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1、FOR SIMULATING A NUCLEAR REACTOR OPERATION XIAOZHONG LI and DA RUAN* elgian Nuclear Research Centre （SCKoCENBoeretang 200, 8-2400 Mol, Belgium （Received 15 March 1999） Based on the background of fuzzy control applications to the first nuclear reactor in Belgium （BRI） at the Belgian Nuclear Research

2、Centre （SCK.CEN）, we have made a real fuzzy logic control demo model. The demo model is suitable for us to test and com- pare some new algorithms of fuzzy control and intelligent systems, which is advantageous because it is always difficult and time-consuming, due to safety aspects, to do all experi

3、ments in a real nuclear environment. In this paper, we first report briefly on the construction of the demo model, and then introduce the results of a fuzzy control, a proportional-integral-derivative （PID） control and an advanced fuzzy control, in which the advanced fuzzy control is a fuzzy control

4、 with an adaptive function that can Self-regulate the fuzzy control rules. Afterwards, we present a comparative study of those three methods. The results have shown that fuzzy control has more advantages in terms of flexibility, robustness, and easily updated facilities with respect to the PID contr

5、ol of the demo model, but that PID control has much higher regulation resolution due to its integration term. The adaptive fuzzy control can dynamically adjust the rule base,therefore it is more robust and suitable to those very uncertain occasions.Keywords: Fuzzy control; PID control; fuzzy adaptiv

6、e control; nuclear reactor I INTRODUCTION Today the techniques of fuzzy logic control are very mature in most engineering areas, but not in nuclear engineering, though some research has been done （Bernard, 1988; Hah and Lee, 1994; Lin et al. 1997; Matsuoka, 1990）. The main reason is that it is impos

7、sible to do experiments in nuclear engineering as easily as in other industrial areas. For example, a reactor is usually not available to any individual. Even for specialists in nuclear engineering, an official licence for doing any on-line test is necessary. That is why we are still conducting proj

8、ects such as fuzzy logic control application in BRl （the first nuclear reactor in Belgium） （Li and Ruan, 1997a; Ruan, 1995; Ruan and Li, 1997; 1998; Ruan and van der Wal, 1998）. In the framework of this project, we find that although there are already many fuzzy logic control applications, it is dif

9、ficult to select the most sui- table for testing and comparison of our algorithms. Moreover, due to the safety regulations of the nuclear reactor, it is not realistic to perform many experiments in BRl. In this situation, we have to conduct part of the pre-processing experiments outside the reactor,

10、 e.g., com- parisons of different methods and the preliminary choices of the parameters. One solution is to make a simulation programme in a computer, but this has the disadvantage that in which, however, the real time property cannot be well reflected. Therefore another solution has adopted, that i

11、s, we designed and made a water-level control system, referred to as the demo model, which is suitable for our testing and experiments. In particular, this demo model （Fig. 1） is designed to simulate the power control principle of BRl （Li et al., 1996a,b; Li and Ruan, 1997b）. In this demo model, our

12、 goal was to control the water level in tower TI at a desired level by means of tuning VL （the valve for large control tower T2） and VS （the valve for small control tower T3）. The pump keeps on working to supply water to T2 and T3. All taps are for manual tuning at this time. VI and V2 valves are us

13、ed to control the water levels in T2 and T3 respectively. For example, when the water level in T2 is lower than photoelectric switch sensor 1 then the on-off valve V, will be opened （on）, and when the water level in T2 is higher than photoelectric switch sensor 2 then the on-off valve Vl will be clo

14、sed （off）. The same is true of V2. Only when both VI and V2 are closed V3 will be opened, because it can decrease the pressure of the pump and thereby prolong its working life. The pressure sensor is used to detect the height of water level in TI. So for TI, it is a dynamic system with two entrances

15、 and one exit for water flow. COMPARATIVE STUDY OF FUZZY CONTROL The Demo Model Structure FIGURE 1 The working principle of the demo model. BRI is a 42-year old research reactor, in which the control method is the simple on-off method. Many methods called traditional meth- ods, when compared to fuzz

16、y logic, are still very new to the BR1 reactor. One of these, proportional-integral-derivative （PID） control, has to be tested as well as fuzzy logic method. So far, we have tested the normal fuzzy control, traditional PID control, and an advanced fuzzy control on this demo model. To obtain a better

17、 demonstration, these three approaches have been programmed and integrated into one con- roller system based on the programmable logic controller （PLC） of the OMRON company. The purpose of tlus paper is to report comparative experimental results of these three methods from the demo model. Section 2

18、simply introduces a normal fuzzy control and its result. Section 3 introduces a PID control and its result. Section 4 introduces an advanced fuzzy control which is able to self-regulate the Fuzzy control rules. Section 5 compares the previous three methods and their results. 2 FUZZY CONTROLThe fuzzy

19、 control algorithm in this demo model is a normal algorithm based on the Mamdani model. To simulate the BRl reactor, we use two fuzzy controllers （FLCl and FLC2） to control VL and VS separately （note: it is possible to use one fuzzy logic controller with two outputs to control VL and VS and the rela

20、ted result can be referred to （Li and Ruan, 1997b）. Let D be the difference between the actual value （P） of water level and the set value （S） and DD be the derivative of D, in other words, the speed and direction of the change of water level. VL and VS represent the control signal to VL （Iarge valve

21、） and VS （small valve）, respectively. When D is too big, we use FLC1 to control VL （main-tuning）; When D is small, we use FLC2 to control VS （fine-tuning）. We choose D and DD as inputs of the fuzzy logic con- troller, and VL or VS as the output of the fuzzy logic controller. D and DD must be fuzzifi

22、ed before fuzzy inference. Suppose the universes of discourse （or input variables intervals） of D and DD are -d, dj and -dd,dd, respectively. We use 7 fuzzy sets to partition hem, i.e., Negative Large （NL）, Negative Middle （NM）, Negative Small （NS）, Zero （ZE）, Positive Small （PS）, Positive Middle （P

23、M）, and Positive Large （PL）. As for VL and VS, because the result of fuzzy reasoning is also a fuzzy linguistic value, the universes of discourse of VL and VS also need to be fuzzified. We use those 7 fuzzy linguistic erms too. Symmetrical trianglar-shaped functions are used to define the membership

24、 functions for input variables （Li et al., 1995; 1996a,b）, and singletons are for output variables （Ornron, 1992）. Each fuzzy controller has one rule base which contains 49 fuzzy control rules. The its rule can be represented as the following form: if D is Ai and DD is Bi, then VL （or VS） is Ci wher

25、e A, Bi, and Ci are fuzzy linguistical values, such as NL, PS, and so on. The above rule is sometimes abbreviated as （Ai, Bi : Ci）. Figure 2 shows a control effect of a synthetic control process. It first goes up from 0 to 20cm then keeps on at 20 an, next drops down from 20 to 10 cm and finally kee

26、ps on at 10 cm. In view of this figure, we know that the fuzzy control has quick responses （quickly approaching the set value） and small overshoot （almost invisible）, but with a small steady error （not so smooth in a steady state）. COMPARATWE STUDY OF FUZZY CONTROL FIGURE 2 The control effect of fuz

27、zy control to the demo model. 3 PID CONTROL In the PID control, it is difficult to control VL and VS separately like the previous fuzzy control with a good control result, because the integration term of the PID control needs some time, and this will result in an oscillation when switching control s

28、ignal between VL and VS. From this point of view the PID control is worse than the fuzzy control. Therefore, in our tests, VL and VS have to be controlled by the same signal. We use the following formula:By substitution, where U（I）: control value to VL and VS at time r; e: the set value-the real val

29、ue at time I; Kp: the proportional parameter and Kp = （1IPB） x loo%, where PB is the proportional band; Ki: the integration FlGURE 3 The trajectory of the water level by the PID control. parameter and Ki = l/Ti where Ti is the integration time; Kd: the differential parameter and Kd = Td where Td is

30、the differential time. In practice, a discrete form of the above formula is used where T, is the sample period. Figure 3 shows a result of the PID control,where PB= l5%, Ti=30s, Td= 10s. In view of this figure, the PID control is very stable （very smooth in steady states）, and has quick responses to

31、o, but with visible overshoots. 4 ADVANCED FUZZY CONTROL The kernel part of the fuzzy logic control is the fuzzy rule base with linguistic terms, though the membership functions and scale factors also have an important effect on the fuzzy logic controller. There are some papers which discuss how to

32、adjust membership functions and/or scale factors （Batur and Kasparian, 1991; Chou and Lu, 1994; Tonshoff and Walter, 1994; Zheng, 1992）. This section focuses on rules. Normally the methods of deriving rules can be broadly divided into two types, sourceable and non-sourceable. The sourceable method means the rules are obtained from some information source, such as human experience or historical input-output