模糊控制外文翻譯--模糊的比較研究控制，pid控制，先進(jìn)的模糊控制用于模擬核反應(yīng)堆運(yùn)行

1、<p><b>　　附錄</b></p><p>　　CONTROL, PID CONTROL, AND </p><p>　　ADVANCED FUZZY CONTROL </p><p>　　FOR SIMULATING A NUCLEAR </p><p>　　REACTOR OPERATION <

2、/p><p>　　XIAOZHONG LI and DA RUAN* </p><p>　　elgian Nuclear Research Centre (SCKoCEN</p><p>　　Boeretang 200, 8-2400 Mol, Belgium </p><p>　　(Received 15 March 1999) &

3、lt;/p><p>　　Based on the background of fuzzy control applications to the first nuclear reactor in Belgium (BRI) at the Belgian Nuclear Research Centre (SCK.CEN), we have made a real fuzzy logic c

4、ontrol 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 </p><p>　　advantageous because it is always difficul

5、t and time-consuming, due to safety aspects, to do all </p><p>　　experiments in a real nuclear environment. In this paper, we first report briefly on the </p><p>　　construction of the de

6、mo model, and then introduce the results of a fuzzy control, </p><p>　　a proportional-integral-derivative (PID) control and an advanced fuzzy control, in which </p><p>　　the advanced fuz

7、zy control is a fuzzy control with an adaptive function that can </p><p>　　Self-regulate the fuzzy control rules. Afterwards, we present a comparative study of those </p><p>　　three methods.

8、 The results have shown that fuzzy control has more advantages in terms </p><p>　　of flexibility, robustness, and easily updated facilities with respect to the PID control of </p><p>　　the d

9、emo model, but that PID control has much higher regulation resolution due to its </p><p>　　integration term. The adaptive fuzzy control can dynamically adjust the rule base,</p><p>　　therefor

10、e it is more robust and suitable to those very uncertain occasions.</p><p>　　Keywords: Fuzzy control; PID control; fuzzy adaptive control; nuclear reactor </p><p>　　I INTRODUCTION </p&

11、gt;<p>　　Today the techniques of fuzzy logic control are very mature in most </p><p>　　engineering areas, but not in nuclear engineering, though some research has been done (Bernard, 1988

12、; Hah and Lee, 1994; Lin et al. 1997; Matsuoka, 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

13、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 w</p><p>　　table for testing and com

14、parison 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-process

15、ing experiments outside the reactor, e.g., com- </p><p>　　parisons of different methods and the preliminary choices of the parameters. One solution is to make a simulation programme in a c

16、omputer, but this has the disadvantage that in which, however, the real time property cannot be well reflected. Therefore another solution has adopted, that is, we designed and made a water-le

17、vel </p><p>　　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 con

18、trol principle of BRl (Li et al., 1996a,b; Li and Ruan, 1997b). </p><p>　　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 l

19、arge 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 used to con

20、trol the water levels in T2 and T3 respectively. For example, when the water level in T2 is lower than photoelectric switch sensor 1 then th</p><p>　　COMPARATIVE STUDY OF FUZZY CONTROL </p>

21、<p>　　The Demo Model Structure </p><p>　　FIGURE 1 The working principle of the demo model. </p><p>　　BRI is a 42-year old research reactor, in which the control method is the simple

22、 on-off method. Many methods 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

23、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 demonstration, t</p><p>　　Sec

24、tion 3 introduces a PID control and its result. </p><p>　　Section 4 introduces an advanced fuzzy control which is able to self-regulate the Fuzzy control rules. Section 5 compares the previous

25、 three methods and their results. </p><p>　　2 FUZZY CONTROL</p><p>　　The fuzzy control algorithm in this demo model is a normal algorithm based on the Mamdani model. To simulate the BRl

26、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 related result ca

27、n 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</p><p>　　(fine-tuning). We choose D and DD as i

28、nputs of the fuzzy logic con- troller, and VL or VS as the output of the fuzzy logic controller. D and DD must be fuzzified before fuzzy inference. Suppose the universes of discourse (or input variables' i

29、ntervals) 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), Pos

30、itive Middle (PM), and P</p><p>　　In view of this figure, we know that the fuzzy control has quick responses (quickly approaching the set value) and small overshoot (almost invisible), bu

31、t with a small steady error (not so smooth in a steady state). </p><p>　　COMPARATWE STUDY OF FUZZY CONTROL </p><p>　　FIGURE 2 The control effect of fuzzy control to the demo model. <

32、/p><p>　　3 PID CONTROL </p><p>　　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 o

33、f the PID control needs some time, and this will 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,

34、 in our tests, VL and VS have to be controlled by the same signal. We use the following formula: </p><p>　　By substitution, </p><p>　　where U(I): control value to VL and VS at time r;

35、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 </p><p>　　FlGURE 3 The trajectory of

36、the water level by the PID control. </p><p>　　parameter and Ki = l/Ti where Ti is the integration time; Kd: the differential parameter and Kd = Td where Td is the differential time. In practice, a d

37、iscrete form of the above formula is used </p><p>　　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 i

38、s very stable (very smooth in steady states), and has quick responses too, but with visible overshoots. </p><p>　　4 ADVANCED FUZZY CONTROL </p><p>　　The kernel part of the fuzzy

39、 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 d

40、iscuss 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

41、 deriving rules can be broa</p><p>　　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.

42、In the case 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

43、well under a dynamic environment. The non-source- able methods are source-free and they produce and cho</p><p>　　genetic algorithms (GA) (Karr, 1991; Lim et al., 1996; Qi and Chin, 1997) (most

44、ly also generating membership functions and scale factors) and self-organizing controllers (SOC) (He er al., 1993; Li et al., 1996a,b; Lin et al., 1997, Procyk and Mamdani, 1979; Shao, 1988; Tanscheit </p>

45、<p>　　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

46、 complex system without a simulation model. Perhaps the SOC is the only method which has the following advantages: objective, adaptive, less computation required, more error-tolerant, and simple. </p><p>　　

47、FIGURE 4 An adaptive function is incorporated into a fuzzy control system. </p><p>　　The general principle of the SOC is that the controller monitors its own performance and adjusts its contr

48、ol 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

49、 a fuzzy control rule table and to use it to assess the performance of the controller rules) (Procyk and Mamdani, 1979), but to design such a perform</p><p>　　and system-independent, therefore

50、 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 contain

51、s 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 contr

52、oller's last behaviour i</p><p>　　4.1 The Principle of the Adaptive Function </p><p>　　Let D and DD represent error (the difference between the actual value and the desired value) and c

53、hange 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,

54、then every rule has the following form: if D is A, DD is Bi, then U is C;, i= 1,2 ,..., n, where A, Bi, and Ci are fuzzy linguistic values and i is an index pointing ou</p><p>　　where 1=NL,2=N

55、M,3=NS,4=ZE,5=PS,6=PMY7=PL. </p><p>　　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 featu

56、re 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 feature part (I), then after the fuzzy controlling using the current control ru

57、les, we measure the water level P(t + l) at the next time which has three possibilities: </p><p>　　P(l) < P(t + 1) <S; </p><p>　　P(t + 1) < S and P(t + 1) <P(t); </p><p

58、>　　P(t+l)>S. </p><p>　　FIGURE 5 Any trajectory has up to four feature sections and four feature points. </p><p>　　The related norm to guide how to change rules is the following: </p>

59、;<p>　　(i) if D(I + 1) 5 0 and DD(t + I) > 0, that is, P(t) < P(t + 1) 5 S, then r[i] = r[i] </p><p>　　(ii) if D(i f 1) < 0 and DD(t + 1) < 0, that is, P(t +1) < S and P(t +

60、 1) < P(t), then r[i] = r[i] +a, </p><p>　　(iii) if D(t + 1) > 0, that is, P(t + 1) > S, then r[i] = r[i] - a, </p><p>　　where a is a step size and a = 1,2,3,4,5,6. In case (i), the

61、 fuzzy con- </p><p>　　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 fuzz

62、y controller makes the water level P(t + 1) further from the set value S, therefore the behaviour of the fuzzy con- troller is not good, the strength is too weak and the action of the corresponding rules 'should

63、 be stronger; In case (iii), the fuzzy controller makes the water level P(t $1) overpass </p><p>　　be adjusted: </p><p>　　which means the ith rule is changed only if it is th

64、e largest activated among those activated rules 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 N

65、L(D) A NM(DD) </p><p>　　with NM(D) A NM(DD), the larger one corresponds to the rule which should be adjusted. </p><p>　　4.2 An Experimental Result </p><p>　　To guarantee no ove

66、rshoot, 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 rul

67、es have the same conclusion part though condition parts are different. Figure 6 illustrates</p><p>　　TABLE I The initial rule table for both FLCl and FLC2 </p><p>　　FIGURE 6 Comparis

68、on between adaptive fuzzy control and fuzzy control. </p><p>　　the comparison result between fuzzy adaptive control and. fuzzy con- </p><p>　　trol with the above rule base. In this exam

69、ple, the set value is 20cm. </p><p>　　Both start from Ocm. During the first stage, i.e., increasing from zero, </p><p>　　some analytic rules manipulate the valves and not fuzzy control.

70、Only </p><p>　　after the water level reaches 18cm does the fuzzy controllers start to </p><p>　　operate VL and VS. Apparently, the adaptive fuzzy control has a much </p><p>

71、　　better result by self-regulating gradually fuzzy control rules. The nor- </p><p>　　mal fuzzy control without adaptive function cannot self-regulate rules, </p><p>　　therefore it cannot dr

72、aw up the water level. </p><p>　　About 10 min later, we observe the rule tables on the screen and find </p><p>　　both rule tables have changed a lot. Table I1 gives the result of FLCl and T

73、able 111 gives the result of FLC2, where the regulated rules are </p><p>　　marked by bold fonts. </p><p>　　4.3 Some Remarks for the Adaptive Function </p><p>　　The initial

74、 idea about the previously described norms of the adaptive function, which was published in (Li et al., 1996a,b), and where a simulated inverted pendulum system and a real industrial heating system were used

75、 to make testings, gave satisfactory results . a The parameter a is influential on the overshoot and response time (rise time). When cr is too big, there will be a large overshoot possibly; when a is too smaI1,

76、possibly there will be a long response time (L</p><p>　　transformed into the initial rules of the adaptive function, the advantage being that the rise time will be shorter (Li and Ruan,

77、 1998). The rule, "if D is ZE and DD is ZE then U is ZE," should be fixed, and this will help the system to become stable. The adaptive function is very helpful in keeping the system stable in a steady s

78、tate. It cannot guarantee no overshoot if the initial rules are randomly selected. The adaptive function cannot adjust membership </p><p>　　5 COMPARATIVE STUDY </p><p>　　Each method

79、 has both advantages and disadvantages, the details of which are described in Table IV, where * is used to represent the degree of a property, and the more *, the higher the degree. For example, the realiz

80、ation of an adaptive fuzzy logic controller (FLC) is more difficult than a normal fuzzy controller, but a normal fuzzy controller is more difficult to realize than a PID controller. The PID control has the smallest

81、static error and steady error. The dynamic reg</p><p>　　For further descriptions of comparative studies between FLC and PID, readers may refer to Boverie et al. (1991), Chao and Teng (1997), Misir et

82、 al. (1996), Mizumoto (1995), Moon (1995), and Wu and Mizumoto (1996). </p><p>　　FIGURE 7 FLC is more robust than PID.</p><p>　　6 CONCLUSION </p><p>　　This paper gives com

83、parisons between fuzzy control, PID control, and advanced fuzzy control based on the experimental results of a demo model which simulates the control principle of the BR1 reactor. Fuzzy control is more robust than

84、 PID control, but with a well-characterized system, such as a reactor, it should be better to use a hybrid method which inherits the advantages of both methods. Furthermore, the adaptive fuzzy control is abl

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