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Design of an intelligent fuzzy logic controller for a nuclear research reactor
Progress in Nuclear Energy, Vol. 46, No. 3-4, pp. 328-347, 2005 at www.sciencedirect.eom_l ~~ N e E ((1) D ~R ~ C T *
Available online s c
© 2005 Elsevier Ltd. All rights reserved
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doi:l 0.1016/j.pnucene.2005.03.014
DESIGN OF AN INTELLIGENT
FUZZY LOGIC
CONTROLLER FOR A NUCLEAR RESEARCH REACTOR
F. ADDA a, C. LARBES b, M. ALLEK", M. L O U D N b
aCentre de Recherche Nucltaire de Draria,BP 43, Sebala Draria, ALGIERS 16000, ALGERIA bEcole Nationale Polyteetmique 10, Avenue Hassan Badi, ALGIERS 16200, ALGERIA ABSTRACT The main objective of this paper is to design an intelligent controller system based on the concepts of fuzzy logic. This latter will be used to control the power of a nuclear reactor. The principle of this controller is based on rules established from experiments used with a classical controller and from the knowledge and the expertise of the operators of the reactor. This intelligent controller could be used in parallel with the actual system, which is semiautomatic, as a decision aided system to assist the operators in the control room. KEYWORDS intelligent controller system, fi!~¢ logic, nuclear reactor, decision aided system. © 2005 Elsevier Ltd. All rights reserved 1. INTRODUCTION The applications of fuzzy logic cover a wide range of areas (Zadeh L. 1994). Fuzzy logic control being one of the most active and used area, its introduction in the nuclear industry is however quite recent (Ruan D., 1995), (Ruan D., 1998), 01uan D., J. Van Der Wal A., 1998). Fuzzy logic control offers many advantages over the conventional control methods. The exact knowledge of the mathematical model of the system is not necessary; it is robust, flexible and well adapted for non linear systems. It offers as well simplicity, ease of implementation and fast execution to make it suitable for real time systems. The safety standards required in the nuclear domain necessitate more severe design criteria in reactor control. This prompted the development of a new generation of robust and intelligent controllers. The combination of fuzzy logic control techniques with human intelligence and expertise is very promising. The main objective of this paper is to demonstrate the use of an intelligent fuzzy logic controller (FLC) in parallel with a classical controller for monitoring and supervising a nuclear reactor in real time. The principle of this controller is based on rules established from experiments used with the classical controller and from the knowledge and the expertise of the operators of the reactor.
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2. BRIEF REVIEW OF FUZZY SETS, FUZZY LOGIC AND FUZZY CONTROL In standard set theory (Driankov D. et al., 1992) (Pedrycz W., 1993), (Zadeh L., 1994), (Buhler H., 1994), an object is either a member of a set or it is not a member at all. Given a universe of objects U and a particular objectx e U , the degree or grade of membership ,uA(x) with respect to a set A c U is: 1 ifx~A /~A(X)=
(1)
0 if x ~ A
,UA(x) : U --~ { 0,1)
The function is called characteristic function in standard set theory. Often, a generalization of this idea is used, for instance, to handle data with error bounds. A degree of membership of one is assigned to all the numbers within some percent error, and all the numbers outside that interval have a degree of membership of zero (Fig. 1. (a)). For the precise case, the membership degree is one at the exact number and zero everywhere else (Fig. 1.(b)). L. Zadeh proposed a further generalization in which some objects are more member of set than others. The degree of membership takes on various values between zero and one, where a zero value indicates complete exclusion and a value of one indicates complete membership. For instance, to express that a temperature is around 25, we may use a triangular membership function (Fig. 1(c)) with its peak at 25 to express the idea that the closer a number is to 25 the better it qualifies.
(a)
u
(b)
u
(e)
Fig. I. Membership functions for crisp and fuzzy data Formally, let U be a collection of objects denoted generally by { u } U is called the universe of discourse and may be continuous or discrete. A fuzzy set A in a universe U is defined by a membership function/G which takes values in the interval [0,1]. u
[o, U
(2)
We can, also, define a fuzzy set as a collection of ordered pairs of a generic element u • U and its grade of membership function'UA(u), i.e.: N
(3) Where N is the number of elements of U. Note that the symbol Y~ here denotes a collection of discrete elements. The corresponding notation for a continuous universe of discourse U is
(4)
A= U
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The support of a fuzzy set A is the crisp set of all points u in U such that AtA > 0. A fuzzy set whose support is a single point in U with/t A = 1 is called a fuzzy singleton. In fuzzy controller design, we often encounter situations where two or more fuzzy sets are involved. For example, in constructing a fuzzy rule, satisfaction of either one of two fuzzy conditions leads to a certain consequence or action. Thus, formal treatments of fuzzy operations are needed. Below are some important ones. Let A and B be two fuzzy sets in U with membership functions/.ta and/.zB, respectively. The union (A u B ) is defined by
A u B --~ max {pA(U),t~(U)}/U F o r u ~ U .
(5)
U
The intersection (A ~ B) is defined by
A n B = ~ nfin {it A(u), i.t~(u)}/u For u ~ U.
(6)
U
It is quite common to use qualitative expressions instead of quantitative values for words that denote measures and counts, such as fairly high, quite a few, not many. This idea leads to the concept of a linguistic variable. A linguistic variable takes on one of a set of labels, i.e., expression, as its value. For instance, the linguistic variable Temperature could take one of the members of the set {low, medium, high} for its value. The labels are given meaning by associating with each one a fuzzy subset of some universe of discourse (Fig. 2.). ~Temp
p
0
25
50
75
100
Tern~rg~re (°C)
Low Medium High Fig. 2. Linguistic variable T e m p e r a t u r e k"
il
Kn°wlede~
FUZZY
Fuzzification
Sensors
-
FUZZY
(crisp)
i
Actuators
Fig. 3. Basic structure of fuzzy logic control
Design of an intelligent fuzzy logic controller
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The structure of a process controlled via a fuzzy controller is shown in Fig.3, which presents the basic components of a filzzy controller: a fuzzification interface, a knowledge base, a data base, inference procedure, and a defiJzzification interface. Usually the fuzzy control rules are expressed in the form of a fuzzy conditional statement Ri: IF u is Ai and.., and v is B~, THEN w is C~, where u, v, and w are fuzzy variables, and A~, B~, and Ci are fuzzy subsets in the universes U , V, and W. The fuzzy rule Ri can be regarded as a fuzzy relation from universe (U and ... andV ) to universeW. If there are n rules, the rule set may be represented by a union of these rules: R = RI ~ R2 ~ ... ~ R,. The resultant w can be induced by the compositional rule of inference w = (u And ... Andv) o R where o denotes the compositional rule of inference. For example, using the sup-min compositional rule, we have: In particular, the most frequently used fi,zzy inference methods in fi)zzy control are Mamdani's fuzzy
pc(w) = { min { lG(u) ..... IUB(V),I~R(U..... V,W)} }.
(7)
implication and Larsen's product fuzzy implication. If the fuzzy variables u 1, v2, and w3 are fuzzy singletons, the inferred results of both implication methods will be the same. wi = nfm { IL~(uo)..... u~,(vo)l • c;
(8)
where uo, vo and we are fuzzy singletons, and Ci is the singleton value of w using the i th rule. After a fuzzy control action is inferred, a non fuzzy control action that best represents the decision is needed. Although there is no systematic procedure to choose a defuzzification strategy, the most common include: the MAXimum criterion method (MAX), which produce the point where membership function of the control action reaches a maximum value; the Mean-Of- Maximum method (MOM) which represents the mean value of maxima when they are not unique; and the Center-Of-Gravity (COG) which generates the center of gravity of the membership function area of the control action (Fig. 4.).
w COG
Fig. 4. Defuzzification strategies
3. MATHEMATICAL MODEL AND TEMPERATURE FEEDBACK In this model, the reactor is described by the well known point kinetics equations with six delayed neutron groups. In this case, the neutron density n (or power level) and the precursor number density are defined by the following equations (Furet J., 1968): where: dn dt
(9)
6
0
~=x
dct = /3i n - 2 c i dt 8
i = 1,...,6
(10)
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ci: i t~ group precursor concentration
~: ith group delayed neutron decay constant (s1)
13i: ith group delayed neutron fraction
0 • Neutron generation time (s)
13' Effective delayed neutron fraction
p • Reactivity
In the simplified case where only one group of delayed neutrons is taken into consideration, the point reactor kinetics equations (9) and (10) become dn dt
-
p - fl 0 -
-
+Ac
n
(11)
dc ~ =
~ n
dt
-
0
.~,c
02)
6
with i=1 ~,i
The three most important parameters characterizing the kinetic behaviour of a nuclear reactor are the reactivity p, the neutron generation time 0, and the effective delayed neutron fraction 13. A variety of experimental techniques have been developed to measure these parameters. Although the above system of equations is not linear, the transfer function of the reactor can be defined around the operating point which corresponds to the critical regime p~0,
n=no,C=Co
(-~t ) = o
(dc.~_)= 0
(13)
If a small sinusoidal reactivity with a magnitude Ap and frequency io~ = p is added to the operating point, then: n = no + &,a,
c = co + Ac,
p = Ap
(14)
The zero-power reactor transfer function is then given by the following expression: The curves in Fig.7 show that the gain is very high at low frequencies, this implies that the reactor is An
1
p+2
neAP - O p(p + 2 + ~ )
(15)
unstable in this region; the gain is constant between fl = M2rc and f2 = 13/2zc0. On the other hand, f2 is inversely proportional toO, then the length of transfer function plateau is inversely proportional to the neutron generation time.
3.1 Behavior of the reactor power with temperature feedback Let us now return to consider the dynamic behaviour o f a reactor with feedback, in particular, we will consider the effects of temperature feedback. The block diagram of the reactor control loop with temperature effects is given in Fig. 5.
333
Design of an intelligent fuzzy logic controller
Ap~
n ~[
r~actor
Fig. 5. Reactor control loop With regard to the reactor which has enriched uranium and moderated water, we can use the following conditions (Fig. 6): Te
Moderator Wa~rflow
Q
< Exchanger
< Ts
Fig. 6. Reactor cooling Te is the inlet temperature which is constant. We take into account only the moderator temperature coefficient a which is negative. • Ts is the outlet temperature. The average temperature of the moderator is defined by: Te + Ts Tin= 2
(16)
The neutron power is defined by: n = Q C ( T s - Te) + M C dTm dt where: Q is the flow rate of water. M is the mass of water contained m the reactor core. C is the water specific heat. In the steady state operation, we have:
no
=
QC(Tso re)
Tmo
-
-
with the reactivity disturbances around the equilibrium point
Tm = Tmo + ATm
n=no+An
(18)
Tso + Te 2
Ts = Tso + ATs
07)
(19)
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We can define the reactor transfer function with temperature feedback by:
(I + 2~Q p)(p+I)
An
(20)
noAP a--~-(P+2)+OP(P+2+~)(~Q p + I ) 2 Q c The coefficient of moderator temperature (x acts as a network feedback, with a gain ~z/2QC and a time constant x = M/2Q. The frequency gain and phase curves are given in Fig. 8 with: Q = 220m3/h, M = 40Kg, o~ = -0.00015/°C. At low frequencies, the gain leads to 2QCkx whatever no, the reactor is stable in this region. At high frequencies the reactor acts as if there is no temperature coefficient, it behaves as a zero power reactor. We conclude that reactivity variation with temperature is the main feedback mechanism determining the inherent stability of a nuclear reactor with respect to short-term fluctuations in power level. 200
200. , ^1~o~- .... ~ .......... g----_ !
~" I ° ° i - - - ~ - ' I
I
I
!
...........
......
_.,_
t0,4
I
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10.2
. . . . . . . .
10 0
L _.I
I + ............
"~ 100 I ' - ' - - - ' - ] . . . . . . . . . . . .
~
00
ol
10 2
,
.,~. . . . . . . . . . .
,
10 ,4
¢ ................
. . . . . . . . . L, . . . . . . . .
!
I 10 "2
.....
~
/
~ . . . . . . --]
&'- - - I
,'--1
10 0
10 2
t0 °
10 2
frequency (Hz)
.........
10-2
I
10 .4
frequency (Hz)
:oo :
i i +.....................
10 0
.100 [ IO 2
Fig. 7. Gain and phase without thermal effect.
i 10,4
~
I 10 -~
,
i
Fig. 8. Gain and phase with thermal effect.
4. REACTOR INSTRUMENTATION AND CONTROL
4.1 Introduction The instrumentation and the control systems are often considered as an essential element in a nuclear reactor installation. It is in the control room where all the decisions are taken on the basis of the important number of the incoming information. The instrumentation and the control systems of the reactor act as an interface between the reactor and the operators. They generally achieve the following functions: •
Measurement of the essential parameters which characterize the operating mode of the reactor, on the basis of which, the operator will be able to proceed to the adequate action.
*
Production of the logical signals in case of exceeding the prefixed thresholds. To each threshold level corresponds a logical signal which is susceptible to manipulate a security action such as: alarms, inhibition of motion of control rods, automatic introduction of control rods, emergency stop or SCRAM, evacuation ...
Design of an intelligent fuzzy logic controller
•
335
To act on organs of command manually or automatically in order to modify operating conditions.
In the conception, it is necessary to take into account the following conditions: • e
The starting and the operation of the reactor must be achieved with safety. One must ensure the emergency stop of the reactor (SCRAM) against any abnormal event that could OCCurS.
4.2. Control loop of the Reactor The considered reactor is controlled by five control rods: two safety rods (SR), two compensation rods (CR) and one fine tuning rod (FR). The value of the reactivity depends on the temperature effects and on the control rods efficiency. The control rods motions are achieved by stepper motors. The safety and compensation rods have a constant velocity of 0.53 mm/s and a total coarse of 640 mm. The fine tuning rod has a variable velocity from 0 to 10.33 mm/s with the same range of 640 mm. The block diagram of the reactor control loop is shown in Fig.9. VR m
q
P /2~cic
th
:~ Pc
,~
PJ
N u c l e a r ~1 ic
1 Reactor'~
MPA
classical controller of fine tuning rod
Stepper Motor
classical
controller of oompensation rod
Stepper Motor
-~
DOttF
thermal _ circuits r
Fig. 9. Block diagram of the reactor control loop The current delivered by the ionization chamber is proportional to the neutron flux present in the reactor core. This current is converted to voltage VM by a linear amplifier and it is compared with the reference voltage VR. We obtain e = 1 - VM/VR (%), this value represents the relative neutron power margin (difference between the measured power and the desired power). If e exceeds 7%, the automatic control is removed. The period T is added to get an activation signal of the automatic monitoring SAPA proportional to s + T variable between -10V to +10V. This signal drives the logics of the motion rods and their command to produce the insertion or the withdrawal of the fine tuning rod with a proportional speed to this signal. This is true as long as the fine tuning rod is confined within the interval boundaries (40%-60%), otherwise the selected control rod CR1 or CR2 is used to adjust the power and to bring back the fine tuning rod to its initial position. The reactivity is the amount of the temperature effects, the fine tuning rod effect and the compensation rod effect.
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E Adda et al
5. EXPERIMENTAL EVALUATION AND VALIDATION OF THE PROPOSED MODEL One test carried out in the reactor was to increase the power from the level 0 to 500 KW and then from 500KW to 750 KW (Fig. 10.). The following parameters were recorded: the power, the position of the control rods, and the rate of change of power. The reactivity, which does not have a direct measure, has been determined by the position of the control rods and their curves of efficiency. These curves show that the power evolution at every moment is function of the reactivity and the rate of change of power. In the transient operation, conditions of non-linearity owed to the delayed neutrons effect deduce a very high response time. The fact also that the motion of control rods is constant and the efficiency of these rods is not a linear function of their position appear an unavoidable overshoot during the transition. In order to simulate and to validate the model of the reactor represented by equations (6) and (7), we approached the experimental curve of reactivity by a linear function (Fig. 11.). Results obtained by simulation (Fig. 12.) show that there is a good similarity agreement with the experimental results, therefore the approximation done on the model taking into account only one delayed neutron group and considering that the reactor is point are acceptable. POWER 750 K~ ..................................
500 K ~
---~j~
/
J
250K~
' 10:10
10 I20
'
10 I30
'
Time (h:mn:s)
' 10:40
Fig. 10. Experimental power evolution between 2 levels ( 500 Kw and 750 Kw )
REACTIVITY O,OO03
]J~
0,¢¢02
Measuredreactivity
o,oool o,oooo
.o,oool .-o,ooo~
i "10:12
/ 1~19
| 10;26
! 10~33
i 10:40
Time (h:mn:s)
Fig. 11. Curves of measured and approximated reactivity
Design of an intelligent fitzzy logic controller
337
9
1.8 x l O
o
i
I
I
1
g / i
i
v
/
t
12F---
0.6 0
I
i
500
J i [
. . . . . . . . . . . . . i...................
J
i
iO00
i
l
'1500
2000
times
Fig. 12. simulated power evolution between 2 levels (500 Kw and 750 Kw)
6. BUILDING OF THE KNOWLEDGE BASE
6.1. Knowledge Acquisition An essential task in the design of an FLC or a rule based system is the knowledge acquisition process (Bemard J. A., 1986), (Bernard J. A., 1988). If this is not done in a thorough and rigorous manner, then the controller cannot function correctly. To collect the knowledge necessary to the design of the FLC, the following techniques were used: •
Attentive observation of the operators during the increase and decrease of the power of the reactor, and taking notes about their actions and on the instruments they watched: the current which is proportional to power and neutron density, rate of change of power, position of the control rods, difference of inlet and outlet temperatures in the reactor core...
•
Acquisition of the nuclear and conventional parameters at different times when the reactor is in operation to monitor its behaviour during the change of levels of the power.
•
From the evolution of these parameters, some operator's actions can be deducted.
•
A questionnaire was established to the operators and their answers are verified attending to operation of the reactor such us the experience is well prepared and the level of the power predefined. These questions are about : o
The reactivity which is the fundamental parameter for controlling the power of a nuclear reactor.
o The important parameters used in the control process of the reactor for the dynamic operation and for the steady state operation. o
The selection of control rods that depends directly on experiments to carry out in the reactor.
o
The precautions to be taken on approach to full power of the reactor. Full power is accomplished with undershoot to avoid the shut-down (SCRAM) of the reactor while respecting limits of operation and safety. Insertion of the control rod will begin when we reach 80% of full power. For the other power levels, the insertion will begin at 90-96% of the desired level.
E Adda et al
338
2=l
os~
j /
/ Fig. 13. D~erem stepsused m flaebmldi~ of~e knowledge based system
Organization and representation of the knowledge base After the knowledge acquisition of the most important parameters, it is necessary to accomplish the following three objectives: •
Identification of the parameters used for the control process such as (power margin, period...).
•
Deduce the verbal labels and their ranges that are used by operators to classify measured value of each parameter.
•
Establish the conditional rules that relate the linguistic labels to specific control action. Power mismatch between the
Rate ofpower variation ]
Motion f o r control Rod
actual power and the desired Dower c
I
,
I
Position o f the
i '¸
2....
~
ftne Rod
" ~
[
......
"~i
:
~
5 ~
1
. ........
Power mismatch between the actaal power and the desired power~ .... d
Motion for thefine Rod ]
1 i~i
i 'v¸i " : ! ~
Motion for control Rod
Fig. 14. Organization and representation of the knowledge base
}
("i
Design of an intelligent fuzzy logic controller
339
7. DESIGN OF THE FLC In the conception of the controller, it was possible to consider only one fuzzy logic controller but the rule base in this case will be cumbersome and the operating modes of the reactor would be difficult to optimise. One has to make a compromise between the speed, the precision and the stability of the system at any mode of operation. For this reason, two fuzzy logic controllers FLC1 and FLC2 were proposed, one for each state of operation: the transient (dynamic) state operation and the steady state operation (Fig. 15) (Adda F., 2001).
~
MORF
~"
MORC
FLC2 PRF
~ MORC
Fig. 15. Fuzzy logic controllers (FLC1 for the transient state operation and FLC2 for the steady state operation) The fuzzy logic controller FLC1 will be used to improve the response time and to minimize the overshoot in the transient state operation. The controller fuzzy logic FLC2 will serve to improve the stability and the precision of the system in the steady state operation. The input variables are: • x is the Power rate (%/s) • e is the relative neutron power margin (%) • PRF is the position of the fine tuning rod (%) The output variables are: • MORC : motion of control rod (mm/s) • MORF : motion of fine control rod (mm/s) The magnitudes of the MORC and the MORF are the speed of the rod, the sign gives the direction.
7.1. Characteristics of FLC1 The design of FLC1 was based on the knowledge and the experience of the operators of the nuclear research reactor. The fi, z~y logic controller FLC1 is depicted in Fig.16 (for an increase of power) and in Fig.17 (for a decrease of power). It is characterized by its: * Membership Functions for the input variables. • Membership Functions for the output variables. • Rule base. * Relation between inputs and outputs.
E Adda et al
340
AND method OR method Implication Agregation .....
~
,
(Prod) (Sum) (Prod) (Max)
,,
,
....
_
i ....
ill
:';; ...................... ,; ...................... ~ . . . . . . . . . . . . . d ................. A
I "-\ /" ,,i "×" ;i[ ~ / //" "\ " " , ~LL-.~-. . . . . . . . . . .
", ..../ "<, / ". / i Y¢ k< -< ! <'"~'~" / " " " " \~ ~'/ / "", \ ]! -/ / ~
. . . . . .
.=.,.',_.,LL _ _
__ _..._Ld_
......
Membership
Functions for
PVS IPS
N 8
NVL
Membership Functions for the input variables ( ~ and P.)
WB
the output v a r i a b l e
[ PM
MORC WBM NA
IPL
I PVL
IVB
IVB
NL
WB
WM
NA
IVB
IVB
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m
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IB
IVB
IVB
1VB
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rVB
WB
for FLC1 ii
Relation between the output variable and the input variables
Fig. 16. Characteristics of the rule based fuzzy eontmllerFLC1 (for the transient mode when the power is increased)
NVL NL NN NS NVS NNZ PVS PS PN PL PVL PM
: : : : : : : : : : : :
Negative very Large. Negative Large. Negative Normal Negative small. Negative Very Small. Negative Near Zdro Positive Very small. Positive Small. Positive Normal. Positive Large. Positive very large Positive Medium
WB WLM WM WS NA IVS IS IM ILM IB IVB
: : : : : : : : : :
Withdrawal Big. Withdrawal larger than the medium. Withdrawa Medium. Withdraw Small. No Access. Insertion Very Small. Insertion Small. Insertion Medium. Insertion Large than Medium Insertion Big. Insertion Very Big
Design of an intelligent fuzzy logic controller
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!"\, /; "\ /' ", / \\ //1
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:
i
111ill Membership Functions for the output variable (MORC)
':/",.,,.3",. :.':",...>'., i
~v~
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WB
WB
WB
WB
NA
PVS
WB
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WB
WB
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WB
WB
NA
PM
WB
WB
WB
IS
IM
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WB
WB
NA
LM
IB
Rules base for FLC1
r,
Relation between the output variable and the input variables
Fig. 17. Characteristics of the rule based fuzzy controller FLC1 (for the transient mode when the power is decreased)
7.2. Characteristics of FLC2 The conception of FLC2 is based on the classical semi-automatic controller functions, its characteristics are given in Fig. 18.
342
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AND method (Prod) % /'',
OR method (Sum) Implioation (Prod) Aggregation (Max)
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WM
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"IMp' : :~ ~N,SL:, •
IS
WS
IB
NA
:~ IS
WM
IB
NA
8
WB
NA
NM
WM
NA
NS
WM
IS
WB
IS
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:
IB
,;~!); :, ::': WM
IS
~
::: ::'
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w~
is
ws
is
PM
WB
IS
ws
i tM
PB
WB
IS,
WS
~S
~,):[i
.
~':: :
'N,~
Rule base for FLC2 ( S t e a d y state m o d e )
,
I!,
i
Membership Functions for the output variable (MORF) III
I
'
I
d~
: q
Membership Functions for the output variable (MORC)
III
I
I
I
Y ?
Relation between the output variables and the input variables
Fig. 18. Characteristics of the rule-based fuzzy controller FLC2 (steady state mode)
NB: NM: NS: ZE: PS: PM: PB:
Negative Big. Negative Medium Negative Small Zero Positive Small Positive Medium Positive Big
LI: Insertion Limit PLI: Near Insertion Limit AC: Around Center PLW: Near Withdrawal Limit LW: Withdrawal Limit
IB : Insertion Big IM : Insertion Medium IP : Insertion Small NA : NO Access W S : Withdraw Small WM: Withdraw Medium W B : Withdraw Big
Design of an intelligent fuzzy logic controller
343
8. VALIDATION AND EVALUATION OF THE CONTROLLERS
The simulation diagram for the Fuzzy Logic Control based on the controllers FLC1 and FLC2 is presented in Fig. 19. n~
&ToC
FLCI
I
"1 , ~
"
l
..........
~'-~
~o/0
MORC
,,
VI.C2
Fig. 19. The Fuzzy Controllers FLCI and FLC2 m closed loop with the nuclear reactor The main blocks constituting this diagram are: - The nuclear reactor core. The input parameter for this block is the reactivity PT, which is the sum of all the reactivities: PRC for the control rods, PRF for the fine tuning rod and pth for the thermal effects. The output parameter is the neutron density. - The FLC1 controller is intended for the transient state operation. Its input parameters are the rate of power evolution 3, the power difference between the actual power and the desired power, e. Its output parameter is the motion of the control rod MORC. The FLC2 controller is intended for the steady state operation. Its input parameters are the position of the fine tuning rod PRF and the power difference between the actual power and the desired power e. Its output parameters are the motions of the fine tuning rod MORE and the control rod MORC. -
The Fuzzy controller FLC1 monitors the big changes in power requests, at start and at any stage of operation, in order to improve the response time and to minimize the overshoot. The FLC2 controller minimizes the power difference obtained by FLC1 in order to improve the stability and the precision of the system. The reactivity is determined by measurements of the inserted positions (heights) of the control rods and the use of the efficiency of the respective rod. These positions are obtained after integration of the output signals of the controllers. This loop has been tested under normal and degraded conditions (i.e. taking into account intemal and external disturbances).
344
E A d d a et al
Power rate (%/s)
Neulron Density (n/em3)
II Precision
-2%
~n~c
52.8s 66s 1.3 l*/ds
ten tr
x$O i ~4
f.
12
praa~c
e
I,T so
o o
too
~
too
150
Time (s)
tso
99,677pcra
PRCmax
51,89%
t/
45.8s
~(a)
Z.31*~/s
¢(tO
-19.1%
/t t= 14L45s p =OPcra, r=O°/ds PRC=
50.04%
Time (s)
PRC (%)
MORC (mm/s)
Reactivitv (~erturbation) t,2 x 1 0 "~
/\
04
0~ AIr 02
0
-0.2
....
FI'
0
5O
100
0.8 / 0.8 0A 0.2
150
Time (s)
50
lOO
'
0
150
Time (s)
Time
(s)
Fig. 20. Simulation results of FLC1 for an increase of power from 250Kw to 750Kw (neutron density from 0.6xl0+9n/em3 to 1.2x10+9 n/era3) with positive perturbation on the reactivity Power rate (%/s)
Neutron Density (n/em3) xlo*
tr zraax pmax
2 ~8
-O.4
PRCmax
tat r(t~t)
°°
~4 -oa 12 ~
10O Time (s)
150
loo
Time (s)
32,907% -0.73%/s 17,7% 83s O'O0106°/ds 2.75%
S (t,~) ti r(ti) s (tO ~z t= 135s r= O°/ds PBC=
PRC (%)
MORC (ram/s)
o/?
p =OPera,
49,913%
Reactivity (due to thermal effect) • 1o "'
03 02 ol
+2,75% 49,17s 55s -0,824%/s -72,494pore
Precision td
50.5
/
~
-
-0t -o2
as
~r
49
-O3
48
-o4 -0s
47 S 5O
loo
Time (s)
5O T i m e ' [ s )
/ 50
100
150
Time ($)
Fig. 21. Simulation Results of FLC1 for power decrease from 750Kw to 500Kw (neutron density from 1.Sxl0+gn/cm3 to 1.2x10 +9n/cm 3) with thermal effect.
345
Design of an intelligent fuzzy logic controller
Neutron Density (n/era3)
Power rate (%/s)
xlO=
Precision=
1,1 135
t,=
,,
pRF~= p,,~= r~= MORF,,~= d~t = 9s ~=0% /s t=80a p=Opcm
125 12
0.08% 0.8359s 0.987s 43.1095% 16.42 pore 3.4°/ds 5.86 mm/s p=Spom PRF=41.8%
t,,=
i
1.1 105 1oo
15o
o
Time(s)
5o
leo
~so
Time (s)
Reactivityintroducedby the fine tuning rod
PRF(%)
MOFR (mm/s)
x to ' 5O
4S
s...._
1
4O 0.5 35
o
50
100
150
~oo
5o
o
~5o
1~o
%
Time (s)
Time (s) )
5o
~o
15o
Time (s)
Fig. 22.Simulation Results of FLC2 for a relative error of-2% and free rod position at critic state FRPc = 41.8%
Neutron Density (rdcm3)
Power rate (°/o/s)
xlo' 1.28
I
1.2~ 1.24 1.Z2
1.2 .
L
1,18 50
0
100
150
200
o
250
50
loo
150
PRF (%)
0.0817%
t~= t,= PRF~= P"~=
0.917s 2.2789s 39.416% -30.74pca~
z =
.6.4o/ds
MORF~= MORC~,~= A t t=Ss M O R C = ?t t=95s p=Opcm P R F =
20O
Time (s)
Time (s)
Precision=
-lO.33mm/ -0.01mm/s 0mm/s 46.70%
Reactivityintroduoedby the fine tuning rod
PRC (%)
55 50
1. f L
45
L
f
40
o1\
\
35 0
loo
150
Time (s)
200
25o
0
50
100
150
Time (s)
200
250
50
100
150
Time (s)
Fig. 23. Simulation Results of FLC2 for a relative error o f +4% and t'me rod position at critic state PRFc =41.8% with thermal effects For (500KW--) neutron density of 1.2xl0+9n/cm3).
200
346
E Adda et al
8.1 FLC Results Interpretation The FLC1 controller was tested for different power levels and with and without the introduction of the thermal effect. The simulation results obtained, Fig. 20 and Fig. 21, show that with FLC1 abrupt movement of the control rod can be avoided which eliminates power peaks. In addition, a good precision (= ± 2.5 %) and a good stability were obtained for all power levels and during an increase and decrease of power. The time response was considerably reduced within the allowed safety standards (power rate less than the maximum authorized). The FLC2 controller was tested with positive and negative errors variations and with and without the introduction of the thermal effect. The simulation results, with and without the thermal effect, show that there is rapid error compensation and a good precision of +0.08 for an error less than + 4 %. These results were compared with those obtained by the actual semi-automatic controller for different power levels. They confirm that with FLC1 and FLC2 much better performances are obtained. Other tests were conducted as well, for example, in case where the fine rod is outside the linear zone. The fuzzy logic controllers acted in the same manner as the classic controller by compensating the error with the control rod and repositioning the fine rod in the linear zone which is between 40% and 60% (Fig. 23.).
9. CONCLUSION AND FUTURE DEVELOPMENT In this work, a rule and a knowledge based fuzzy logic controller was developed. The used rules model the classical controller and the operator's knowledge and expertise. Simulation tests were carried out on this controller and showed that the control strategy was considerably improved comparing to the semiautomatic controller. The fi~z~ logic controller has successfully simulated and translated the operator's decisions under normal and degraded conditions. This controller improved the performances of the reactor in terms of the response time, the overshoot, the stability, the precision and the robustness which are required for its safe exploitation. Further works will be carried out in the near future to resolve the problem of the commutation between the two controllers FLC1 and FLC2 which is the main problem encountered in this controller. Another perspective is to design and built an intelligent simulator based on this controller and on an e-learning technologies for the training of operators.
REFERENCES Adda F. (2001), Application de la Commande Floue au ContrOle d'un R~acteur Nucl~aire de Recherche. th~se de magister, Eeole Nationale Polytechnique Alger. Bernard J. A., Laning D.D. (1984), Digital Control of Power Transients in a Nuclear Reactor. IEEE Transacaons on Nuclear Science, Vol. NS-31, No 1, February. Bernard J.A., Ray A., Kwork I~S., Lanning D.D. (1985), Design and Experimental Evaluation of a Fuzzy System for the Control of Reactor Power. American Control Conference, Vol. 3, pp. 1466-1474 Boston, MA, June. Bernard J. A. (1986), The Construction and Use of a Knowledge Base in the Real Time Control of Research Reactor Power. 6th symposium on power plant dynamics control, and testing, vol. 57, pp. 1-25. Knoxville, April. Bernard J. A. (1988), Use of a Rule-Based System for Process Control. IEEE Control Systems Magazine, pp. 3-13.
Design of an intelligentfuzzy logiccontroller
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Driankov D., Hellendoorn H., Reinfrank M. (1992),An Introduction to Fuzzy Control Springer-Verlap. Duderstadt J.J., Hamilton L.J. (1976), Nuclear reactor Analysis. John Wiley & Sons, Inc. Furet J. (1968), ContrOle et Electronique des R~acteurs Nucl~aires. Masson et Cie. Hansruedi Buhler (1994), R~glage par logiquefloue. Presses polytechniques et universitaires romandes. Jamshidi M., Vadiee N.(1993), Timothy J. Ross, Fuzzy Logic and Control, Software and Hardware Applications. PTR Prentice-Hall, Inc. Pedrycz W. (1993), Fuzzy Control andFuzzy Systems, Second extended edition, Research Studies Press LTD - John Wiley & Sons Inc. Ruan D. (1995), Fuzzy logic in the nuclear research world. Fuzzy Sets and Systems, 74 (1) 5-13. Ruan D. (1998), Intelligent systems in nuclear applications. Int. J. of Intelligent Systems, 13 (2/3) 115-125. Ruan D., Li X. (1998), Fuzzy-logic control applications to the Belgian Nuclear Reactor 1 (BR1). Computers and Artificiallntelligence, 17 (2-3) 127-150. Ruan D., Van Der Wal A. J. (1998), Controlling the power output of a nuclear reactor with fuzzy logic. Information Sciences, 110 151-177. Zadeh L. (1973), Outline of a New Approach to the Analysis of Complex Systems and Decision Processes. IEEE Trans. Syst. Man and Cybernetics, vol. SMC-3, pp. 28-44. Zadeh L. (1988), Fuzzy Logic. IEEE Computer, pp. 83-93, April. Zadeh L. (1994), The Fuzzy Systems Handbook. Earl Cox The Metus Systems Group Chappaqua, New York.
Available online s c
© 2005 Elsevier Ltd. All rights reserved
ELSEVIER www.elsevier.com/locate/pnuc ene
Printed in Great Britain 0149-1970/$ - see front matter
doi:l 0.1016/j.pnucene.2005.03.014
DESIGN OF AN INTELLIGENT
FUZZY LOGIC
CONTROLLER FOR A NUCLEAR RESEARCH REACTOR
F. ADDA a, C. LARBES b, M. ALLEK", M. L O U D N b
aCentre de Recherche Nucltaire de Draria,BP 43, Sebala Draria, ALGIERS 16000, ALGERIA bEcole Nationale Polyteetmique 10, Avenue Hassan Badi, ALGIERS 16200, ALGERIA ABSTRACT The main objective of this paper is to design an intelligent controller system based on the concepts of fuzzy logic. This latter will be used to control the power of a nuclear reactor. The principle of this controller is based on rules established from experiments used with a classical controller and from the knowledge and the expertise of the operators of the reactor. This intelligent controller could be used in parallel with the actual system, which is semiautomatic, as a decision aided system to assist the operators in the control room. KEYWORDS intelligent controller system, fi!~¢ logic, nuclear reactor, decision aided system. © 2005 Elsevier Ltd. All rights reserved 1. INTRODUCTION The applications of fuzzy logic cover a wide range of areas (Zadeh L. 1994). Fuzzy logic control being one of the most active and used area, its introduction in the nuclear industry is however quite recent (Ruan D., 1995), (Ruan D., 1998), 01uan D., J. Van Der Wal A., 1998). Fuzzy logic control offers many advantages over the conventional control methods. The exact knowledge of the mathematical model of the system is not necessary; it is robust, flexible and well adapted for non linear systems. It offers as well simplicity, ease of implementation and fast execution to make it suitable for real time systems. The safety standards required in the nuclear domain necessitate more severe design criteria in reactor control. This prompted the development of a new generation of robust and intelligent controllers. The combination of fuzzy logic control techniques with human intelligence and expertise is very promising. The main objective of this paper is to demonstrate the use of an intelligent fuzzy logic controller (FLC) in parallel with a classical controller for monitoring and supervising a nuclear reactor in real time. The principle of this controller is based on rules established from experiments used with the classical controller and from the knowledge and the expertise of the operators of the reactor.
328
Design of an intelligentfuzzy logic controller
329
2. BRIEF REVIEW OF FUZZY SETS, FUZZY LOGIC AND FUZZY CONTROL In standard set theory (Driankov D. et al., 1992) (Pedrycz W., 1993), (Zadeh L., 1994), (Buhler H., 1994), an object is either a member of a set or it is not a member at all. Given a universe of objects U and a particular objectx e U , the degree or grade of membership ,uA(x) with respect to a set A c U is: 1 ifx~A /~A(X)=
(1)
0 if x ~ A
,UA(x) : U --~ { 0,1)
The function is called characteristic function in standard set theory. Often, a generalization of this idea is used, for instance, to handle data with error bounds. A degree of membership of one is assigned to all the numbers within some percent error, and all the numbers outside that interval have a degree of membership of zero (Fig. 1. (a)). For the precise case, the membership degree is one at the exact number and zero everywhere else (Fig. 1.(b)). L. Zadeh proposed a further generalization in which some objects are more member of set than others. The degree of membership takes on various values between zero and one, where a zero value indicates complete exclusion and a value of one indicates complete membership. For instance, to express that a temperature is around 25, we may use a triangular membership function (Fig. 1(c)) with its peak at 25 to express the idea that the closer a number is to 25 the better it qualifies.
(a)
u
(b)
u
(e)
Fig. I. Membership functions for crisp and fuzzy data Formally, let U be a collection of objects denoted generally by { u } U is called the universe of discourse and may be continuous or discrete. A fuzzy set A in a universe U is defined by a membership function/G which takes values in the interval [0,1]. u
[o, U
(2)
We can, also, define a fuzzy set as a collection of ordered pairs of a generic element u • U and its grade of membership function'UA(u), i.e.: N
(3) Where N is the number of elements of U. Note that the symbol Y~ here denotes a collection of discrete elements. The corresponding notation for a continuous universe of discourse U is
(4)
A= U
330
EAdda et al
The support of a fuzzy set A is the crisp set of all points u in U such that AtA > 0. A fuzzy set whose support is a single point in U with/t A = 1 is called a fuzzy singleton. In fuzzy controller design, we often encounter situations where two or more fuzzy sets are involved. For example, in constructing a fuzzy rule, satisfaction of either one of two fuzzy conditions leads to a certain consequence or action. Thus, formal treatments of fuzzy operations are needed. Below are some important ones. Let A and B be two fuzzy sets in U with membership functions/.ta and/.zB, respectively. The union (A u B ) is defined by
A u B --~ max {pA(U),t~(U)}/U F o r u ~ U .
(5)
U
The intersection (A ~ B) is defined by
A n B = ~ nfin {it A(u), i.t~(u)}/u For u ~ U.
(6)
U
It is quite common to use qualitative expressions instead of quantitative values for words that denote measures and counts, such as fairly high, quite a few, not many. This idea leads to the concept of a linguistic variable. A linguistic variable takes on one of a set of labels, i.e., expression, as its value. For instance, the linguistic variable Temperature could take one of the members of the set {low, medium, high} for its value. The labels are given meaning by associating with each one a fuzzy subset of some universe of discourse (Fig. 2.). ~Temp
p
0
25
50
75
100
Tern~rg~re (°C)
Low Medium High Fig. 2. Linguistic variable T e m p e r a t u r e k"
il
Kn°wlede~
FUZZY
Fuzzification
Sensors
-
FUZZY
(crisp)
i
Actuators
Fig. 3. Basic structure of fuzzy logic control
Design of an intelligent fuzzy logic controller
331
The structure of a process controlled via a fuzzy controller is shown in Fig.3, which presents the basic components of a filzzy controller: a fuzzification interface, a knowledge base, a data base, inference procedure, and a defiJzzification interface. Usually the fuzzy control rules are expressed in the form of a fuzzy conditional statement Ri: IF u is Ai and.., and v is B~, THEN w is C~, where u, v, and w are fuzzy variables, and A~, B~, and Ci are fuzzy subsets in the universes U , V, and W. The fuzzy rule Ri can be regarded as a fuzzy relation from universe (U and ... andV ) to universeW. If there are n rules, the rule set may be represented by a union of these rules: R = RI ~ R2 ~ ... ~ R,. The resultant w can be induced by the compositional rule of inference w = (u And ... Andv) o R where o denotes the compositional rule of inference. For example, using the sup-min compositional rule, we have: In particular, the most frequently used fi,zzy inference methods in fi)zzy control are Mamdani's fuzzy
pc(w) = { min { lG(u) ..... IUB(V),I~R(U..... V,W)} }.
(7)
implication and Larsen's product fuzzy implication. If the fuzzy variables u 1, v2, and w3 are fuzzy singletons, the inferred results of both implication methods will be the same. wi = nfm { IL~(uo)..... u~,(vo)l • c;
(8)
where uo, vo and we are fuzzy singletons, and Ci is the singleton value of w using the i th rule. After a fuzzy control action is inferred, a non fuzzy control action that best represents the decision is needed. Although there is no systematic procedure to choose a defuzzification strategy, the most common include: the MAXimum criterion method (MAX), which produce the point where membership function of the control action reaches a maximum value; the Mean-Of- Maximum method (MOM) which represents the mean value of maxima when they are not unique; and the Center-Of-Gravity (COG) which generates the center of gravity of the membership function area of the control action (Fig. 4.).
w COG
Fig. 4. Defuzzification strategies
3. MATHEMATICAL MODEL AND TEMPERATURE FEEDBACK In this model, the reactor is described by the well known point kinetics equations with six delayed neutron groups. In this case, the neutron density n (or power level) and the precursor number density are defined by the following equations (Furet J., 1968): where: dn dt
(9)
6
0
~=x
dct = /3i n - 2 c i dt 8
i = 1,...,6
(10)
332
E Adda et al
ci: i t~ group precursor concentration
~: ith group delayed neutron decay constant (s1)
13i: ith group delayed neutron fraction
0 • Neutron generation time (s)
13' Effective delayed neutron fraction
p • Reactivity
In the simplified case where only one group of delayed neutrons is taken into consideration, the point reactor kinetics equations (9) and (10) become dn dt
-
p - fl 0 -
-
+Ac
n
(11)
dc ~ =
~ n
dt
-
0
.~,c
02)
6
with i=1 ~,i
The three most important parameters characterizing the kinetic behaviour of a nuclear reactor are the reactivity p, the neutron generation time 0, and the effective delayed neutron fraction 13. A variety of experimental techniques have been developed to measure these parameters. Although the above system of equations is not linear, the transfer function of the reactor can be defined around the operating point which corresponds to the critical regime p~0,
n=no,C=Co
(-~t ) = o
(dc.~_)= 0
(13)
If a small sinusoidal reactivity with a magnitude Ap and frequency io~ = p is added to the operating point, then: n = no + &,a,
c = co + Ac,
p = Ap
(14)
The zero-power reactor transfer function is then given by the following expression: The curves in Fig.7 show that the gain is very high at low frequencies, this implies that the reactor is An
1
p+2
neAP - O p(p + 2 + ~ )
(15)
unstable in this region; the gain is constant between fl = M2rc and f2 = 13/2zc0. On the other hand, f2 is inversely proportional toO, then the length of transfer function plateau is inversely proportional to the neutron generation time.
3.1 Behavior of the reactor power with temperature feedback Let us now return to consider the dynamic behaviour o f a reactor with feedback, in particular, we will consider the effects of temperature feedback. The block diagram of the reactor control loop with temperature effects is given in Fig. 5.
333
Design of an intelligent fuzzy logic controller
Ap~
n ~[
r~actor
Fig. 5. Reactor control loop With regard to the reactor which has enriched uranium and moderated water, we can use the following conditions (Fig. 6): Te
Moderator Wa~rflow
Q
< Exchanger
< Ts
Fig. 6. Reactor cooling Te is the inlet temperature which is constant. We take into account only the moderator temperature coefficient a which is negative. • Ts is the outlet temperature. The average temperature of the moderator is defined by: Te + Ts Tin= 2
(16)
The neutron power is defined by: n = Q C ( T s - Te) + M C dTm dt where: Q is the flow rate of water. M is the mass of water contained m the reactor core. C is the water specific heat. In the steady state operation, we have:
no
=
QC(Tso re)
Tmo
-
-
with the reactivity disturbances around the equilibrium point
Tm = Tmo + ATm
n=no+An
(18)
Tso + Te 2
Ts = Tso + ATs
07)
(19)
334
E A d d a et al
We can define the reactor transfer function with temperature feedback by:
(I + 2~Q p)(p+I)
An
(20)
noAP a--~-(P+2)+OP(P+2+~)(~Q p + I ) 2 Q c The coefficient of moderator temperature (x acts as a network feedback, with a gain ~z/2QC and a time constant x = M/2Q. The frequency gain and phase curves are given in Fig. 8 with: Q = 220m3/h, M = 40Kg, o~ = -0.00015/°C. At low frequencies, the gain leads to 2QCkx whatever no, the reactor is stable in this region. At high frequencies the reactor acts as if there is no temperature coefficient, it behaves as a zero power reactor. We conclude that reactivity variation with temperature is the main feedback mechanism determining the inherent stability of a nuclear reactor with respect to short-term fluctuations in power level. 200
200. , ^1~o~- .... ~ .......... g----_ !
~" I ° ° i - - - ~ - ' I
I
I
!
...........
......
_.,_
t0,4
I
I- ..................
10.2
. . . . . . . .
10 0
L _.I
I + ............
"~ 100 I ' - ' - - - ' - ] . . . . . . . . . . . .
~
00
ol
10 2
,
.,~. . . . . . . . . . .
,
10 ,4
¢ ................
. . . . . . . . . L, . . . . . . . .
!
I 10 "2
.....
~
/
~ . . . . . . --]
&'- - - I
,'--1
10 0
10 2
t0 °
10 2
frequency (Hz)
.........
10-2
I
10 .4
frequency (Hz)
:oo :
i i +.....................
10 0
.100 [ IO 2
Fig. 7. Gain and phase without thermal effect.
i 10,4
~
I 10 -~
,
i
Fig. 8. Gain and phase with thermal effect.
4. REACTOR INSTRUMENTATION AND CONTROL
4.1 Introduction The instrumentation and the control systems are often considered as an essential element in a nuclear reactor installation. It is in the control room where all the decisions are taken on the basis of the important number of the incoming information. The instrumentation and the control systems of the reactor act as an interface between the reactor and the operators. They generally achieve the following functions: •
Measurement of the essential parameters which characterize the operating mode of the reactor, on the basis of which, the operator will be able to proceed to the adequate action.
*
Production of the logical signals in case of exceeding the prefixed thresholds. To each threshold level corresponds a logical signal which is susceptible to manipulate a security action such as: alarms, inhibition of motion of control rods, automatic introduction of control rods, emergency stop or SCRAM, evacuation ...
Design of an intelligent fuzzy logic controller
•
335
To act on organs of command manually or automatically in order to modify operating conditions.
In the conception, it is necessary to take into account the following conditions: • e
The starting and the operation of the reactor must be achieved with safety. One must ensure the emergency stop of the reactor (SCRAM) against any abnormal event that could OCCurS.
4.2. Control loop of the Reactor The considered reactor is controlled by five control rods: two safety rods (SR), two compensation rods (CR) and one fine tuning rod (FR). The value of the reactivity depends on the temperature effects and on the control rods efficiency. The control rods motions are achieved by stepper motors. The safety and compensation rods have a constant velocity of 0.53 mm/s and a total coarse of 640 mm. The fine tuning rod has a variable velocity from 0 to 10.33 mm/s with the same range of 640 mm. The block diagram of the reactor control loop is shown in Fig.9. VR m
q
P /2~cic
th
:~ Pc
,~
PJ
N u c l e a r ~1 ic
1 Reactor'~
MPA
classical controller of fine tuning rod
Stepper Motor
classical
controller of oompensation rod
Stepper Motor
-~
DOttF
thermal _ circuits r
Fig. 9. Block diagram of the reactor control loop The current delivered by the ionization chamber is proportional to the neutron flux present in the reactor core. This current is converted to voltage VM by a linear amplifier and it is compared with the reference voltage VR. We obtain e = 1 - VM/VR (%), this value represents the relative neutron power margin (difference between the measured power and the desired power). If e exceeds 7%, the automatic control is removed. The period T is added to get an activation signal of the automatic monitoring SAPA proportional to s + T variable between -10V to +10V. This signal drives the logics of the motion rods and their command to produce the insertion or the withdrawal of the fine tuning rod with a proportional speed to this signal. This is true as long as the fine tuning rod is confined within the interval boundaries (40%-60%), otherwise the selected control rod CR1 or CR2 is used to adjust the power and to bring back the fine tuning rod to its initial position. The reactivity is the amount of the temperature effects, the fine tuning rod effect and the compensation rod effect.
336
E Adda et al
5. EXPERIMENTAL EVALUATION AND VALIDATION OF THE PROPOSED MODEL One test carried out in the reactor was to increase the power from the level 0 to 500 KW and then from 500KW to 750 KW (Fig. 10.). The following parameters were recorded: the power, the position of the control rods, and the rate of change of power. The reactivity, which does not have a direct measure, has been determined by the position of the control rods and their curves of efficiency. These curves show that the power evolution at every moment is function of the reactivity and the rate of change of power. In the transient operation, conditions of non-linearity owed to the delayed neutrons effect deduce a very high response time. The fact also that the motion of control rods is constant and the efficiency of these rods is not a linear function of their position appear an unavoidable overshoot during the transition. In order to simulate and to validate the model of the reactor represented by equations (6) and (7), we approached the experimental curve of reactivity by a linear function (Fig. 11.). Results obtained by simulation (Fig. 12.) show that there is a good similarity agreement with the experimental results, therefore the approximation done on the model taking into account only one delayed neutron group and considering that the reactor is point are acceptable. POWER 750 K~ ..................................
500 K ~
---~j~
/
J
250K~
' 10:10
10 I20
'
10 I30
'
Time (h:mn:s)
' 10:40
Fig. 10. Experimental power evolution between 2 levels ( 500 Kw and 750 Kw )
REACTIVITY O,OO03
]J~
0,¢¢02
Measuredreactivity
o,oool o,oooo
.o,oool .-o,ooo~
i "10:12
/ 1~19
| 10;26
! 10~33
i 10:40
Time (h:mn:s)
Fig. 11. Curves of measured and approximated reactivity
Design of an intelligent fitzzy logic controller
337
9
1.8 x l O
o
i
I
I
1
g / i
i
v
/
t
12F---
0.6 0
I
i
500
J i [
. . . . . . . . . . . . . i...................
J
i
iO00
i
l
'1500
2000
times
Fig. 12. simulated power evolution between 2 levels (500 Kw and 750 Kw)
6. BUILDING OF THE KNOWLEDGE BASE
6.1. Knowledge Acquisition An essential task in the design of an FLC or a rule based system is the knowledge acquisition process (Bemard J. A., 1986), (Bernard J. A., 1988). If this is not done in a thorough and rigorous manner, then the controller cannot function correctly. To collect the knowledge necessary to the design of the FLC, the following techniques were used: •
Attentive observation of the operators during the increase and decrease of the power of the reactor, and taking notes about their actions and on the instruments they watched: the current which is proportional to power and neutron density, rate of change of power, position of the control rods, difference of inlet and outlet temperatures in the reactor core...
•
Acquisition of the nuclear and conventional parameters at different times when the reactor is in operation to monitor its behaviour during the change of levels of the power.
•
From the evolution of these parameters, some operator's actions can be deducted.
•
A questionnaire was established to the operators and their answers are verified attending to operation of the reactor such us the experience is well prepared and the level of the power predefined. These questions are about : o
The reactivity which is the fundamental parameter for controlling the power of a nuclear reactor.
o The important parameters used in the control process of the reactor for the dynamic operation and for the steady state operation. o
The selection of control rods that depends directly on experiments to carry out in the reactor.
o
The precautions to be taken on approach to full power of the reactor. Full power is accomplished with undershoot to avoid the shut-down (SCRAM) of the reactor while respecting limits of operation and safety. Insertion of the control rod will begin when we reach 80% of full power. For the other power levels, the insertion will begin at 90-96% of the desired level.
E Adda et al
338
2=l
os~
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/ Fig. 13. D~erem stepsused m flaebmldi~ of~e knowledge based system
Organization and representation of the knowledge base After the knowledge acquisition of the most important parameters, it is necessary to accomplish the following three objectives: •
Identification of the parameters used for the control process such as (power margin, period...).
•
Deduce the verbal labels and their ranges that are used by operators to classify measured value of each parameter.
•
Establish the conditional rules that relate the linguistic labels to specific control action. Power mismatch between the
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Design of an intelligent fuzzy logic controller
339
7. DESIGN OF THE FLC In the conception of the controller, it was possible to consider only one fuzzy logic controller but the rule base in this case will be cumbersome and the operating modes of the reactor would be difficult to optimise. One has to make a compromise between the speed, the precision and the stability of the system at any mode of operation. For this reason, two fuzzy logic controllers FLC1 and FLC2 were proposed, one for each state of operation: the transient (dynamic) state operation and the steady state operation (Fig. 15) (Adda F., 2001).
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7.1. Characteristics of FLC1 The design of FLC1 was based on the knowledge and the experience of the operators of the nuclear research reactor. The fi, z~y logic controller FLC1 is depicted in Fig.16 (for an increase of power) and in Fig.17 (for a decrease of power). It is characterized by its: * Membership Functions for the input variables. • Membership Functions for the output variables. • Rule base. * Relation between inputs and outputs.
E Adda et al
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7.2. Characteristics of FLC2 The conception of FLC2 is based on the classical semi-automatic controller functions, its characteristics are given in Fig. 18.
342
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Design of an intelligent fuzzy logic controller
343
8. VALIDATION AND EVALUATION OF THE CONTROLLERS
The simulation diagram for the Fuzzy Logic Control based on the controllers FLC1 and FLC2 is presented in Fig. 19. n~
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Fig. 19. The Fuzzy Controllers FLCI and FLC2 m closed loop with the nuclear reactor The main blocks constituting this diagram are: - The nuclear reactor core. The input parameter for this block is the reactivity PT, which is the sum of all the reactivities: PRC for the control rods, PRF for the fine tuning rod and pth for the thermal effects. The output parameter is the neutron density. - The FLC1 controller is intended for the transient state operation. Its input parameters are the rate of power evolution 3, the power difference between the actual power and the desired power, e. Its output parameter is the motion of the control rod MORC. The FLC2 controller is intended for the steady state operation. Its input parameters are the position of the fine tuning rod PRF and the power difference between the actual power and the desired power e. Its output parameters are the motions of the fine tuning rod MORE and the control rod MORC. -
The Fuzzy controller FLC1 monitors the big changes in power requests, at start and at any stage of operation, in order to improve the response time and to minimize the overshoot. The FLC2 controller minimizes the power difference obtained by FLC1 in order to improve the stability and the precision of the system. The reactivity is determined by measurements of the inserted positions (heights) of the control rods and the use of the efficiency of the respective rod. These positions are obtained after integration of the output signals of the controllers. This loop has been tested under normal and degraded conditions (i.e. taking into account intemal and external disturbances).
344
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345
Design of an intelligent fuzzy logic controller
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200
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E Adda et al
8.1 FLC Results Interpretation The FLC1 controller was tested for different power levels and with and without the introduction of the thermal effect. The simulation results obtained, Fig. 20 and Fig. 21, show that with FLC1 abrupt movement of the control rod can be avoided which eliminates power peaks. In addition, a good precision (= ± 2.5 %) and a good stability were obtained for all power levels and during an increase and decrease of power. The time response was considerably reduced within the allowed safety standards (power rate less than the maximum authorized). The FLC2 controller was tested with positive and negative errors variations and with and without the introduction of the thermal effect. The simulation results, with and without the thermal effect, show that there is rapid error compensation and a good precision of +0.08 for an error less than + 4 %. These results were compared with those obtained by the actual semi-automatic controller for different power levels. They confirm that with FLC1 and FLC2 much better performances are obtained. Other tests were conducted as well, for example, in case where the fine rod is outside the linear zone. The fuzzy logic controllers acted in the same manner as the classic controller by compensating the error with the control rod and repositioning the fine rod in the linear zone which is between 40% and 60% (Fig. 23.).
9. CONCLUSION AND FUTURE DEVELOPMENT In this work, a rule and a knowledge based fuzzy logic controller was developed. The used rules model the classical controller and the operator's knowledge and expertise. Simulation tests were carried out on this controller and showed that the control strategy was considerably improved comparing to the semiautomatic controller. The fi~z~ logic controller has successfully simulated and translated the operator's decisions under normal and degraded conditions. This controller improved the performances of the reactor in terms of the response time, the overshoot, the stability, the precision and the robustness which are required for its safe exploitation. Further works will be carried out in the near future to resolve the problem of the commutation between the two controllers FLC1 and FLC2 which is the main problem encountered in this controller. Another perspective is to design and built an intelligent simulator based on this controller and on an e-learning technologies for the training of operators.
REFERENCES Adda F. (2001), Application de la Commande Floue au ContrOle d'un R~acteur Nucl~aire de Recherche. th~se de magister, Eeole Nationale Polytechnique Alger. Bernard J. A., Laning D.D. (1984), Digital Control of Power Transients in a Nuclear Reactor. IEEE Transacaons on Nuclear Science, Vol. NS-31, No 1, February. Bernard J.A., Ray A., Kwork I~S., Lanning D.D. (1985), Design and Experimental Evaluation of a Fuzzy System for the Control of Reactor Power. American Control Conference, Vol. 3, pp. 1466-1474 Boston, MA, June. Bernard J. A. (1986), The Construction and Use of a Knowledge Base in the Real Time Control of Research Reactor Power. 6th symposium on power plant dynamics control, and testing, vol. 57, pp. 1-25. Knoxville, April. Bernard J. A. (1988), Use of a Rule-Based System for Process Control. IEEE Control Systems Magazine, pp. 3-13.
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Driankov D., Hellendoorn H., Reinfrank M. (1992),An Introduction to Fuzzy Control Springer-Verlap. Duderstadt J.J., Hamilton L.J. (1976), Nuclear reactor Analysis. John Wiley & Sons, Inc. Furet J. (1968), ContrOle et Electronique des R~acteurs Nucl~aires. Masson et Cie. Hansruedi Buhler (1994), R~glage par logiquefloue. Presses polytechniques et universitaires romandes. Jamshidi M., Vadiee N.(1993), Timothy J. Ross, Fuzzy Logic and Control, Software and Hardware Applications. PTR Prentice-Hall, Inc. Pedrycz W. (1993), Fuzzy Control andFuzzy Systems, Second extended edition, Research Studies Press LTD - John Wiley & Sons Inc. Ruan D. (1995), Fuzzy logic in the nuclear research world. Fuzzy Sets and Systems, 74 (1) 5-13. Ruan D. (1998), Intelligent systems in nuclear applications. Int. J. of Intelligent Systems, 13 (2/3) 115-125. Ruan D., Li X. (1998), Fuzzy-logic control applications to the Belgian Nuclear Reactor 1 (BR1). Computers and Artificiallntelligence, 17 (2-3) 127-150. Ruan D., Van Der Wal A. J. (1998), Controlling the power output of a nuclear reactor with fuzzy logic. Information Sciences, 110 151-177. Zadeh L. (1973), Outline of a New Approach to the Analysis of Complex Systems and Decision Processes. IEEE Trans. Syst. Man and Cybernetics, vol. SMC-3, pp. 28-44. Zadeh L. (1988), Fuzzy Logic. IEEE Computer, pp. 83-93, April. Zadeh L. (1994), The Fuzzy Systems Handbook. Earl Cox The Metus Systems Group Chappaqua, New York.