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A simulation study on the application of a fuzzy algorithm to a feedwater control system in a nuclear power plant
Reliability Engineering and System Safety 28 (1990) 319-335
A Simulation Study on the Application of a Fuzzy Algorithm to a Feedwater Control System in a Nuclear Power Plant S. T e r u n u m a , K. K i s h i w a d a , * H. T a k a h a s h i , T. Iijima & H. H a y a s h i Power Reactor and Nuclear Fuel Development Corporation, Fugen Nuclear Power Station, 3 Myojin-cho Tsuruga-shi Fukui-ken, Japan (Received 17 August 1988; accepted 25 August 1989)
ABSTRACT The feedwater control system is responsible for maintaining the steam drum water level at the set point. The response of the feedwater system is so slow that it is difficult to maintain an optimal water level by using a traditional PI (Proportional-Integral) controller. The objectives of the present study are to apply the fuzzy control method, which can utilize the flexibility and the heuristic control strategy employed by humans, to the feedwater control system in a H W R (Heavy Water Reactor) type nuclear power plant, and to improve the starting performance on a steam drum water level control. Numerical simulations on the step and ramp response for the water level set point and the reactor power, and on the response after manual closing of the feedwater control valve have been performed. The results of the study show that fuzzy control can reflect successfully the experience gained in skilled manual operation. It is expected that fuzzy control can contribute to the reduction of human errors and to the improvement of the reliability and safety of plant operation.
1 INTRODUCTION Since electric power generated by nuclear power stations is increasing in the world, the reliability and safety of a nuclear power plant becomes more important. * To whom correspondence should be addressed at: Power Reactor and Nuclear Fuel Development Corporation, 1-9-13 Akasaka Minato-ku, Tokyo 107, Japan. 319 Reliability Engineering and System Safety 0951-8320/90/$03-50 O 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain
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A nuclear power plant consists of many components and systems and most of them are controlled by proportional-integral (PI) or proportionalintegral-differential (PID) controllers. However, some of the systems such as the feedwater control system, which is difficult to optimally control with these traditional controllers because of its slow response time, are often controlled manually by a skilled operator who has flexible and heuristic control strategy. The fuzzy control system which can utilize the control strategy employed by humans has been developed to apply to the feedwater control system instead of the traditional PI controller.
2 C O N C E P T OF F U Z Z Y C O N T R O L Fuzzy logic has its origin in the paper 'Fuzzy Sets' described by Zadeh. 1 More often than not, the classes of objects encountered in the real physical world do not have precisely defined criteria of membership. For example, 'the class of beautiful women', or 'the class of tall men', do not constitute classes or sets in the usual mathematical sense of these terms. However, the fact remains that such imprecisely defined 'classes' play an important role in human thinking, particularly in the domains of pattern recognition, communication of information, skilled operation of machinery or plant, etc. A fuzzy set is a class of objects with a continuum of membership grades. Such a set is characterized by a membership function which assigns to each object a membership grade ranging between zero and one. Since applicability of fuzzy logic to a steam engine control was first proposed by Mamdani, 2 many studies have been reported using the fuzzy control method. The method has also been applied to actual industrial processes, such as a cement kiln, 3 a water purification plant 4 and an automatic train operation system, 5 all of which have been put to practical use. Also in the nuclear engineering field, the fuzzy control application has been reported, such as a fuzzy controller designed for the experimental reactor at M I T (Massachusetts Institute of Technology)6 and for a BWR (Boiling Water Reactor) recirculation flow control system. 7
3 O U T L I N E OF T H E R E A C T O R F E E D W A T E R C O N T R O L SYSTEM IN F U G E N Fugen is a prototype heavy water moderated, boiling light water cooled, pressure tube type reactor with 165 MW electric output. The feedwater control system regulates the steam drum water level by adjusting the feed water flow rate. Since the feedwater flow rate changes as
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much as 0 to 460ton/h with the reactor power, the different capacity valves--the primary valve and the sub-valve--are used in the following way. (1)
Below 18% of the rated reactor power, the sub-valve opening is regulated by a PI controller using the steam drum water level as a signal. (2) Over 18% of the rated reactor power, the primary valve opening is regulated by a PI controller using three signals; the steam drum water level, the feedwater flow rate and the steam flow rate. A schematic flow diagram of the feedwater control system is shown in Fig. 1. At the low power level, the steam drum water level is sometimes controlled manually by an operator because the PI controller takes a long time to settle to the steam drum water level when the reactor power changes. In the case of manual control, however, the best result cannot always be obtained even if under the same plant condition or by the same operator. On the other hand, a fuzzy controller responds to the incoming signals according to fuzzy linguistic control rules which are reflected by the knowledge of skilled operators and adjusted to give the correct response. Therefore, it is expected that near to the best response, which might be obtained by skilled operation, can be realized constantly by a fuzzy controller.
4 F U Z Z Y C O N T R O L SYSTEM D E S I G N
4.1 Outline of fuzzy control system In the case of controlling the steam d r u m water level manually below 18 % of the rated reactor power, plant parameters, which skilled operators observe mainly during operation, are as follows. (1) The steam drum water level and level set point (2) The sub-valve opening and the turbine bypass valve opening (3) The reactor power Usually, skilled operators decide a corrective action for the sub-valve opening based on these parameters. Accordingly, the processes for consideration are converted to 'If-Then' style fuzzy linguistic rules. These rules are divided into three kinds of rule base (RB-1, RB-2 and RB-3) depending on the parameters mentioned above and each rule base is fed to the corresponding inference part of the fuzzy control system as shown below.
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(1) The inference part (I) concerned with the steam drum water level: In
(2)
(3)
the inference part (I), the corrective action (UI) is inferred from L E and CL which means a difference between the steam d r u m water level and the level set point, and a change in the water level. 'Corrective action' means a regulation demand of feedwater flow rate and the sub-valve opening is regulated to satisfy the demand. The inference part (11) concerned with thefeedwater flow and the steam flow: In the inference part (II), the corrective action (U2) is inferred from FE2 which means a difference between the feedwater flow and the steam flow. Since the feedwater flow and the steam flow are too low to be measured accurately at the low power level, the feedwater flow is calculated from the sub-valve opening and the steam flow is calculated from the turbine bypass valve opening. The inference part (III) concerned with the feedwater flow and the reactor power: In the inference part (III), the corrective action (U3) is inferred from FE 3 which means a difference between the feedwater flow and the target feedwater flow depending on the reactor power. The feedwater flow rate is calculated from the sub-valve opening in the same way as the inference part (II). The target feedwater flow is calculated in the following way. The inlet flow to the steam drum involves the feedwater flow whose temperature is continuously about 40°C at the low power level and the return flow from the primary coolant purification system whose temperature is about 190°C and the flow rate is kept at 60 ton/h as shown in Fig. 2. Thus, the inlet temperature depends on the feedwater flow r a t e - - t h e inlet temperature decreases when the feedwater flow increases. The curve shown in Fig. 3, which indicates the most suitable feedwater temperature depending on the reactor power, is obtained by a least squares method using the data from the feedwater temperature and Inlet temperature
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Fig. 2. Detail of the feedwater flow line.
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the reactor power. According to the relationship shown in Fig. 3, the target feedwater flow rate is calculated from the reactor power to prove the inlet temperature to be the most suitable value. The membership functions and the rule bases used in each inference part are shown in Figs 4 and 5.
4.2 Inference methodology 4.2.1 Data processing
Each of the plant parameters is processed into a form acceptable to the fuzzy controller, such as LE, CL, F E 2 and F E 3. Since the fluctuation of the plant parameters includes components of noise, it is necessary to eliminate the noise of each parameter; the plant parameters which are used in the fuzzy controller are processed by a mean value circuit, a time lag of first order circuit, a filter circuit and a combination of these parameters. The most suitable constant for each circuit is established individually. Moreover, since F E 2 and F E 3 are calculated based on the sub-valve opening and the turbine bypass valve opening, they are not so accurately obtained and these evaluation errors cause permanent offset of the steam
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Fig. 4. Membership function for propositions.
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Fig. 5. Rule bases RB-1, RB-2 and RB-3. drum water level. Therefore, F E 2 and F E s are compensated by the corrective flow rates which are evaluated every ten seconds from the steam drum water level change value during the evaluation unit time. Hence, F E 2 and F E 3 are obtained from the following equations, where the third term of each equation represents the corrective flow rate. F E 2 ( t ) = F f ( t ) -- Fs(t) + A V - {I a' F f ( t ) d t - I a' Fs(t) dt}
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Ff(t): Fs(t): rp(t): AV: At:
Calculated value of the feedwater flow rate (ton/h) Calculated value of the steam flow rate (ton/h) Target value of the feedwater flow rate (ton/h) Mass change read by change in the steam d r u m water level during the evaluation unit time (ton) Evaluation unit time (h)
4.2.2 Fuzzy inference Fuzzy inference is performed by some linguistic control rules as illustrated here. If LE is NB and CL is PS then corrective action is P M
(3)
If LE is N M and CL is P M then corrective action is ZO
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Here the former propositions following 'If' are called the antecedent parts and the latter proposition following 'then' is called the consequent part. There are 35 control rules in RB-1 including the above rules and they are shown in the rule matrix table of Fig. 5. The characters such as NB, NM, NS, ZO, PS, P M and PB are fuzzy linguistic variables as shown below.
NB: NM: NS: ZO: PS: PM: PB:
Negative Big Negative M e d i u m Negative Small Zero Positive Small Positive M e d i u m Positive Big
These fuzzy linguistic variables are defined respectively by the membership functions concerned with every LE, CL, FE 2, FE 3 and U 1 ~ U 3. Let us consider the inference part (I) by way of example to explain the inference m e t h o d o l o g y when referring to Fig. 6. LE For example, when LE is -- l l . l m m , W~o ( - 11.1) and W ~L Es ( - 11-1), which mean separately the compatibility grade for LE is ZO and for LE is NS, are described as follows. W~oe(- 11.1) = 0.67 LE W~s ( - I 1-1) = 0.33
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separately the compatibility grade for 'CL is NS' and for 'CL is NB', are described as follows. I4~N~(--0"15 ) = 0-50
(7)
W~N~(--0"15)= 0"50
(8)
The other variables such as W~e~(-0"15), W~p~t(-0"15) are all '0.0'. According to these variables, the compatibility grade for each of the rules is obtained as follows.
W(ZOLE,NsCL)=min{W~(--ll'I), W(NS te, NSCL)=min{W~g(-ll'l), W(NSLE,NBCL)=min{W~g(-ll.1), W(zoLE, NBCL)=min{W~g(--ll.1),
WCsL(--0"15)}=0"50 W~N~(-0"15)} =0"33 wC~(-0"15)} =0"33 wC~(--0.15)} =0.50
(9) (10) (11) (12)
where W(A rE, Bct') means a compatibility grade for a rule'if LEis A and CL is B then ~'. The compatibility grades for the other rules are all '0"0'. Then, each of the triangular formed membership functions Xc(u), which express the proposition of the consequent part of each of the rules 'then corrective action is C', is reformed in trapezia form so that the height of the trapezium is equal to the grade W(A rE, BcL) for the rule, and then these new trapezia formed membership functions are superimposed as the following equation.
X*(u) = max {Xc(U)}
(13)
where X*(u) is a membership function which expresses the fuzzy sets of a corrective action. At last, the center of gravity of the function X*(u) is calculated by way of an output 'UI'. U~ =
X*(u)u du - 0.632 ~"X*(u) du
(14)
4.2.3 Synthesis method of U1, U2 and U3 The three corrective action signals UI, U2 and U3 which are obtained from the each inference part (I), (II) and (III) are synthesized by the following equation. U=mlf I +m2U 2 +m3U3 (O
(15)
Equation (15) is based on the control strategy of skilled operators like that where the water level difference (LE) is much larger than the other two kinds of flow difference (FE2, FE3), and the sub-valve should be adjusted to reduce
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S. Terunurna, K. Kishiwada, H. Takahashi, T. Bjima, H. Hayashi
the water level difference regardless of the others. That is to say, the weight gain m 1, m 2 and m 3 are determined by the following rules. If L E is large then make m 1 large If F E e is large then make m 2 large If F E 3 is large then make m 3 large
(16) (17) (18)
Below 8% o f the rated reactor power, however, the feedwater flow should be regulated not so much by the reactor power as by the other outflow from the steam drum such as steam flow for a turbine gland or an air ejector of the turbine condenser. These kinds of outflow rate are very low and cannot be measured, but they would be included in the corrective flow rate concerned with F E 2 which is calculated from eqn (1). Therefore, the weight gain m 3 is made zero below 8 % of the rated reactor power regardless o f the rule (18). 5 SIMULATION 5.1 Simulation code Simulation code 'FUCTES' used for simulation analysis is made by rebuilding Fugen A T R (Advanced Thermal Reactor) Simulation Code . . . . . . . . . .
FUCTES
-
Water level Level set point Reactor power Data Processing Sub valve opening
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Outline of'FUCTES'.
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2400
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Simulation result o f response against the changing steam drum water level set point (step changing from Omm to - lOOmm).
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E E r o
8o0
800 Time
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1600
2400
3200
1600 (second)
2400
3200
Simulation result o f response after manual closing of the sub-valve (manual closing of 20%).
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L
E
I 0
A 800
1600 Time (second)
800
1600
2400
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Simulation result of response against the changing reactor power (step change of 5%).
'FASIC' which simulates the dynamics of the main processes of a Fugen power plant including the feedwater control system. Several kinds of simulation analysis were performed as follows. (1) Response against change in the steam drum water level set point (step change from 0 to - 1 0 0 mm) (2) Response after manual closing of the sub-valve (step closing of 20%) (3) Response against change in the reactor power (step change of 5% and ramp change of 0.6%/min) In each case, added disturbance is selected to be much larger than it might be normally in the ordinary plant operation. A diagram of FUCTES is shown in Fig. 7. 5.2 Results
The simulation results are shown in Figs 8 to 11. In all cases, it is clearly shown that the steam drum water level is controlled excellently by the fuzzy
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control over such a large disturbance. The two responses which are obtained by manual control with the same operator and the response of the PI controller against the ramp change in the reactor power are also shown in Fig. 11. In the case of the PI control, the sub-valve is closed at first and then opened, because the steam generation in the reactor core becomes active with the reactor power increasing and the steam drum water level rising temporarily. In the cases of manual control and also fuzzy control, however, since the sub-valve is opened in the early stage of the reactor power increasing, the steam drum water level is kept slightly higher than the set point. Thus Fig. 11 shows that fuzzy control has good potential to reflect successfully experience gained in skilled manual operation.
334
S. Terunuma, K. Kishiwada, H. Takahashi, T. Iijima, H. Hayashi
6 DISCUSSION We plan to manufacture a fuzzy control pilot system and to perform an operation test where an operator regulates the sub-valve opening according to the output of the pilot system, and the following matters have been studied.
6.1 Calculation time In order to apply the fuzzy control pilot system to the plant, a calculation time of less than 0"5 sec/inference is necessary, because the fuzzy control control system is required to pick up the signals every second and it takes 0.5 s to display its inference procedures. In an actual pilot system, since a microcomputer would be used for economic reasons and the calculation time with the present program is about 2s, it is necessary to shorten its calculation time. The improvement would be performed by simplifying the programs and running both data processing programs and fuzzy inference programs in parallel.
6.2 Countermeasures against change in plant condition The weight gain (ml, m2 and m3) must play an important role against change in the reactor power from 0 to 18%. The logic is based on the skilled operators' strategy mentioned in section 4.2.3. However, for example, when the sub-valve is replaced with a new one which has different characteristics, it is assumed that the control rules and the membership functions have to be redetermined. We have also studied a self-organizing fuzzy controller which studies control results and improves its own control rules automatically. According to the study, it can be said that the self-organizing fuzzy controller is very useful for improving the control rules, which have been tuned up at the first stage, as a result of small changes in the plant condition.
6.3 Man-machine interface Operators suggest that the system situation described as follows should be displayed in real time: (1) condition of the parameters such as the steam drum water level, level set point and the other control variables which are used in the fuzzy control system. This enables the operator to grasp the plant condition on feedwater control at a glance and to deal with any trouble at an early stage in the event, if it happens.
,4 simulation study of a fuzzy algorithm control method
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(2) the control rules programmed in the fuzzy control system and those ones which are used to obtain the output. This enables the operator to understand how the output of the control system has been produced. Accordingly, we plan to add a display device in an actual system in order to improve the man-machine interface.
7 CONCLUSION This paper has proposed to apply a fuzzy control method to the H W R feedwater control system. F r o m the response simulation, the fuzzy control has good potential to reflect successfully experience gained in skilled manual operation. The authors examined the performance and basic characteristics of the controller by typical step and ramp responses, since these responses could clarify the fundamental characteristics of the controller. The fuzzy control pilot system has been developed from the results, and further work on the pilot system performance evaluation using a Fugen real plant will be done in the near future.
REFERENCES 1. Zadeh, L. A., Fuzzy sets. Information & Control, 8 (1965) 338-53. 2. Mamdani, E. H., Applications of fuzzy algorithms for control of a simple dynamic plant. Proc. IEEE, 121(12) (1974) 1585-8. 3. Mamdani, E. H., Ostergaard, J. J. & Lembessis, E., Use of fuzzy logic for implementing rule-based control of industrial processes. TIME~Studies Management Science, 20 (1984) 428-45. 4. Tong, R. M., Beck, M. B. & Latten, A., Fuzzy control of the activated wastewater treatment process. Automatica, 16 (1980) 659-701. 5. Yasunobu, S., Miyamoto, S. & Thara, K., Fuzzy control for automatic train operation system. Proc. Int. Conf. on Transportation Systems, 1983, pp. 39-45. 6. Bernard, J. A., Kwok, K. S. & Lanning, D. D., Experimental evaluation of fuzzy logic in closed-loop reactor control. Trans. Am. Nuclear Society, 49 (1985) 392-93. 7. Arakawa, A., Sekimizu, K. & Sumida, S., Fuzzy logic control application for BWR recirculation flow control system. J. Nuclear Science & Technology, 25(3) (1988) 263-73.
A Simulation Study on the Application of a Fuzzy Algorithm to a Feedwater Control System in a Nuclear Power Plant S. T e r u n u m a , K. K i s h i w a d a , * H. T a k a h a s h i , T. Iijima & H. H a y a s h i Power Reactor and Nuclear Fuel Development Corporation, Fugen Nuclear Power Station, 3 Myojin-cho Tsuruga-shi Fukui-ken, Japan (Received 17 August 1988; accepted 25 August 1989)
ABSTRACT The feedwater control system is responsible for maintaining the steam drum water level at the set point. The response of the feedwater system is so slow that it is difficult to maintain an optimal water level by using a traditional PI (Proportional-Integral) controller. The objectives of the present study are to apply the fuzzy control method, which can utilize the flexibility and the heuristic control strategy employed by humans, to the feedwater control system in a H W R (Heavy Water Reactor) type nuclear power plant, and to improve the starting performance on a steam drum water level control. Numerical simulations on the step and ramp response for the water level set point and the reactor power, and on the response after manual closing of the feedwater control valve have been performed. The results of the study show that fuzzy control can reflect successfully the experience gained in skilled manual operation. It is expected that fuzzy control can contribute to the reduction of human errors and to the improvement of the reliability and safety of plant operation.
1 INTRODUCTION Since electric power generated by nuclear power stations is increasing in the world, the reliability and safety of a nuclear power plant becomes more important. * To whom correspondence should be addressed at: Power Reactor and Nuclear Fuel Development Corporation, 1-9-13 Akasaka Minato-ku, Tokyo 107, Japan. 319 Reliability Engineering and System Safety 0951-8320/90/$03-50 O 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain
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S. Terunuma, K. Kishiwada, H. Takahashi, T. lijima, H. Hayashi
A nuclear power plant consists of many components and systems and most of them are controlled by proportional-integral (PI) or proportionalintegral-differential (PID) controllers. However, some of the systems such as the feedwater control system, which is difficult to optimally control with these traditional controllers because of its slow response time, are often controlled manually by a skilled operator who has flexible and heuristic control strategy. The fuzzy control system which can utilize the control strategy employed by humans has been developed to apply to the feedwater control system instead of the traditional PI controller.
2 C O N C E P T OF F U Z Z Y C O N T R O L Fuzzy logic has its origin in the paper 'Fuzzy Sets' described by Zadeh. 1 More often than not, the classes of objects encountered in the real physical world do not have precisely defined criteria of membership. For example, 'the class of beautiful women', or 'the class of tall men', do not constitute classes or sets in the usual mathematical sense of these terms. However, the fact remains that such imprecisely defined 'classes' play an important role in human thinking, particularly in the domains of pattern recognition, communication of information, skilled operation of machinery or plant, etc. A fuzzy set is a class of objects with a continuum of membership grades. Such a set is characterized by a membership function which assigns to each object a membership grade ranging between zero and one. Since applicability of fuzzy logic to a steam engine control was first proposed by Mamdani, 2 many studies have been reported using the fuzzy control method. The method has also been applied to actual industrial processes, such as a cement kiln, 3 a water purification plant 4 and an automatic train operation system, 5 all of which have been put to practical use. Also in the nuclear engineering field, the fuzzy control application has been reported, such as a fuzzy controller designed for the experimental reactor at M I T (Massachusetts Institute of Technology)6 and for a BWR (Boiling Water Reactor) recirculation flow control system. 7
3 O U T L I N E OF T H E R E A C T O R F E E D W A T E R C O N T R O L SYSTEM IN F U G E N Fugen is a prototype heavy water moderated, boiling light water cooled, pressure tube type reactor with 165 MW electric output. The feedwater control system regulates the steam drum water level by adjusting the feed water flow rate. Since the feedwater flow rate changes as
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much as 0 to 460ton/h with the reactor power, the different capacity valves--the primary valve and the sub-valve--are used in the following way. (1)
Below 18% of the rated reactor power, the sub-valve opening is regulated by a PI controller using the steam drum water level as a signal. (2) Over 18% of the rated reactor power, the primary valve opening is regulated by a PI controller using three signals; the steam drum water level, the feedwater flow rate and the steam flow rate. A schematic flow diagram of the feedwater control system is shown in Fig. 1. At the low power level, the steam drum water level is sometimes controlled manually by an operator because the PI controller takes a long time to settle to the steam drum water level when the reactor power changes. In the case of manual control, however, the best result cannot always be obtained even if under the same plant condition or by the same operator. On the other hand, a fuzzy controller responds to the incoming signals according to fuzzy linguistic control rules which are reflected by the knowledge of skilled operators and adjusted to give the correct response. Therefore, it is expected that near to the best response, which might be obtained by skilled operation, can be realized constantly by a fuzzy controller.
4 F U Z Z Y C O N T R O L SYSTEM D E S I G N
4.1 Outline of fuzzy control system In the case of controlling the steam d r u m water level manually below 18 % of the rated reactor power, plant parameters, which skilled operators observe mainly during operation, are as follows. (1) The steam drum water level and level set point (2) The sub-valve opening and the turbine bypass valve opening (3) The reactor power Usually, skilled operators decide a corrective action for the sub-valve opening based on these parameters. Accordingly, the processes for consideration are converted to 'If-Then' style fuzzy linguistic rules. These rules are divided into three kinds of rule base (RB-1, RB-2 and RB-3) depending on the parameters mentioned above and each rule base is fed to the corresponding inference part of the fuzzy control system as shown below.
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(1) The inference part (I) concerned with the steam drum water level: In
(2)
(3)
the inference part (I), the corrective action (UI) is inferred from L E and CL which means a difference between the steam d r u m water level and the level set point, and a change in the water level. 'Corrective action' means a regulation demand of feedwater flow rate and the sub-valve opening is regulated to satisfy the demand. The inference part (11) concerned with thefeedwater flow and the steam flow: In the inference part (II), the corrective action (U2) is inferred from FE2 which means a difference between the feedwater flow and the steam flow. Since the feedwater flow and the steam flow are too low to be measured accurately at the low power level, the feedwater flow is calculated from the sub-valve opening and the steam flow is calculated from the turbine bypass valve opening. The inference part (III) concerned with the feedwater flow and the reactor power: In the inference part (III), the corrective action (U3) is inferred from FE 3 which means a difference between the feedwater flow and the target feedwater flow depending on the reactor power. The feedwater flow rate is calculated from the sub-valve opening in the same way as the inference part (II). The target feedwater flow is calculated in the following way. The inlet flow to the steam drum involves the feedwater flow whose temperature is continuously about 40°C at the low power level and the return flow from the primary coolant purification system whose temperature is about 190°C and the flow rate is kept at 60 ton/h as shown in Fig. 2. Thus, the inlet temperature depends on the feedwater flow r a t e - - t h e inlet temperature decreases when the feedwater flow increases. The curve shown in Fig. 3, which indicates the most suitable feedwater temperature depending on the reactor power, is obtained by a least squares method using the data from the feedwater temperature and Inlet temperature
Feedwater control sub- valve
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Feedwater flow:vanable / temperature: 40"C! from primary coolant purification system flow: 30 ton/hour / temperature: 190"C!
Fig. 2. Detail of the feedwater flow line.
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the reactor power. According to the relationship shown in Fig. 3, the target feedwater flow rate is calculated from the reactor power to prove the inlet temperature to be the most suitable value. The membership functions and the rule bases used in each inference part are shown in Figs 4 and 5.
4.2 Inference methodology 4.2.1 Data processing
Each of the plant parameters is processed into a form acceptable to the fuzzy controller, such as LE, CL, F E 2 and F E 3. Since the fluctuation of the plant parameters includes components of noise, it is necessary to eliminate the noise of each parameter; the plant parameters which are used in the fuzzy controller are processed by a mean value circuit, a time lag of first order circuit, a filter circuit and a combination of these parameters. The most suitable constant for each circuit is established individually. Moreover, since F E 2 and F E 3 are calculated based on the sub-valve opening and the turbine bypass valve opening, they are not so accurately obtained and these evaluation errors cause permanent offset of the steam
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Fig. 4. Membership function for propositions.
PB
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Fig. 5. Rule bases RB-1, RB-2 and RB-3. drum water level. Therefore, F E 2 and F E s are compensated by the corrective flow rates which are evaluated every ten seconds from the steam drum water level change value during the evaluation unit time. Hence, F E 2 and F E 3 are obtained from the following equations, where the third term of each equation represents the corrective flow rate. F E 2 ( t ) = F f ( t ) -- Fs(t) + A V - {I a' F f ( t ) d t - I a' Fs(t) dt}
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A simulation study of a fuzzy algorithm control method
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(2)
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Calculated value of the feedwater flow rate (ton/h) Calculated value of the steam flow rate (ton/h) Target value of the feedwater flow rate (ton/h) Mass change read by change in the steam d r u m water level during the evaluation unit time (ton) Evaluation unit time (h)
4.2.2 Fuzzy inference Fuzzy inference is performed by some linguistic control rules as illustrated here. If LE is NB and CL is PS then corrective action is P M
(3)
If LE is N M and CL is P M then corrective action is ZO
(4)
Here the former propositions following 'If' are called the antecedent parts and the latter proposition following 'then' is called the consequent part. There are 35 control rules in RB-1 including the above rules and they are shown in the rule matrix table of Fig. 5. The characters such as NB, NM, NS, ZO, PS, P M and PB are fuzzy linguistic variables as shown below.
NB: NM: NS: ZO: PS: PM: PB:
Negative Big Negative M e d i u m Negative Small Zero Positive Small Positive M e d i u m Positive Big
These fuzzy linguistic variables are defined respectively by the membership functions concerned with every LE, CL, FE 2, FE 3 and U 1 ~ U 3. Let us consider the inference part (I) by way of example to explain the inference m e t h o d o l o g y when referring to Fig. 6. LE For example, when LE is -- l l . l m m , W~o ( - 11.1) and W ~L Es ( - 11-1), which mean separately the compatibility grade for LE is ZO and for LE is NS, are described as follows. W~oe(- 11.1) = 0.67 LE W~s ( - I 1-1) = 0.33
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separately the compatibility grade for 'CL is NS' and for 'CL is NB', are described as follows. I4~N~(--0"15 ) = 0-50
(7)
W~N~(--0"15)= 0"50
(8)
The other variables such as W~e~(-0"15), W~p~t(-0"15) are all '0.0'. According to these variables, the compatibility grade for each of the rules is obtained as follows.
W(ZOLE,NsCL)=min{W~(--ll'I), W(NS te, NSCL)=min{W~g(-ll'l), W(NSLE,NBCL)=min{W~g(-ll.1), W(zoLE, NBCL)=min{W~g(--ll.1),
WCsL(--0"15)}=0"50 W~N~(-0"15)} =0"33 wC~(-0"15)} =0"33 wC~(--0.15)} =0.50
(9) (10) (11) (12)
where W(A rE, Bct') means a compatibility grade for a rule'if LEis A and CL is B then ~'. The compatibility grades for the other rules are all '0"0'. Then, each of the triangular formed membership functions Xc(u), which express the proposition of the consequent part of each of the rules 'then corrective action is C', is reformed in trapezia form so that the height of the trapezium is equal to the grade W(A rE, BcL) for the rule, and then these new trapezia formed membership functions are superimposed as the following equation.
X*(u) = max {Xc(U)}
(13)
where X*(u) is a membership function which expresses the fuzzy sets of a corrective action. At last, the center of gravity of the function X*(u) is calculated by way of an output 'UI'. U~ =
X*(u)u du - 0.632 ~"X*(u) du
(14)
4.2.3 Synthesis method of U1, U2 and U3 The three corrective action signals UI, U2 and U3 which are obtained from the each inference part (I), (II) and (III) are synthesized by the following equation. U=mlf I +m2U 2 +m3U3 (O
(15)
Equation (15) is based on the control strategy of skilled operators like that where the water level difference (LE) is much larger than the other two kinds of flow difference (FE2, FE3), and the sub-valve should be adjusted to reduce
330
S. Terunurna, K. Kishiwada, H. Takahashi, T. Bjima, H. Hayashi
the water level difference regardless of the others. That is to say, the weight gain m 1, m 2 and m 3 are determined by the following rules. If L E is large then make m 1 large If F E e is large then make m 2 large If F E 3 is large then make m 3 large
(16) (17) (18)
Below 8% o f the rated reactor power, however, the feedwater flow should be regulated not so much by the reactor power as by the other outflow from the steam drum such as steam flow for a turbine gland or an air ejector of the turbine condenser. These kinds of outflow rate are very low and cannot be measured, but they would be included in the corrective flow rate concerned with F E 2 which is calculated from eqn (1). Therefore, the weight gain m 3 is made zero below 8 % of the rated reactor power regardless o f the rule (18). 5 SIMULATION 5.1 Simulation code Simulation code 'FUCTES' used for simulation analysis is made by rebuilding Fugen A T R (Advanced Thermal Reactor) Simulation Code . . . . . . . . . .
FUCTES
-
Water level Level set point Reactor power Data Processing Sub valve opening
Turbine bypass valve opening
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Control Rule Base
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Outline of'FUCTES'.
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1600 (second)
2400
3200
Simulation result o f response after manual closing of the sub-valve (manual closing of 20%).
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Simulation result of response against the changing reactor power (step change of 5%).
'FASIC' which simulates the dynamics of the main processes of a Fugen power plant including the feedwater control system. Several kinds of simulation analysis were performed as follows. (1) Response against change in the steam drum water level set point (step change from 0 to - 1 0 0 mm) (2) Response after manual closing of the sub-valve (step closing of 20%) (3) Response against change in the reactor power (step change of 5% and ramp change of 0.6%/min) In each case, added disturbance is selected to be much larger than it might be normally in the ordinary plant operation. A diagram of FUCTES is shown in Fig. 7. 5.2 Results
The simulation results are shown in Figs 8 to 11. In all cases, it is clearly shown that the steam drum water level is controlled excellently by the fuzzy
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control over such a large disturbance. The two responses which are obtained by manual control with the same operator and the response of the PI controller against the ramp change in the reactor power are also shown in Fig. 11. In the case of the PI control, the sub-valve is closed at first and then opened, because the steam generation in the reactor core becomes active with the reactor power increasing and the steam drum water level rising temporarily. In the cases of manual control and also fuzzy control, however, since the sub-valve is opened in the early stage of the reactor power increasing, the steam drum water level is kept slightly higher than the set point. Thus Fig. 11 shows that fuzzy control has good potential to reflect successfully experience gained in skilled manual operation.
334
S. Terunuma, K. Kishiwada, H. Takahashi, T. Iijima, H. Hayashi
6 DISCUSSION We plan to manufacture a fuzzy control pilot system and to perform an operation test where an operator regulates the sub-valve opening according to the output of the pilot system, and the following matters have been studied.
6.1 Calculation time In order to apply the fuzzy control pilot system to the plant, a calculation time of less than 0"5 sec/inference is necessary, because the fuzzy control control system is required to pick up the signals every second and it takes 0.5 s to display its inference procedures. In an actual pilot system, since a microcomputer would be used for economic reasons and the calculation time with the present program is about 2s, it is necessary to shorten its calculation time. The improvement would be performed by simplifying the programs and running both data processing programs and fuzzy inference programs in parallel.
6.2 Countermeasures against change in plant condition The weight gain (ml, m2 and m3) must play an important role against change in the reactor power from 0 to 18%. The logic is based on the skilled operators' strategy mentioned in section 4.2.3. However, for example, when the sub-valve is replaced with a new one which has different characteristics, it is assumed that the control rules and the membership functions have to be redetermined. We have also studied a self-organizing fuzzy controller which studies control results and improves its own control rules automatically. According to the study, it can be said that the self-organizing fuzzy controller is very useful for improving the control rules, which have been tuned up at the first stage, as a result of small changes in the plant condition.
6.3 Man-machine interface Operators suggest that the system situation described as follows should be displayed in real time: (1) condition of the parameters such as the steam drum water level, level set point and the other control variables which are used in the fuzzy control system. This enables the operator to grasp the plant condition on feedwater control at a glance and to deal with any trouble at an early stage in the event, if it happens.
,4 simulation study of a fuzzy algorithm control method
335
(2) the control rules programmed in the fuzzy control system and those ones which are used to obtain the output. This enables the operator to understand how the output of the control system has been produced. Accordingly, we plan to add a display device in an actual system in order to improve the man-machine interface.
7 CONCLUSION This paper has proposed to apply a fuzzy control method to the H W R feedwater control system. F r o m the response simulation, the fuzzy control has good potential to reflect successfully experience gained in skilled manual operation. The authors examined the performance and basic characteristics of the controller by typical step and ramp responses, since these responses could clarify the fundamental characteristics of the controller. The fuzzy control pilot system has been developed from the results, and further work on the pilot system performance evaluation using a Fugen real plant will be done in the near future.
REFERENCES 1. Zadeh, L. A., Fuzzy sets. Information & Control, 8 (1965) 338-53. 2. Mamdani, E. H., Applications of fuzzy algorithms for control of a simple dynamic plant. Proc. IEEE, 121(12) (1974) 1585-8. 3. Mamdani, E. H., Ostergaard, J. J. & Lembessis, E., Use of fuzzy logic for implementing rule-based control of industrial processes. TIME~Studies Management Science, 20 (1984) 428-45. 4. Tong, R. M., Beck, M. B. & Latten, A., Fuzzy control of the activated wastewater treatment process. Automatica, 16 (1980) 659-701. 5. Yasunobu, S., Miyamoto, S. & Thara, K., Fuzzy control for automatic train operation system. Proc. Int. Conf. on Transportation Systems, 1983, pp. 39-45. 6. Bernard, J. A., Kwok, K. S. & Lanning, D. D., Experimental evaluation of fuzzy logic in closed-loop reactor control. Trans. Am. Nuclear Society, 49 (1985) 392-93. 7. Arakawa, A., Sekimizu, K. & Sumida, S., Fuzzy logic control application for BWR recirculation flow control system. J. Nuclear Science & Technology, 25(3) (1988) 263-73.