4 are the concentrations of the F2, F3 and F4. The product concentration, C4, is determined by F2JF3 and

4. ABNORAL SITUATION CORRECTION

C2JC3.

In this section, the operation planning for the abnormal situation correction based on the controller configuration is explained.

The control structure in figure 1 is expressed by the CE-matrix in figure 14. The ratio, F2JF3, is the

4.1 Example Scenario of an Abnormal Situation

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However, if the magnitude of the product flow rate change is too large, the output of the flow rate controller, which is FICl in figure 16, exceeds the upper limit of Ll. When the set-point signal of Lt continues to exceeds the upper limit, the cascade controller must be abandoned.

The causes of the abnormal situation, which is considered in this section, is the sticking of the valve, V2. The valve opening had been fixed at the value at the steady state value. When the command to increase the product flow rate was given, the ratio controller increased the set-point value of F2. While the flow controller of F2 tried to increase the opening of V2, it could not be changed.

RT

1"0 ' ~ ,'F4-:'1'2 F3

lit . "V 1

is assumed that the valve sticking was distinguished by using a fault diagnosis system. The countermeasure planning is the problem to be considered.

1

Fl :F'2YR'J F2+F3 C2 C3 C2/ C3 C4

1

1

1

It

n.

'4 .

F3

4.2. Countermeasure based on a cascade control

A

1

F2+F3 C2 C3 C2IC3

1

C4

The level of the feed tank, Lt, was controlled variable in the normal situation. The set-point of Lt has an allowable range. Therefore, the set-point of Lt can be utilized as a manipulated variable with the upper and lower limits. Lt can increase F2 even if V2 is fixed. The ratio control can be achieved by the manipulation of Ll. This countermeasure can be expressed by the cascade control shown in figure 16.

Fig. 18 Reachability matrix of the countermeasure shown in fig. 16.

4.3. Countermeasure instead of the cascade control In this case, the set-point of Lt is set at the upper limit to obtain the maximum flow rate corresponding to the fixed opening of V2 . The options of the controller CE-rnatrices can be generated automatically because their structures are simple. Elements are "1" or "0". Each column has only one "I". The diagonal elements for state variables are "I". It is possible to judge the existence of the controller configuration to control all controlled variables. In this case, it can be judged that there are not any manipulated variables to control F2. One of the controlled variables must be abandoned. Even if the set-point of L2 is considered as the manipulated variable, F2JF3 and F4 cannot be controlled simultaneously. The F4 control is abandoned in this example scenario.

Fig. 16 Increment of Lt instead of V 1 increase The controller CE-matrix of the configuration including the cascade control is shown in figure 17. eT

L1

l2 F4 F2 F3 Fl F2/ F3 F2+F3 C2 C3 CVC3

C4

II

l2 F4 F3 Fl 1F2/ F3 F2+F3 C2 C3 C2/C3 C4 VI

V3 V4

Fig. 17 Controller CE-matrix for the countermeasure shown in fig. 16 Fig. 19 Controller rearrangement according to the fixed opening of V2.

Figure 18 shows that the countermeasure is effective.

213

solution of the problem,

Figure 19 shows the countermeasure for this situation. The ratio control is achieved by manipulating F3 instead of F2. The tank level, L2, is controlled by F4 instead of F3. The product flow rate, F4, is determined by the flow rate, F2, which is determined by V2 and Ll. The controller CE-matrices for this countermeasure is shown in figure 20.

This algorithm is useful for not only abnormal situation correction but also plant wide controller design. Configuration including cascade controllers and ratio controllers can be designed. It can be executed without any quantitative information. Therefore, the model building is easy. The controller configurations can be automatically generated because the structures of the matrices are very simple. And their availability can be judged by using Boolean matrix multiplication. It is almost impossible to fmd the cause of the fault without any other options, although many algorithms have been proposed for fault diagnosis. Because the number of sensors is short for fault diagnosis, the large number of options are obtained by using fault diagnosis systems. It is serious problem that the adequate countermeasures are different among the options. For some options, cooling might be a good countermeasure. But it might be dangerous for other options. This countermeasure planning algorithm can be applied to each options of the fault If the adequate countermeasure is situation. common for the all options, it can be applied even if the cause is not limited yet. If the adequate countermeasures are different between options of the fault cause, the options, which must be distinguished, are found. Therefore, this algorithm is useful to make fault diagnosis systems effective.

The change of the controller configuration is expressed by the (F4,L2) and (F3,F21F3) elements. The reachability matrix is shown in figure 21. It is shown that the master controllers for F2IF3 and L2 and the slave controllers for F3 and F4 can work. L1 l2 F4 F2 FJ Fl F2/ F3 F2+FJ C2 C3 C2IC3

C2

L1 l2 F4 F2

C4

AO

Fl F2/ FJ F2+FJ C2 C3 C2IC3 C4 VI 1 rm.~m ~@4 V3 V4

If:i1 @M?: tKili: .Ill gh~~ Jt:th& it~W~W ~m% lW:$ llfftlfJ mtt*m~ 1

1

..·.. a

Fig. 20 Controller CE-matrix for the countermeasure shown in fig. 19 ······ 1F2

•.

: .•...

••.... :

•••.

11

I

liEt!

Fl ~IF2+F3 C21C31C2IC31 C4

1 1

1

The supports for the decision making of the timing or magnitude of operation are also necessary for operators. Qualitative consideration should be added to the result of the proposed procedure. This method can be considered as the first step to bridge the discontinuity between fault diagnosis and countermeasure planning.

.~ . "'"I . 1--+-+--+--+--1--+-+--+--1

.• ... •••

F2 Fl

IF2+F3

1

1 1

1

C3 IC2IC3 C4

1 1

1 1

1

Fig. 21 Reachability matrix of the countermeasure shown in fig. 19.

REFERENCES

Hamaguchi, T., T. Kamiya, A. Yoneya, Y. Hashimoto and Y. Togari, Controller Configuration Design and Troubleshooting Planning Using CE-Matrices, Kagaku Kougaku Ronbunshu, 25(3), pp. 384-388

5. CONCLUSION In abnormal situation, operators change the controller mode from auto to manual. They must operate many manipulated variables manually. Human being is not good at thinking many problems simultaneously. The controller configuration proposed by this algorithm is based on single loop controllers. For operators, the manipulation in focusing their attention on one sensed variables is not difficult. The problem to select the adequate pair of the manipulated variable and sensed variable is very important. The proposed algorithm can fmd the

(1999)

Hamaguchi, T., Y. Hashimoto, A. Yoneya and Y. Togari, Countermeasures Planning based on Controller Configuration, Proceedings of the lASTED Internarional Conference Intellignet Systems and Control 2000, pp.205-209 (2000a) Hamaguchi, T., G Yonemura, Y. Hashimoto, A. Yoneya and Y. Togari, Selection of Operating Modes in Abnormal Plant Conditions, Proceedings of PSE Asia 2000, pp.565-570 (2000b)

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