1、附錄CONTROL, PID CONTROL, AND ADVANCED FUZZY CONTROL 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 reacto

2、r in Belgium (BRI) at the Belgian Nuclear Research 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

3、-consuming, due to safety aspects, to do all experiments 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

4、which the advanced fuzzy control is a fuzzy control 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 easi

5、ly updated facilities with respect to the PID control 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.

6、Keywords: Fuzzy control; PID control; fuzzy adaptive 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; M

7、atsuoka, 1990). The main reason is that it is impossible 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

8、necessary. That is why we are still conducting projects 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 alrea

9、dy many fuzzy logic control applications, it is difficult 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

10、the pre-processing experiments outside the reactor, 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 reflec

11、ted. Therefore another solution has adopted, that is, 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., 19

12、96a,b; Li and Ruan, 1997b). In this demo model, our 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

13、manual tuning at this time. VI and V2 valves are used 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 s

14、witch sensor 2 then the on-off valve Vl will be closed (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. S

15、o for TI, it is a dynamic system with two entrances 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

16、called traditional meth- ods, when compared to fuzzy 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 f

17、uzzy control on this demo model. To obtain a better 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

18、these three methods from the demo model. Section 2 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

19、methods and their results. 2 FUZZY CONTROLThe fuzzy 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

20、 with two outputs to control VL and VS and the related 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

21、 VS represent the control signal to VL (Iarge valve) 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 t

22、he fuzzy logic controller. D and DD must be fuzzified 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),

23、 Zero (ZE), Positive Small (PS), Positive Middle (PM), 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

24、-shaped functions are used to define the membership 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:

25、if D is Ai and DD is Bi, then VL (or VS) is Ci where 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 a

26、n, next drops down from 20 to 10 cm and finally keeps 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

27、OF FUZZY CONTROL FIGURE 2 The control effect of fuzzy 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 wil

28、l result in an oscillation when switching control signal 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 t

29、o VL and VS at time r; e: the set value-the real value 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:

30、 the differential parameter and Kd = Td where Td is 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

31、smooth in steady states), and has quick responses too, 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 con

32、troller. There are some papers which discuss how to 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, so

33、urceable and non-sourceable. The sourceable method means the rules are obtained from some information source, such as human experience or historical input-output data. Experience has been widely used by the fuzzy engineers, especially by the early fuzzy engineers. The problem of using human experien

34、ce is that it is time-consuming, and to some degree subjective. In order to overcome these problems, particularly avoiding the subjectivity, historical input -output data-if available can be used. To obtain rules from such data, many methods are used, one of the popular approaches is neural net- wor

35、ks (NN) (Berenji and Khedkar, 1992; Halgamuge and Glesner, 1994; Jang, 1992; Kosko, 1992; Li et al., 1995; Lin ez al., 1995; Takagi and Hayashi, 1991; Wang and Mendel, 1992). One problem of the sourceable method is that it depends strictly on the source which will be transformed into rules. In the c

36、ase that the source is noisy, then the rules might be biased. Another problem of the sourceable method is that it is usually non-adaptive, i.e., all the rules are fixed, therefore it cannot perform well under a dynamic environment. The non-source- able methods are source-free and they produce and ch

37、oose rules according to a performance measurement of the controller, such as genetic algorithms (GA) (Karr, 1991; Lim et al., 1996; Qi and Chin, 1997) (mostly also generating membership functions and scale factors) and self-organizing controllers (SOC) (He er al., 1993; Li et al., 1996a,b; Lin et al

38、., 1997, Procyk and Mamdani, 1979; Shao, 1988; Tanscheit and Scharf, 1988; Wu et al., 1992). With GA it is possible to find integratedly optimal parameters but GA is very computation rich, and furthermore, it is almost impossible to apply GA in a real complex system without a simulation model. Perha

39、ps the SOC is the only method which has the following advantages: objective, adaptive, less computation required, more error-tolerant, and simple. FIGURE 4 An adaptive function is incorporated into a fuzzy control system. The general principle of the SOC is that the controller monitors its own perfo

40、rmance and adjusts its control rules to improve performance for time-varying and unknown plants. The problem of the SOC show to perform the performance measurement. The basic way is to design a performance measurement table which looks like a fuzzy control rule table and to use it to assess the perf

41、ormance of the controller rules) (Procyk and Mamdani, 1979), but to design such a performance measurement table is also very difficult (Chung and Oh, 1993) and it is system-dependent. Based on the SOC, this section will introduce an adaptive method which uses a set of new norms to replace the ormer

42、performance measurement. The new norms are very simple and system-independent, therefore they can be easily applied to most fuzzy controllers. In this section, the advanced fuzzy control means the above SOC, in other words, a fuzzy control with an adaptive function, where the adaptive function conta

43、ins two steps: performance judgement and changing fuzzy control rules. Figure 4 illustrates how an adaptive function is incorporated into the fuzzy control system. At the beginning of each cycle, the controllers last behaviour is judged and then the rule base is changed accordingly. In this cycle, t

44、he controller will use the new rule base and output the result to the controlled object. The behaviour of the new rule base will be judged and changed again in the next cycle. 4.1 The Principle of the Adaptive Function Let D and DD represent error (the difference between the actual value and the des

45、ired value) and change in error, respectively. Let D(t) and DD(t) represent error and change in error at time t, respectively. They are two input variables. Let U be an output variable, and assume thetotal number of the rules is n, then every rule has the following form: if D is A, DD is Bi, then U

46、is C;, i= 1,2 ,., n, where A, Bi, and Ci are fuzzy linguistic values and i is an index pointing out each rules position in the rule table (or the rule data file). Useri to represent the fuzzy control magnitude (conclusion fuzzy set) of the ith rule, and let simply where 1=NL,2=NM,3=NS,4=ZE,5=PS,6=PM

47、Y7=PL. In general, a control locus may be expressed with Fig. 5, and it can be regarded as having up to four feature sections and four feature points. For each feature part, we offer a norm to guide the regulation of the fuzzy control rules. For example, the current water level P(t) is in the featur

48、e part (I), then after the fuzzy controlling using the current control rules, we measure the water level P(t + l) at the next time which has three possibilities: P(l) P(t + 1) S; P(t + 1) S and P(t + 1) S. FIGURE 5 Any trajectory has up to four feature sections and four feature points. The related n

49、orm to guide how to change rules is the following: (i) if D(I + 1) 5 0 and DD(t + I) 0, that is, P(t) P(t + 1) 5 S, then ri = ri (ii) if D(i f 1) 0 and DD(t + 1) 0, that is, P(t +1) S and P(t + 1) 0, that is, P(t + 1) S, then ri = ri - a, where a is a step size and a = 1,2,3,4,5,6. In case (i), the

50、fuzzy con- troller makes the water level P(t f 1) closer to the set value S, therefore the behaviour of the fuzzy controller is good, no rules should be changed; In case (ii), the fuzzy controller makes the water level P(t + 1) further from the set value S, therefore the behaviour of the fuzzy con-

51、troller is not good, the strength is too weak and the action of the corresponding rules should be stronger; In case (iii), the fuzzy controller makes the water level P(t $1) overpass the set value S, therefore the behaviour of the fuzzy controller is not good, the strength is too strong and the acti

52、on of the corresponding rules should be weakened. Not all rules but some of those that are activated in last cycle should be regulated. We use the following formula to describe which should be adjusted: which means the ith rule is changed only if it is the largest activated among those activated rul

53、es which have the same conclusion part. For example, (NL, NM : PL) and (NM, NM : PL) are two activated rules and have the same conclusion part, i.e., PL. Comparing NL(D) A NM(DD) with NM(D) A NM(DD), the larger one corresponds to the rule which should be adjusted. 4.2 An Experimental Result To guara

54、ntee no overshoot, the best way is to initialize all rules as the same conclusion part: NL, as shown in Table I. In this table, for example, NL at the row 2 and column 3 means: if D is NM and DD is NL then VL or VS is NL. All rules have the same conclusion part though condition parts are different.

55、Figure 6 illustratesTABLE I The initial rule table for both FLCl and FLC2 FIGURE 6 Comparison between adaptive fuzzy control and fuzzy control. the comparison result between fuzzy adaptive control and. fuzzy con- trol with the above rule base. In this example, the set value is 20cm. Both start from Ocm. During the first stage, i.e., increasing from zero, some analytic rules manipulate the valves and not fuzzy control. Only after the water level reac