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Neuro-Fuzzy Generalized Predictive Control of Boiler Steam Temperature
ELSEVIER
Copyright © IFAC Power Plants and Power Systems Control, Seoul, Korea, 2003
IFAC PUBLICATIONS www.elsevier.comllocale/ifac
NEURO-FUZZY GENERALIZED PREDICTIVE CONTROL OF BOILER STEAM TEMPERATURE
.
.
Xiang-Jie Liu , !':elipe Lara-Rosano , •• Marino Sanchez Parra , Raul Garduiio Ramirez
.
Centro de Ciencias Aplicadas y Desarrollo Tecnologico, UNAM, Mexico City. D.F 04510, Mexico Electric Research Institute, Cuernavaca, Morelos CP 62490 Mexico
..
Abstract: A neuro-fuzzy network predictive approach is introduced to design a control system for boiler steam temperature process. While the nonlinear process is modeled by neuro-fuzzy technique containing local CARlMA model, traditional generalized predictive control method can be extended to nonlinear case in a neuro-fuzzy fashion. The proposed method was found to provide a satisfactory performance over the 200MW superheater steam temperature system. Copyright © 2003 IFAC Keywords: neuro-fuzzy networks, nonlinear control, steam temperature
1. INTRODUCTION
of parameter estimation algorithm could act to accentuate process disturbances. Problems with unmodelled dynamics and on-line adaption of controllers may not be acceptable in power plants for reasons of reliability(Wu and Hogg, 1991).
Continuous processes in power plant and power station are complex systems characterized by nonlinearity, uncertainty and load disturbance. Applying of traditional control methods encounter great difficulties while the process working condition changes within a large operation range. The effective way is to develop advanced modelling and control strategy on them.
Principally, nonlinear process requires nonlinear predictive control for optimum performance. Nevertheless, controller incorporating a nonlinear model may require tremendous computational burden which may disqualify it for on-line application. With specific nonlinear model, the explicit control law may prove a difficult or even impossible task. To incorporate the linear method, Prasad et a/.(1998) proposed a local model networks based multivariable predictive control, which has been simulated on a 200MW oil-fired drum-boiler thermal power plant.
Generalized predictive control (GPC) methods have been proved to be an effective method over linear model and are frequently applied in nonlinear control in an adaptive framework, designing the control law on the basis of a linearised model of the controlled system, which is reestimated periodically to fit the actual operation point with online estimation by recursive identification techniques. The linearised model may be acceptable only in the case where the process is working around the operating point. An adaptive approach may fail if abrupt changes in the operation point are requested by the control specifications or determined by the specific nonlinearity of the system. Self-tuning controller requires continuous on-line identification with injection of additional disturbance into the plant for sufficiently rich excitation of plant dynamics. Failure
It is noticed that much of the complex process in
power plant could be controlled by manual operation of the experienced operator, which is based on the enough knowledge of the object. This offer effective modelling and control method for automatic control system. The recent developed neurofuzzy network(Brown and Harris, 1994) could be an effective way to the modelling of such nonlinear system in that fuzzy rules could easily express the expert knowledge in linguistic form while neural
213
networks posses the learning ability of approximating nonlinear functions with arbitrary accuracy. In the neuro-fuzzy networks, the whole envelope of process operation is divided into several operating regions. In each region a local reduced-order model is used to approximate the process. Fuzzy logic representing human operator's language expression provides an appropriate means to define operation regions. Thus respectively the local predictive control strategy could be constituted. This paper develops a nonlinear neuro-fuzzy network modelling and predictive control method and then apply it to the superheater steam temperature control system on 200MW unit steam-boiler. Associate Memory Network(AMN) is used as process predictive model because it provides a direct link between artificial neural networks and the fuzzy systems. Transient process input-output data are then used to train the network. With the established neurofuzzy model, a set of relative local GPC controllers are composed under different operation regions to constitute the neuro-fuzzy controller. The performance of the control system has been verified by the simulation process and then tested on superheater steam temperature process.
1
c::
o
tl 20.5
'"
~ g
2
1
x2
0 0
x1
Fig.2 Multivariate basis function The B-spline network is initially designed to specify the shape(order) of each of the univariate basis functions, and this implicitly determines the number of basis functions mapped to for a particular network input. There exist recurrence relationship for evaluating the membership of a univariate Bspline basis function with R inner knots(Brown and Harris, 1994). Denoting the jib univariate basis function of order k by f.J£ (x), jib knot by Ai and the jib interval by [A,j_P A,j] . The basis functions are defmed on a bounded support and the output of the basis function is positive on its support, f.J£ (x) == 0, x ~ [A,J-k ,A,J]
and
f.J£ (x) > 0, X E (A,j_k' A,j) .The sum of the outputs of
the
basis
functions
is
always
one,
i.e
Lf.J£ (x) == l~ x E [x min , x max ] ' J
2 NEURO-FUZZY NETWORK MODELLING
The neuro-fuzzy network shown in figure I could be expressed as a set of fuzzy production rules: IF operating condition i (XI is positive small, and
With the following general single-input single-output nonlinear dynamic system: y(t) == f[y(t -I)"", y(t - n~), u(t - d)"",
(1) u(t - d - n~ + I), e(t -I),,,,, e(t - )]+ e(t)/L\ where f[.] is a smooth nonlinear function such that a Taylor series expansion exists, a local linear model at an operating point O(t) can be given by the following CARIMA model: A(Z-' )y(t) == Z-d B(Z-I )L\u(t) + C(Z-I )e(t) (2)
n;
"', x" is negative large) THEN local linear CARIMA model i : Yi(t) = GilYi(t -1) + ·"Gi".Yi(t - no) + bio/),ui(t - d) + ... + bill. /),ui(t - d - nb ) + ei(t) + ... + Ci"c ei(t - ne)
or
where A(Z-')==M(z-'), B(Z-') and C(Z-I) are
The multivariate basis function is obtained by:
"
polynomials in z -I, the backward shift operator. They are function of the operating point O(t). Therefore, the nonlinear model could be decomposed into several linear or nearly linear models at different operation points. The total model could be represented by a B-spline AMN shown in figure I. The antecedent variables [x p x 2 ",x,,]representing different operation points are the inputs of the AMN. The output of the network model yet) could be combination of local linear models Yi (t) . univariate
muttiyari~
~~fu~an
~~~~~
A;(Z-')Yi(t) == Z-d B,(Z-I)L\ui(t) + Ci(z-I)ei(t) (3)
a,(x)==nf.JA,(x k k=1
)
(4)
k
where i == 1,2, .. " p and n is the dimension of the input vector x(t). p is the total number of memory required in the network given by
"
p== n(R; +kJ
(5)
i=J
Thus the desirable properties of the univariate Bspline basis functions are all extended in a natural way to the multivariate basis functions. They are defined on hyperrectangles of size (k, x k 2 x··· x k,,) and therefore possess a bounded support. The output is positive inside this domain and zero outside. Fig.2 shows the multivariate basis function formed from two ,order 2, univariate basis function.
a,
The model output is the synthesizing of these p rules:
0,
l-------'--~.y,
Fig.1 Nonlinear neurofuzzy network model
214
N
p
J = E{Lqj[La;
p
(12)
+ LAj[La;u;(/+ j-IW j=1 ;=J
Choose the cost function to be: 1 2 I ~ 2 J = 2. e = 2. (y - y)
With interactions among those subsystems, the minimization of this cost function requires large computing burden. An alternative approximated cost function could be acquired for the simplification with Cauchy inequality,
(7)
where y is the network prediction, and y is the plant output. Training parameter could be changed in the direction of the negative gradient:
..:.aij
uaij
aJ
bi! =-g ab;!
;=1
ay ay; ( ) ~ ( I) =-ge ~~'. ~_. =-gea; x y; 1-
aJ =-g ~_.
.
p
[La;(y;(/+ j)- y,(t+ J)W p
~ p L[a;(y;(/+ ) - y,(/+ j»]2
vy, uaIJ
ay ay; =-ge ay; obi!
;=1
=-gea;(x)u;(/-d-m)
[fa;u;(1 +) _1)]2
~P
;=1
I~I
where
~ nii
(8) (9)
0 ~ m ~ nb
N
M
M
j=d
;=J
M
p
j=1
+ L(aYLAj[u;(t+) -I)f
(10) q j and Aj are respectively the weighting factors for
;=1
j=1
=f(a;)2J;
the prediction error and control energy; y, (I +) is
(14)
;;)
where
the ith step reference trajectory, d is time delay taken as minimum costing horizon, N and M are maximum costing horizon for prediction and control variables respectively. The control policy is given by the weighted sum ofp sets oflocal control policies:
N
M
J; = E{Lq}y;(t+ j)- Y,(t+ j)f}+ LA)U;(t+ j -I)f j=d j=J (15)
The derivation procedure shows that the essence of minimization of J is the same as that of J;. Thus the problem changes to the minimization of J; in each local model.
(11)
;=1
LlU; (t)
N
p
=E{L(a;)2 Lqj[y;(/+ j)- y,(/+ jW}
J = E{~>jrY(t + j) - Y,(t + j)f} + LA)~U(t + j -I)f
where
p
+ LLAj[a;u;(/+ )_1)]2 j=1 ;=1
For the purpose of generalised predictive control, the cost function to be minimized is:
Llu(/) = fa;Llu;(/)
p
E{LLq)a;(y(t+ ) - y,(/+ ))]2} j=d ;=1
3.1 The problemformulalion wilh approximalion
j=d
(13)
;=1
Equation (13) means the sum of the weighted squared errors can be the basis for establishing an upper bound of the original objective function. And
3 NONLINEAR NEURO-FUZZY NETWORK GENERALIZED PREDICTIVE CONTROL
N
f[a;u;(1 + ) _1)]2
is the relative control action in each
local region, a; is the same as that defined in the neuro-fuzzy modelling equation (4) since the contribution of the output estimated by the ith submodel to the overall process evaluation should be considered the same as that by the ith local control action to the overall system controller. This also meet the idea of T-5 model. It is different from T-5 method in that the "consequence" does not necessarily contain the "premise" part. With this control structure, the system eliminates the controller switch problem and provides a much more smooth control performance in process operation. With model (6) and control policy (11), equation (10) could be expressed as:
3.2 Controller
Equation (15) could be rewritten in a matrix form as: J; = E{[Y;(t + I) - Y,(t + l)f Q;[Y;(t + I) - Y,(t + I)]}
+ ~U/ (t)T;~U;(t)
(16)
The control law by the ith sub-system can be identified as(Clarke el aI., 1987): LlU; (I) = (G; T QG; + A)-I G; T Q[Y, (I + I) (17)
- F;LlU; (I -I) - S; (z -I )y; (I)]
where Y;(I + I) = [)I; (I + 1),)1;(1 +2),···,)1;(1 + p)f
215
Yr (t + I) =Ly r (t + I),
Y (t + 2), ... ,Y r
I'1U, (t) = [l'1u, (t), l'1u, (t t1U,(t - I) = [t1u i (t G,
r
(t + P) f
applied for the superheater temperature system in a multi-stage control manner to reduce the time constant of each stage and improve the control trait. Q The rated superheated steam temperature is 540 C.
+ I)"", l'1u i (t + M -I)f
n b ),C1u,(t
-
+ 1),"',t1u,(t -I)f
nb
(t + I) = [R il (Z-I )ei (t + 1)"" RiP (Z-I )e, (t + p)f
S, (Z-I)
= [Sil (Z-I ),Si2 (Z-I),'"
Sj(z-I)and
are
R,(z-I)
The task of the superheater in boiler-turbine system is to heat the steam by combustion gas and then send it to turbine. As shown in figure 3, the steam coming from the boiler drum passes through the lowtemperature superheater and receives a spray water injection before passing through the radiant-type platen superheater. The steam then receives a second spray water injection before passing through the high-temperature superheater. A properly control system by superheater water spray should maintain strictly the steam temperature within the permitted range( ± I QC in transient process and ±5 QC in steady state). Higher temperature could damage the superheater and the high-pressure-turbine by high heat strength. Lower temperature could decrease the running efficiency of the whole steam-boiler. By reducing temperature fluctuations, mechanical stress causing microcracks is diminished, therefore plant life is increased and maintenance cost is decreased, This is obviously the motivation for GPC control, since the variance of the steam temperature is directly related to economic and safety performance.
,SiP (z-I)f
in
the
Diophantine
equation: (18)
1= A,(z-')R'j(z-')+z-iS,/z-')
and: G,(z-') = B, (z -I )R, (Z-I) _g
-
+g
j,O
7-
),1-
1 +"'+g
~[ g;,
=
diag(qil' qj2'''', q,p)
g~,P-1
F,
~
g;,lIb
[
g;"•., .
g~II~+P-'
(19-c)
= diag(A, I ' A'2"", A,M)
°
g; 0
G,
°
(19-b)
= g i,' + S i,obi-i
g i+I"
Q, T,
( 19-a)
7-(lIb+i- l )
jJJb"'"j-! ....
g;,o
,
gp-I,P-2 j gl,lIb-1
( 19-d)
j gp-M+I,P-M PxM
,
g2,lIb
, g P,lIb +P-2
g;,2 g;,3
g~,P+l
g;,1 j gZ,2 g~,p
The superheater outlet steam temperature can be affected by many factors such as steam flow, combustion condition, feedwater temperature, steam enthalpy and combustion gas temperature. Totally speaking, three main factors dominate the superheater outlet steam temperature: load power, gas flow and superheater inlet steam temperature. These are also the reasons why a conventional PIDbased control strategy is often unable to perform satisfactorily. Many efforts have been put into developing and testing more advance control schemes on different boiler plants, like adaptive simulation-model-based control of fossil-fuel-fired thermal power plant(Nakamura et aI., 1995) and feedforward control based on new measuring techniques on a 256MW Unit(Tommy, 1999). The intention of this section is to develop the nonlinear model of steam temperature with the proposed neurofuzzy method based on dynamic experiment of the 200 MW Unit and then constitute the relative non linear GPC controllers.
PXllb
(l9-e) The optimization control variables are M steps into the future based on the control horizon. Only the first control action is implemented, using a receding horizon principle, i.e, l'1u, (t) = d il T [Yr (t + 1) - F,l'1U j (t -1) - S, (Z-I )y, (t)]
where d il T = 0,0,'" ,O)(G, T QGi + A) -I G j T Q is the first row of the matrix (G/ QG, + Ar' G/ Q.
4 NEURO-FUZZY MODELLING AND CONTROL OF BOILER STEAM TEMPERATURE 1
to turbine
f-----M---, 2
-->-->-->-->-
3
2
=:: =::
combustion gas flow
_540 r - - - - - - - - - - - - - - ,
~
low-temperature platen high·temperature supemeater superheater tuperheater
'5
ro
Q;
~535 2
1--- superheater spray valve 2---superheater spray 3---feedwater valve 4---economiser Fig. 3 Depict of boiler superheater steam system
E
Ol'"
The process considered is the pulverized coal-firing 200MW steam-boiler used for electric power generation. It produces 670 tons of steam per hour at maximum continuous rating. The final superheated steam pressure is 16,7MPa. Two stage sprayers were
time(mJn)
530 0
2
4
5
Fig.4 Dynamic response(solid line) under 18% step change in the second stage spray flow and its fitting curve(circled line)
216
~
Considering the output "steam temperature B" with the control input spray PIJ' dynamic of the steam temperature process could be depicted to be a second order representation (Liu and Zhou, 1999): G(s)
B
Kp
pIJ(s)
(T1s+I)(T2 s+l)
=- - =
e- ts
5045
r---~---~--------'
§
(20)
'"CD
-E
time(min)
CD
~ 525 L...O---5~---1~O---1~5----"'20
Fig.6 Comparison of boiler system(solid line), global linear model(dotted line) and neuro-fuzzy model(dashed line) responses Table 2 Neuro-fuzzy GPC control law parameters (F,=O)
Load High
200
Fig.5 Local division of five membership function Figure 4 shows real-time dynamic response of steam temperature under 180MW load condition and its fitting curve. The linear model (20) is, however, extremely local in nature, and do not recognize the non-linear nature of the process. Load operation leads to changes in operating point right across the whole operating range. With the neurofuzzy modelling in section 2, load operation is divided into five regions as shown in figure 5. This division is based on the operator's former experience, which considers that 200MW is high load, 180MW is medium high load, 160MW is medium load, 140MW is medium low load and 120MW is low load. Since the length of superheater tube is about tens of meters, there exists time delay from the superheater spray flow to the change of superheater outlet steam temperature. The average time delay r = 30s is assumed to be uniform and taken as minimum control horizon. Let C i = I to make ei (t) an uncorrelated random sequence of zero mean. The identified five-region neuro-fuzzy model is shown in Table I.
Medium high
B
Higtl
1- 2.8824z- 1 + 2.7682z-2 - 0.8858z-3
MediI.m higJl MediJ.m MediI.m
1-2.8940z- 1 +2.7915z- 2 -0.8975z- 3
0.0035 0.0028 0.0023 OJXH9
1- 2.9200z- 1 + 2.8416z- 2 - 0.9216z- 3
OJXH6
39.9 - 69.2z- 1 + 30.3z- 2 46.2-81.0z-' +35.8z- 2 1
Medium low
38.9 - 68.1z- 1 + 30.2z- 2 44.7 -79.1z-' + 35.4z- 2 1
2
29.4 - 49.9z- + 21.5Z- ] 35.6-61.5z-' + 26.9z- 2 [
Low
42.3 -73.9z- 1 + 32.6z- 2 49.8 - 87.7z-' + 38.9z- 2
0.586
o,353] 0.423 0.493 [ 0.563
[
0'328~ 0.401 0.478 0.559
2
1
[
[
0.375] 0.445 0.520
2
27,7 - 47.2z- + 20.4Z- ] 33.2 - 57.5z-' + 25.2z- 2 [
29,9 - 50.9z- + 22.0Z- ] 36.5 - 63.0z-' + 27.6z- 2 43.4 -76.0z-' + 33.6z- 2 50.8 - 89.8z-' + 40.0z- 2
o,301] 0.371 0.445 [ 0.524
The neuro-fuzzy GPC is established based on neurofuzzy model. Simulation of steam temperature transient process was conducted under five different load condition. Sampling time and control time are both chosen as 5 seconds. The following parameters: P=10, d=6, M=8, Q=I, A.=O.lxI, after evaluated in a test and trial mode, are used to achieve an active control. Table 2 lists the control law parameters. Fig.7 shows simulation of steam temperature(dotted line) under set-point tracking using neuro-fuzzy GPC controller.
low
Low
1
Medium
j
1- 2.9130z-' + 2.8279z-2 - 0.9149z- 3
1- 2.9000z-' + 2.8100z- 2 - 0.9100z- 3
0,390] 0.452 0.512 [ 0.570
28.0-47.2Z- +20.3Z_2] 33.8 - 57.9z- 1 + 25.1z- 2 [
Table I Neuro-fuzzy model identification parameters Ai
23.3-45.9Z-' +19.6Z-2]
32.9 - 56.lz- 1 + 24.2z- 2 38.7 - 66.8z-' + 29.1z- 2 [ 44.7 -78.0z- 1 + 34.3z- 2
P'545 ID
Also a global linear model is acquired with the same I/O data in the whole operation region. The real-time open-loop response shows that the neuro-fuzzy model can nearly perfectly describe the nonlinear dynamic behavior but the global linear model can not match the plant. The reason is that linear model could hardly representative nonlinear plant, no matter what kind of identification method has been used.
5
1§540
"
CD Cl.
E
~535
~5lJ
.,
.'
CD
1il
time(min)
525'--
o
__ _ 15 20
~
5
10
~
_____' 25
Fig.7 Simulation of steam temperature tracking
217
~ tu
~525
time(min)
g.
Fig.8 Diagram of boiler control system
if)
0
20
40
60
EO
100
Fig.! 0 Comparison of the proposed method on neuro-fuzzy model(solid line) and on linear model(dotted line)
The real-time control system is applied in the cascade form (Fig.8). Neurofuzzy GPC controller acts as the principal controller, containing five local GPC controllers. Two controllers are working at the same time, decided by load signal through five triangular membership functions. The subordinate loop adjusts the superheater water spray with ordinary P controller, so as to give a forward response and overcome the inner disturbance quickly. Combustion gas flow acts as feed forward variable(disturbance).
5 CONCLUSION Nonlinear process in power plant can be modeled by neuro-fuzzy modelling technique. The neuro-fuzzy model composed of a series of CARIMA models could represent system nonlinearity perfectly. With the relative GPC strategy, the control system could reach a near optimal structure. The proposed predictive control method is particularly suitable for nonlinear process which can be divided into several local operating regions and thus greatly advance online applications. The effort required to develop a neuro-fuzzy predictive model of the specific plant. The advantage is shown in the modelling and control of boiler steam temperature system, which is a typical complex industrial process. In such a way, the proposed method offered an engineering approximation approach for a class of nonlinear industrial system which are formerly difficult to be controlled by traditional method.
Figure 9 shows the response of the steam temperature under changing load conditions( 1%- 2.5% /min). While the steam temperature fluctuate due to changing load, the system overcome the disturbance in a satisfactory way. Steam temperature overshoot no more than ± 7°C in transient process. The result is similar to that of (Tommy,1999), which is tested on a 380MW unit, under coal mill stop disturbance. ~ 545
*''""
REFERENCE
-E g.S25 (f)
Brown, M. & Harris, C. J. (1994). Neurojuzzy adaptive modelling and control. Prentice Hall. Clarke, D.W., Mohtadi, C. and Tuffs, P.S., Generalized predictive control(l987). Parts J and 2, Automatica" 23, (2), 137-160. Nakamura, H., Toyoda, Y., and Oda, K.(l995). An adaptive control system for steam temperature of fossil-fuel-fired thermal power plant. IFAC Symp. on Power Plant and Power Systems(pp.201-206). Cancun, Mexico. Prasad G., E.Swidenbank and B.W.Hogg,(l998). A local model networks based multivariable predictive control strategy for thermal power plants. Automatica, ,34(10), 1195-1204. Tommy Moelbak.(l999). Advanced control of superheater steam temperatures-an evaluation Control based on practical applications. Engineering Practice, (7), 1-10 Wu, Q.H., and Hogg, B.W.(l991). Laboratory evaluation of adaptive controllers for synchronous generators, Automatica, 127(5), 845-852 Xiang-Jie Liu and Xiaoxin Zhou(l999). Identification of Boiler Models and Its Fuzzy Logic Strategy. Proc. the 14th IFAC World Congress. Volume 0 (pp. 149-154).Beij ing China.
time{min)
o
20
40
60
eo
100
Fig.9-a Response of the steam temperature 200
leo
"0
ro
.QHiO
time(minute)
o
20
40
60
80
100
Fig.9-b Changing load condition To make a comparison, the proposed nonlinear controller has been simulated on both neuro-fuzzy model and on linear model(under 140MW) under the same changing load condition. Figure 10 shows that while the load changes at 140MW(t=20min), the responses of steam temperature by the two models are similar. While the load changes at 190MW(t=60min), the response offered by neurofuzzy model is superior to that of linear model.
218
Copyright © IFAC Power Plants and Power Systems Control, Seoul, Korea, 2003
IFAC PUBLICATIONS www.elsevier.comllocale/ifac
NEURO-FUZZY GENERALIZED PREDICTIVE CONTROL OF BOILER STEAM TEMPERATURE
.
.
Xiang-Jie Liu , !':elipe Lara-Rosano , •• Marino Sanchez Parra , Raul Garduiio Ramirez
.
Centro de Ciencias Aplicadas y Desarrollo Tecnologico, UNAM, Mexico City. D.F 04510, Mexico Electric Research Institute, Cuernavaca, Morelos CP 62490 Mexico
..
Abstract: A neuro-fuzzy network predictive approach is introduced to design a control system for boiler steam temperature process. While the nonlinear process is modeled by neuro-fuzzy technique containing local CARlMA model, traditional generalized predictive control method can be extended to nonlinear case in a neuro-fuzzy fashion. The proposed method was found to provide a satisfactory performance over the 200MW superheater steam temperature system. Copyright © 2003 IFAC Keywords: neuro-fuzzy networks, nonlinear control, steam temperature
1. INTRODUCTION
of parameter estimation algorithm could act to accentuate process disturbances. Problems with unmodelled dynamics and on-line adaption of controllers may not be acceptable in power plants for reasons of reliability(Wu and Hogg, 1991).
Continuous processes in power plant and power station are complex systems characterized by nonlinearity, uncertainty and load disturbance. Applying of traditional control methods encounter great difficulties while the process working condition changes within a large operation range. The effective way is to develop advanced modelling and control strategy on them.
Principally, nonlinear process requires nonlinear predictive control for optimum performance. Nevertheless, controller incorporating a nonlinear model may require tremendous computational burden which may disqualify it for on-line application. With specific nonlinear model, the explicit control law may prove a difficult or even impossible task. To incorporate the linear method, Prasad et a/.(1998) proposed a local model networks based multivariable predictive control, which has been simulated on a 200MW oil-fired drum-boiler thermal power plant.
Generalized predictive control (GPC) methods have been proved to be an effective method over linear model and are frequently applied in nonlinear control in an adaptive framework, designing the control law on the basis of a linearised model of the controlled system, which is reestimated periodically to fit the actual operation point with online estimation by recursive identification techniques. The linearised model may be acceptable only in the case where the process is working around the operating point. An adaptive approach may fail if abrupt changes in the operation point are requested by the control specifications or determined by the specific nonlinearity of the system. Self-tuning controller requires continuous on-line identification with injection of additional disturbance into the plant for sufficiently rich excitation of plant dynamics. Failure
It is noticed that much of the complex process in
power plant could be controlled by manual operation of the experienced operator, which is based on the enough knowledge of the object. This offer effective modelling and control method for automatic control system. The recent developed neurofuzzy network(Brown and Harris, 1994) could be an effective way to the modelling of such nonlinear system in that fuzzy rules could easily express the expert knowledge in linguistic form while neural
213
networks posses the learning ability of approximating nonlinear functions with arbitrary accuracy. In the neuro-fuzzy networks, the whole envelope of process operation is divided into several operating regions. In each region a local reduced-order model is used to approximate the process. Fuzzy logic representing human operator's language expression provides an appropriate means to define operation regions. Thus respectively the local predictive control strategy could be constituted. This paper develops a nonlinear neuro-fuzzy network modelling and predictive control method and then apply it to the superheater steam temperature control system on 200MW unit steam-boiler. Associate Memory Network(AMN) is used as process predictive model because it provides a direct link between artificial neural networks and the fuzzy systems. Transient process input-output data are then used to train the network. With the established neurofuzzy model, a set of relative local GPC controllers are composed under different operation regions to constitute the neuro-fuzzy controller. The performance of the control system has been verified by the simulation process and then tested on superheater steam temperature process.
1
c::
o
tl 20.5
'"
~ g
2
1
x2
0 0
x1
Fig.2 Multivariate basis function The B-spline network is initially designed to specify the shape(order) of each of the univariate basis functions, and this implicitly determines the number of basis functions mapped to for a particular network input. There exist recurrence relationship for evaluating the membership of a univariate Bspline basis function with R inner knots(Brown and Harris, 1994). Denoting the jib univariate basis function of order k by f.J£ (x), jib knot by Ai and the jib interval by [A,j_P A,j] . The basis functions are defmed on a bounded support and the output of the basis function is positive on its support, f.J£ (x) == 0, x ~ [A,J-k ,A,J]
and
f.J£ (x) > 0, X E (A,j_k' A,j) .The sum of the outputs of
the
basis
functions
is
always
one,
i.e
Lf.J£ (x) == l~ x E [x min , x max ] ' J
2 NEURO-FUZZY NETWORK MODELLING
The neuro-fuzzy network shown in figure I could be expressed as a set of fuzzy production rules: IF operating condition i (XI is positive small, and
With the following general single-input single-output nonlinear dynamic system: y(t) == f[y(t -I)"", y(t - n~), u(t - d)"",
(1) u(t - d - n~ + I), e(t -I),,,,, e(t - )]+ e(t)/L\ where f[.] is a smooth nonlinear function such that a Taylor series expansion exists, a local linear model at an operating point O(t) can be given by the following CARIMA model: A(Z-' )y(t) == Z-d B(Z-I )L\u(t) + C(Z-I )e(t) (2)
n;
"', x" is negative large) THEN local linear CARIMA model i : Yi(t) = GilYi(t -1) + ·"Gi".Yi(t - no) + bio/),ui(t - d) + ... + bill. /),ui(t - d - nb ) + ei(t) + ... + Ci"c ei(t - ne)
or
where A(Z-')==M(z-'), B(Z-') and C(Z-I) are
The multivariate basis function is obtained by:
"
polynomials in z -I, the backward shift operator. They are function of the operating point O(t). Therefore, the nonlinear model could be decomposed into several linear or nearly linear models at different operation points. The total model could be represented by a B-spline AMN shown in figure I. The antecedent variables [x p x 2 ",x,,]representing different operation points are the inputs of the AMN. The output of the network model yet) could be combination of local linear models Yi (t) . univariate
muttiyari~
~~fu~an
~~~~~
A;(Z-')Yi(t) == Z-d B,(Z-I)L\ui(t) + Ci(z-I)ei(t) (3)
a,(x)==nf.JA,(x k k=1
)
(4)
k
where i == 1,2, .. " p and n is the dimension of the input vector x(t). p is the total number of memory required in the network given by
"
p== n(R; +kJ
(5)
i=J
Thus the desirable properties of the univariate Bspline basis functions are all extended in a natural way to the multivariate basis functions. They are defined on hyperrectangles of size (k, x k 2 x··· x k,,) and therefore possess a bounded support. The output is positive inside this domain and zero outside. Fig.2 shows the multivariate basis function formed from two ,order 2, univariate basis function.
a,
The model output is the synthesizing of these p rules:
0,
l-------'--~.y,
Fig.1 Nonlinear neurofuzzy network model
214
N
p
J = E{Lqj[La;
p
(12)
+ LAj[La;u;(/+ j-IW j=1 ;=J
Choose the cost function to be: 1 2 I ~ 2 J = 2. e = 2. (y - y)
With interactions among those subsystems, the minimization of this cost function requires large computing burden. An alternative approximated cost function could be acquired for the simplification with Cauchy inequality,
(7)
where y is the network prediction, and y is the plant output. Training parameter could be changed in the direction of the negative gradient:
..:.aij
uaij
aJ
bi! =-g ab;!
;=1
ay ay; ( ) ~ ( I) =-ge ~~'. ~_. =-gea; x y; 1-
aJ =-g ~_.
.
p
[La;(y;(/+ j)- y,(t+ J)W p
~ p L[a;(y;(/+ ) - y,(/+ j»]2
vy, uaIJ
ay ay; =-ge ay; obi!
;=1
=-gea;(x)u;(/-d-m)
[fa;u;(1 +) _1)]2
~P
;=1
I~I
where
~ nii
(8) (9)
0 ~ m ~ nb
N
M
M
j=d
;=J
M
p
j=1
+ L(aYLAj[u;(t+) -I)f
(10) q j and Aj are respectively the weighting factors for
;=1
j=1
=f(a;)2J;
the prediction error and control energy; y, (I +) is
(14)
;;)
where
the ith step reference trajectory, d is time delay taken as minimum costing horizon, N and M are maximum costing horizon for prediction and control variables respectively. The control policy is given by the weighted sum ofp sets oflocal control policies:
N
M
J; = E{Lq}y;(t+ j)- Y,(t+ j)f}+ LA)U;(t+ j -I)f j=d j=J (15)
The derivation procedure shows that the essence of minimization of J is the same as that of J;. Thus the problem changes to the minimization of J; in each local model.
(11)
;=1
LlU; (t)
N
p
=E{L(a;)2 Lqj[y;(/+ j)- y,(/+ jW}
J = E{~>jrY(t + j) - Y,(t + j)f} + LA)~U(t + j -I)f
where
p
+ LLAj[a;u;(/+ )_1)]2 j=1 ;=1
For the purpose of generalised predictive control, the cost function to be minimized is:
Llu(/) = fa;Llu;(/)
p
E{LLq)a;(y(t+ ) - y,(/+ ))]2} j=d ;=1
3.1 The problemformulalion wilh approximalion
j=d
(13)
;=1
Equation (13) means the sum of the weighted squared errors can be the basis for establishing an upper bound of the original objective function. And
3 NONLINEAR NEURO-FUZZY NETWORK GENERALIZED PREDICTIVE CONTROL
N
f[a;u;(1 + ) _1)]2
is the relative control action in each
local region, a; is the same as that defined in the neuro-fuzzy modelling equation (4) since the contribution of the output estimated by the ith submodel to the overall process evaluation should be considered the same as that by the ith local control action to the overall system controller. This also meet the idea of T-5 model. It is different from T-5 method in that the "consequence" does not necessarily contain the "premise" part. With this control structure, the system eliminates the controller switch problem and provides a much more smooth control performance in process operation. With model (6) and control policy (11), equation (10) could be expressed as:
3.2 Controller
Equation (15) could be rewritten in a matrix form as: J; = E{[Y;(t + I) - Y,(t + l)f Q;[Y;(t + I) - Y,(t + I)]}
+ ~U/ (t)T;~U;(t)
(16)
The control law by the ith sub-system can be identified as(Clarke el aI., 1987): LlU; (I) = (G; T QG; + A)-I G; T Q[Y, (I + I) (17)
- F;LlU; (I -I) - S; (z -I )y; (I)]
where Y;(I + I) = [)I; (I + 1),)1;(1 +2),···,)1;(1 + p)f
215
Yr (t + I) =Ly r (t + I),
Y (t + 2), ... ,Y r
I'1U, (t) = [l'1u, (t), l'1u, (t t1U,(t - I) = [t1u i (t G,
r
(t + P) f
applied for the superheater temperature system in a multi-stage control manner to reduce the time constant of each stage and improve the control trait. Q The rated superheated steam temperature is 540 C.
+ I)"", l'1u i (t + M -I)f
n b ),C1u,(t
-
+ 1),"',t1u,(t -I)f
nb
(t + I) = [R il (Z-I )ei (t + 1)"" RiP (Z-I )e, (t + p)f
S, (Z-I)
= [Sil (Z-I ),Si2 (Z-I),'"
Sj(z-I)and
are
R,(z-I)
The task of the superheater in boiler-turbine system is to heat the steam by combustion gas and then send it to turbine. As shown in figure 3, the steam coming from the boiler drum passes through the lowtemperature superheater and receives a spray water injection before passing through the radiant-type platen superheater. The steam then receives a second spray water injection before passing through the high-temperature superheater. A properly control system by superheater water spray should maintain strictly the steam temperature within the permitted range( ± I QC in transient process and ±5 QC in steady state). Higher temperature could damage the superheater and the high-pressure-turbine by high heat strength. Lower temperature could decrease the running efficiency of the whole steam-boiler. By reducing temperature fluctuations, mechanical stress causing microcracks is diminished, therefore plant life is increased and maintenance cost is decreased, This is obviously the motivation for GPC control, since the variance of the steam temperature is directly related to economic and safety performance.
,SiP (z-I)f
in
the
Diophantine
equation: (18)
1= A,(z-')R'j(z-')+z-iS,/z-')
and: G,(z-') = B, (z -I )R, (Z-I) _g
-
+g
j,O
7-
),1-
1 +"'+g
~[ g;,
=
diag(qil' qj2'''', q,p)
g~,P-1
F,
~
g;,lIb
[
g;"•., .
g~II~+P-'
(19-c)
= diag(A, I ' A'2"", A,M)
°
g; 0
G,
°
(19-b)
= g i,' + S i,obi-i
g i+I"
Q, T,
( 19-a)
7-(lIb+i- l )
jJJb"'"j-! ....
g;,o
,
gp-I,P-2 j gl,lIb-1
( 19-d)
j gp-M+I,P-M PxM
,
g2,lIb
, g P,lIb +P-2
g;,2 g;,3
g~,P+l
g;,1 j gZ,2 g~,p
The superheater outlet steam temperature can be affected by many factors such as steam flow, combustion condition, feedwater temperature, steam enthalpy and combustion gas temperature. Totally speaking, three main factors dominate the superheater outlet steam temperature: load power, gas flow and superheater inlet steam temperature. These are also the reasons why a conventional PIDbased control strategy is often unable to perform satisfactorily. Many efforts have been put into developing and testing more advance control schemes on different boiler plants, like adaptive simulation-model-based control of fossil-fuel-fired thermal power plant(Nakamura et aI., 1995) and feedforward control based on new measuring techniques on a 256MW Unit(Tommy, 1999). The intention of this section is to develop the nonlinear model of steam temperature with the proposed neurofuzzy method based on dynamic experiment of the 200 MW Unit and then constitute the relative non linear GPC controllers.
PXllb
(l9-e) The optimization control variables are M steps into the future based on the control horizon. Only the first control action is implemented, using a receding horizon principle, i.e, l'1u, (t) = d il T [Yr (t + 1) - F,l'1U j (t -1) - S, (Z-I )y, (t)]
where d il T = 0,0,'" ,O)(G, T QGi + A) -I G j T Q is the first row of the matrix (G/ QG, + Ar' G/ Q.
4 NEURO-FUZZY MODELLING AND CONTROL OF BOILER STEAM TEMPERATURE 1
to turbine
f-----M---, 2
-->-->-->-->-
3
2
=:: =::
combustion gas flow
_540 r - - - - - - - - - - - - - - ,
~
low-temperature platen high·temperature supemeater superheater tuperheater
'5
ro
Q;
~535 2
1--- superheater spray valve 2---superheater spray 3---feedwater valve 4---economiser Fig. 3 Depict of boiler superheater steam system
E
Ol'"
The process considered is the pulverized coal-firing 200MW steam-boiler used for electric power generation. It produces 670 tons of steam per hour at maximum continuous rating. The final superheated steam pressure is 16,7MPa. Two stage sprayers were
time(mJn)
530 0
2
4
5
Fig.4 Dynamic response(solid line) under 18% step change in the second stage spray flow and its fitting curve(circled line)
216
~
Considering the output "steam temperature B" with the control input spray PIJ' dynamic of the steam temperature process could be depicted to be a second order representation (Liu and Zhou, 1999): G(s)
B
Kp
pIJ(s)
(T1s+I)(T2 s+l)
=- - =
e- ts
5045
r---~---~--------'
§
(20)
'"CD
-E
time(min)
CD
~ 525 L...O---5~---1~O---1~5----"'20
Fig.6 Comparison of boiler system(solid line), global linear model(dotted line) and neuro-fuzzy model(dashed line) responses Table 2 Neuro-fuzzy GPC control law parameters (F,=O)
Load High
200
Fig.5 Local division of five membership function Figure 4 shows real-time dynamic response of steam temperature under 180MW load condition and its fitting curve. The linear model (20) is, however, extremely local in nature, and do not recognize the non-linear nature of the process. Load operation leads to changes in operating point right across the whole operating range. With the neurofuzzy modelling in section 2, load operation is divided into five regions as shown in figure 5. This division is based on the operator's former experience, which considers that 200MW is high load, 180MW is medium high load, 160MW is medium load, 140MW is medium low load and 120MW is low load. Since the length of superheater tube is about tens of meters, there exists time delay from the superheater spray flow to the change of superheater outlet steam temperature. The average time delay r = 30s is assumed to be uniform and taken as minimum control horizon. Let C i = I to make ei (t) an uncorrelated random sequence of zero mean. The identified five-region neuro-fuzzy model is shown in Table I.
Medium high
B
Higtl
1- 2.8824z- 1 + 2.7682z-2 - 0.8858z-3
MediI.m higJl MediJ.m MediI.m
1-2.8940z- 1 +2.7915z- 2 -0.8975z- 3
0.0035 0.0028 0.0023 OJXH9
1- 2.9200z- 1 + 2.8416z- 2 - 0.9216z- 3
OJXH6
39.9 - 69.2z- 1 + 30.3z- 2 46.2-81.0z-' +35.8z- 2 1
Medium low
38.9 - 68.1z- 1 + 30.2z- 2 44.7 -79.1z-' + 35.4z- 2 1
2
29.4 - 49.9z- + 21.5Z- ] 35.6-61.5z-' + 26.9z- 2 [
Low
42.3 -73.9z- 1 + 32.6z- 2 49.8 - 87.7z-' + 38.9z- 2
0.586
o,353] 0.423 0.493 [ 0.563
[
0'328~ 0.401 0.478 0.559
2
1
[
[
0.375] 0.445 0.520
2
27,7 - 47.2z- + 20.4Z- ] 33.2 - 57.5z-' + 25.2z- 2 [
29,9 - 50.9z- + 22.0Z- ] 36.5 - 63.0z-' + 27.6z- 2 43.4 -76.0z-' + 33.6z- 2 50.8 - 89.8z-' + 40.0z- 2
o,301] 0.371 0.445 [ 0.524
The neuro-fuzzy GPC is established based on neurofuzzy model. Simulation of steam temperature transient process was conducted under five different load condition. Sampling time and control time are both chosen as 5 seconds. The following parameters: P=10, d=6, M=8, Q=I, A.=O.lxI, after evaluated in a test and trial mode, are used to achieve an active control. Table 2 lists the control law parameters. Fig.7 shows simulation of steam temperature(dotted line) under set-point tracking using neuro-fuzzy GPC controller.
low
Low
1
Medium
j
1- 2.9130z-' + 2.8279z-2 - 0.9149z- 3
1- 2.9000z-' + 2.8100z- 2 - 0.9100z- 3
0,390] 0.452 0.512 [ 0.570
28.0-47.2Z- +20.3Z_2] 33.8 - 57.9z- 1 + 25.1z- 2 [
Table I Neuro-fuzzy model identification parameters Ai
23.3-45.9Z-' +19.6Z-2]
32.9 - 56.lz- 1 + 24.2z- 2 38.7 - 66.8z-' + 29.1z- 2 [ 44.7 -78.0z- 1 + 34.3z- 2
P'545 ID
Also a global linear model is acquired with the same I/O data in the whole operation region. The real-time open-loop response shows that the neuro-fuzzy model can nearly perfectly describe the nonlinear dynamic behavior but the global linear model can not match the plant. The reason is that linear model could hardly representative nonlinear plant, no matter what kind of identification method has been used.
5
1§540
"
CD Cl.
E
~535
~5lJ
.,
.'
CD
1il
time(min)
525'--
o
__ _ 15 20
~
5
10
~
_____' 25
Fig.7 Simulation of steam temperature tracking
217
~ tu
~525
time(min)
g.
Fig.8 Diagram of boiler control system
if)
0
20
40
60
EO
100
Fig.! 0 Comparison of the proposed method on neuro-fuzzy model(solid line) and on linear model(dotted line)
The real-time control system is applied in the cascade form (Fig.8). Neurofuzzy GPC controller acts as the principal controller, containing five local GPC controllers. Two controllers are working at the same time, decided by load signal through five triangular membership functions. The subordinate loop adjusts the superheater water spray with ordinary P controller, so as to give a forward response and overcome the inner disturbance quickly. Combustion gas flow acts as feed forward variable(disturbance).
5 CONCLUSION Nonlinear process in power plant can be modeled by neuro-fuzzy modelling technique. The neuro-fuzzy model composed of a series of CARIMA models could represent system nonlinearity perfectly. With the relative GPC strategy, the control system could reach a near optimal structure. The proposed predictive control method is particularly suitable for nonlinear process which can be divided into several local operating regions and thus greatly advance online applications. The effort required to develop a neuro-fuzzy predictive model of the specific plant. The advantage is shown in the modelling and control of boiler steam temperature system, which is a typical complex industrial process. In such a way, the proposed method offered an engineering approximation approach for a class of nonlinear industrial system which are formerly difficult to be controlled by traditional method.
Figure 9 shows the response of the steam temperature under changing load conditions( 1%- 2.5% /min). While the steam temperature fluctuate due to changing load, the system overcome the disturbance in a satisfactory way. Steam temperature overshoot no more than ± 7°C in transient process. The result is similar to that of (Tommy,1999), which is tested on a 380MW unit, under coal mill stop disturbance. ~ 545
*''""
REFERENCE
-E g.S25 (f)
Brown, M. & Harris, C. J. (1994). Neurojuzzy adaptive modelling and control. Prentice Hall. Clarke, D.W., Mohtadi, C. and Tuffs, P.S., Generalized predictive control(l987). Parts J and 2, Automatica" 23, (2), 137-160. Nakamura, H., Toyoda, Y., and Oda, K.(l995). An adaptive control system for steam temperature of fossil-fuel-fired thermal power plant. IFAC Symp. on Power Plant and Power Systems(pp.201-206). Cancun, Mexico. Prasad G., E.Swidenbank and B.W.Hogg,(l998). A local model networks based multivariable predictive control strategy for thermal power plants. Automatica, ,34(10), 1195-1204. Tommy Moelbak.(l999). Advanced control of superheater steam temperatures-an evaluation Control based on practical applications. Engineering Practice, (7), 1-10 Wu, Q.H., and Hogg, B.W.(l991). Laboratory evaluation of adaptive controllers for synchronous generators, Automatica, 127(5), 845-852 Xiang-Jie Liu and Xiaoxin Zhou(l999). Identification of Boiler Models and Its Fuzzy Logic Strategy. Proc. the 14th IFAC World Congress. Volume 0 (pp. 149-154).Beij ing China.
time{min)
o
20
40
60
eo
100
Fig.9-a Response of the steam temperature 200
leo
"0
ro
.QHiO
time(minute)
o
20
40
60
80
100
Fig.9-b Changing load condition To make a comparison, the proposed nonlinear controller has been simulated on both neuro-fuzzy model and on linear model(under 140MW) under the same changing load condition. Figure 10 shows that while the load changes at 140MW(t=20min), the responses of steam temperature by the two models are similar. While the load changes at 190MW(t=60min), the response offered by neurofuzzy model is superior to that of linear model.
218