Adaptive control for the steam temperature of thermal power plants

Adaptive control for the steam temperature of thermal power plants

Pergamon 0967-0661(94)00018-2 ComrolEng Pracuce,Vol 2, No 4,pp 567-575,1994 Copyright© 1994ElscvacrScac~,eeLtd PnnteAm Grc~tBntm~Allnghtsrv~rvcd 0967...

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Pergamon 0967-0661(94)00018-2

ComrolEng Pracuce,Vol 2, No 4,pp 567-575,1994 Copyright© 1994ElscvacrScac~,eeLtd PnnteAm Grc~tBntm~Allnghtsrv~rvcd 0967-0661/94$7 00 + 0 00

ADAPTIVE CONTROL FOR THE STEAM TEMPERATURE OF THERMAL POWER PLANTS S. Matsumura*, K. Ogata**, S. FuJli**, H. Shioya*** and H. Nakamura*** *Electrw Power Research and Development Center, Chubu Electric Power Co, Inc , M~dor~-ku, Nagoya, 459 Japan **School of Engineering, Nagoya Umversay, Chdmsa-ku, Nagoya, 464-01, Japan ***Department of Apphed Systems, Badey Japan Co, I,M, Sh~zuoka-ken, Tagata-gun, Ntrayama-cho, 410-21 Japan

Abstract A dascrete time adaptive control system was apphed to the steam temperature control of a boder for electric power generatmn In the system, the adaptive controllers are installed m parallel with the conventmnal PID controllers for superheated and reheated steam temperatures The plant dynarmcs was described with polynormals whose parameters are adaptively estimated from the plant data The adaptive control signals are synthesazed on the basis of the estimated parameters so as to aclueve the specified control objective The system was apphed to a 375MW plant and found to reahze far better control performance than the conventional PID control system Keywords. Adaptive control, Discrete time systems, Steam temperature, Boders, Power plant, PID control, Nonlinear systems, Robustness

1 INTRODUCTION In large-capacity, high-pressure, high-temperature boilers for electric power generation, steam temperatures must be kept accurately within small devmtlons around their specified values In order to maintain nominal plant efficiency and to ensure the safety and maximum eqmpment life of the plant For the steam temperature control, PID control systems are widely used which are composed of control elements designed using sophLstlcated concepts and tuned by skilled tuning engineers so as to cope with the process nonlinearity and possible changes m boiler conditions With such a P I D control system tuned for some probable plant condltlons, however, it LS difficult to realize desirable control performance for all plant conditions that might be encountered m the actual plant operatlon In order to overcome the above-mentioned problems inherent In the PID control system, applications of the so-called advanced control systems have been suggested by specialmts m the field of power plant control, e g Corl and Maffezzonl (1984), Surgenor and Pleper (1992), etc One of the present authors also developed an optimal 567

regulator system for steam temperatures of power plants furnished with load-adaptive gain scheduling function (Nakamura and Akalke, 1981, Nakamura and Uchlda, 1989), which has been Implemented at more than 20 fossil-fired power plants in Japan and abroad since its first implementation m 1978 However, because of the recent fuel situation, the number of coal-fired power plants has been increasing year by year, whose steam-temperature dynamics is affected largely by the properties of the coal, furnace conditions such as the fouhng or seasomng of boiler tubes, etc Under these circumstances, it sometimes happens that the performance of the optimal control system deteriorates because of the discrepancy between the behavior of the actual plant and that of the state equation, which is a state-space mathematical expression of the plant dynanncs An appropriate means to cope with such a situation would be the adoption of an adaptive control system in which control parameters are adJusted by means of on-hne, real-time algorithm so that desired control characteristics may be reahzed regardless of the variations of plant dynamics This is the principal reason that led the authors to the


S Matsumurael al

study introduced in this paper Referring to the adaptive control system, the theory has been introduced In many studies such as those by Monopoll (1974) on Model Reference Adaptive Control with an augmented error signals Narendra and Valavanl (1979) describing the direct and Indirect approaches of the continuous time adaptive control, Goodwin, et al (1980) on discrete time adaptive control system, a comprehensive survey by ~strom (1983) etc Since 1980's when the theory on the stabihty of the adaptive control systems was estabhshed by the above works, many examples of applIcatmns of adaptive control systems to practical plants have also been reported However, only a few examples of Its application to power plants have been reported so far Although Irving and Dang Van Mien (1981) discuss the Discrete Time Model Reference Multi-variable Adaptive Control Apphcation to electric power plants, their control objective IS the boiler of a nuclear power plant with conmderably different characterlStlCS from the fossil-fired plant which is the control objective of the present author study Other applications to power plant control by Atom et al (1984), Fessl (1986), and ]kkesson (1987) employ an approach using an indirect self-tuning controller In contrast with this, the present authors have attempted to verify the capability and performance of the direct adaptive controller applied to fossil-fired plants As the prehmlnary study, some of the present authors tried to examine the control performance of the adaptive control system on a simulation study basis (Ogata, et al 1991) and found that the discrete time direct adaptive control system achieved desirable performance if the plant model was ex-

pressed by properly chosen process variables and appropriate consideration was paid to the control system design The results of this simulation studs were used as the basis of the adaptive control system which will be described In this paper In this paper, the outline of the boiler process, control system configuration, and basic theory for controller design will be described Then field test results obtained by the proposed adaptive control system will be shown to demonstrate its fine control performance Some remarks on the problems that should be solved in the future are briefly referred to in the conclusion

2 CONTROL SYSTEM Figure 1 shows a conceptual view of a largecapacity drum-type boiler for electric power generation The mm of the proposed adaptive control system is to maintain the steam temperatures at the outlet of the superheater (Yl) and the reheater (Y2) at thmr specffied set-point values, regardless of the changes in the plant load, propertles of the fuel, conditions of the furnace, and so forth For the sake of convenience, the superheater outlet steam temperature will be referred to as SHT and the reheater outlet steam temperature as RHT In Figure 1, SHT IS controlled by adjusting the flow rate of the atemperator spray (Ul), a small portion of the feedwater Injected into the atemperator, while RHT is regulated by controlling the flow rate of flue gas reclrculatlon by the mampulatzon of the GRF damper (u2) Since the superheater and the reheater are aligned In series In the furnace, mutual interaction usually takes place between the SttT control system and the RHT control system Alemperator

Fig 1 Conceptual view of drum-type boiler



--~ ATEMPERATOR ~'3i |











~- l+-


L...._e ~ %



= r,





. I




] I

Y= "



W F]g 2 Configuration of control system Among the disturbances to the boiler process, the change m plant load is the largest one As the plant load follows almost immediately after the MWD, 1 e, megawatt demand or the load command from the system's dispatch center, the MWD m convemently regarded as a measurable index of the plant load, henceforth, the symbol MWD will be used to represent the plant load Figure 2 schematically shows the configurations of the steam temperature control system of a drum-type boiler As shown In Fig 2, the conventional SHT control system forms a cascade configuration, consisting of the main and minor controllers, while the conventional RHT control system is composed of a single loop For both the SHT and RHT control systems the adaptive controllers are installed in parallel with the conventional controllers so as to support them The conventional controllers comprise P, I, and D elements and function generators to compensate for process nonhnearity which is dependent on the magmtude of the plant load In ad&tIon to the above, a signal generator, producmg the feedforward control signal called BIR (Boiler Input Rate), which temporarily supplies the difference of the stored energy m the boiler tubes, IS used for large and fast load changes the effects of the change In plant load on SHT and RHT are shown in Figure 2 with the symbol of w depicted In arrow marks to the superheater and reheater processes The function generator (w, w) In Fig 2 is the BIR signal generator whose output signal temporarily appears m response to the changes m MWD (shown with the symbol of w, w)

3 THEORY FOR CONTROLLER DESIGN Power plant dynamics virtually comprises a contmuous time, nonlinear, time-varying, distributedparameter system with unknown parameters In the following, however, controller design is performed under the assumption that the plant dynamics can be adequately represented by a discrete time model with an ARMA structure, the model parameters to be used for control signal synthesis are adaptively adjusted on-hne so that they may represent process dynamics properly 3 1 Plant model The plant dynamics is represented for each of the SHT and RHT with a Single Input Single Output (SISO) system with disturbance compensation In the following, only the SIlT control system is described

A(z-1)el(k) = z-dlBl(Z-1)ul(k) + z-d~B2(z-1)u2(k) + z-dwC(z-1)w(k)


where z -1 is a umt delay operator, k is a positive Integer, and A(z -1) Bl(z-1), B2(z-I), C(z -1) are polynomials expressed with respect to z - 1 1 e , A(z -1) = 1 + alz -1 + Bl(z -1) = bl0 + bllz -1 +

B2(z -1) = b20 + b21z -1 + C(z -1) = CO"JrCl z-1 -["

..~ an z - n

+blml z-ml + b2m2Z-m2 Jr CqZ - q

In Eq (1), el(k)=control error (deviation of controlled variable yl(k) from its set-point value), ul (k)=control Input to the system (adaptive controller output),


S Matsumura et al


u2(k)=feedforward control signal related to the rate of change in MWD, w(k)=MWD (measurable disturbance to the plant) that affects plant dynamics directly In Eq (1) and (2), the following conditions are assumed 1) The polynormal pairs A(z -1) and Bl(Z-1), A(z -1) and B2(z-1), A(z -1) and C(z -1) are coprime, respectively, 2) The coefficients a,,bl~, b2,, c, in Eq (2) are unknown but constant process parameters, and the order n, ml, m2, and q are known from a priori knowledge about the process model,


+ B2(z-1)R(z-1)u2(k -

+ C ( z - 1 ) R ( z - 1 ) w ( k - dw) = Ri(z-1)ul(k-

dl) + S ( z - 1 ) e l ( k - dl)

+ R 2 ( z - ~ ) ~ ( k - d2) + R e ( z - ~ ) ~ ( k - d~) = oTff(k -- dl),


RI(Z -1) -- Bl(z-1)R(z -1) = rl0 + rllZ -1 +

+ rlml+dl_l z-(ml+dl-1)

R2(z -1) - B2(z-1)R(z -1) = r2o + r21 z-1 + + r2m2+dl_l z-(m2+dl-1) [~c(z -1) -- C(z-1)R(z -1 ) --- rC0 + rCl z-1 +

+ rCq+dl_lZ -(q+dl-1)

3) dead time dl, d2, dw are also known a priori and satisfy the relationship d2 _> dl _> 1, dw > d l > 1,

o r = [rl0,e0r],

4) Bl(Z -1) is an asymptotically stable polynomial

r2o, , r2m2+dl-1, rCo, , rCq+dl-1] CT(k)=[u~(k-1), , u l ( k - ml - d l + 1),

The aim of the control is to keep the plant output variable (in this case the steam temperature) at its reference value, m other words, to synthesize the control signal ul(k), asymptohcally satisfying the regulation problem described in the following equations

el(k), ,el(k-n+l),u2(k+dl-d2), u2(k - m2 - d2 + 1), w(k + dl - dw), w ( k - q - dw + 1)]

D(z-1)el(k + dl) = 0, D(z -1) = 1 + dlz -1 +

el(0) # 0, + dnz -n,

(3) (4)

where D(z -1) is a polynomial that specifies the characteristics of convergence of error e 1 D ( z - 1) is provided properly by the designer


~0T = [rll,

er(k) = [ul(k),C[(k)] ,rlml+dl-l,so,


, ,

Equation(6) provides an alternative representation of the process dynamics described by Eq (1), the coefficients s,,r I t ,r2,,rc~, comprising S ( z - 1). Rl(Z-1), R2(z-1), Rc(z-1), are the parameters relating to at, bl~, b2~. c, The number of these parameters are n, (rnl + dl), (rn2 + dl), (q + dl), respectively, and (n + ml + rn2 + q + 3dl) in all Since the number of the parameters In Eq (1) is (n+ml+m2+q+3)

, ffdl

> 1, E q ( 6 ) is a

non-minimal realization of Eq (1) 3 2 Alternative representatmn of the plant 3 3 Controller design (Ogata el al, 1991) First, the structure of the controller is determined under the assumption that process parameters al, ,an, bl0, ,blml, b20, , b2m2,co, ,cq, are given For this purpose, it is known that the polynormals R ( z - i ) , S ( z - 1 ) , satisfying the following relationship, can be uniquely determined, D(z -1) = A(z-1)R(z -]) + z - d i S ( z - I ) ,


By using Eq (6), Eq (3) can be expressed as

D(z-1)el(k + dl) = bloul(k) + 00T¢0(k) = 0, (7) where bl0 Is equal to rl0 Accordingly, from Eqs (6) and (7) the control signal satisfying the afore-mentioned control objective can be obtained as follows

S(z -1) ~-(a2-ax) S2(z-~ I u2(k) nl(z_l)el(k) - _ Bl(z-1



R(z - 1 ) = 1+ rlz - 1 +

+ rdl_l z-(d1-1)

S(z -1) = so + slz -1 +

+ Sn_l z - ( n - l )

Multiplying both sides of Eq (5) by e~(k) and using the relationship in Eq (1) gives

D(z-1)el(k) = A(z-1)R(z-1)el(k) + z-alS(z-1)el(k) = Bl(z-1)R(z-1)ul(k - dl) + S(z-1)el(k - dl)


z_(dw_dl )

C(z -1)

1 T

B~(z-~) w(k) = -V~oOO Co(k)

(8) As long as the conditions d2 >_ dl and dw >_ 1 hold, the control signal ul(k) in Eq (8) can be realized without using the future values of el(k), Ul(k), U2(k), and w(k) When the plant parameters are unknown, ul(k)

Steam Temperatureof Thermal Power Plants m Eq (8) cannot actually be realized In the actual system, therefore, the estimated parameters {b'10(k),0T(k)} are substituted for the unknown ( n + m l + m 2 + 3 d l ) parameters {bl0,00T} m Eq (8) Thus the control signal is composed as follows Ui(k ) --


OT(k)i~o(k )



Figure 3 shows the structure of the adaptive control system based on the above-mentmned design method It Is probable in the actual control that plant parameters will vary largely depending upon the magnitude of the plant load To cope with such a situation plant parameters are expressed with the first-order algebraic equation described with respect to MWD as follows 0 = 0~ + w ( k -

dl)O b


= [Oat, 0 br] [(r(k = Oer(C(k




dl), w(k




dl)] T (11)



Since plant parameters are actually unknown, the control signal ul(k) is computed by Eq (13) m which 0c m Eq (12) is replaced by its estimated vector 0C(k), that Is, ^cT


1 ^ b 0o (k)(o(k) ut(k) = - b~10(k) + w(klblo(k)


In Eq (13), ff b~l~(k) and b~lb0(k) are mfimtes,mal, ui(k) approaches an mfimte value To avoid such abnormal con&tmn, ul(k) Is deterrmned to minimlze the following criterion function

I(k) = [D(z-1)e](k +

dl)] 2 + eul(k) 2



= -



b~10(k) +wtkJ°~°~k)

[gl0(/~) + w(k)b~lb0(k)12 + C



Oo (k/o(k) (141

where ~tl r


bl~ +w(k)blbo O° (°(k)'

Then the control signal Is computed by Eq (14) instead of Eq (13), which ehmlnates dlvlmon by zero by providing an appropriate small value of e




tq(k) = -


Then, Eq (6) can be written as


Hence, Eq (12) Is used in place of Eq (8) for the computatmn of control signal Ul (k)

0~ r = [0~ T, 00bT ], ¢~r(k)= [;/(k),w(k);/(k)]

The parameter adjustment algorithm will he described at the end of this sectmn

D(z-1)ei(k) = [Oa + w(k


3 4 Parameter adjustment Algorithm ._

a T ],/#r = [rloa ,/90

O~~ = [rl~, r2~, 0obr = [rl~, r2b0,


b r ],/9, r =[0 aT ,0 bT] /90

, r l ran l + d l _ 1 , Sg, , r2a2+di_i, , T i rbo l + d 1 - 1 , ' r 2 rbn 2 T d I - 1 ,

rc~, sbo, b TOo,

~ s na- - I , a

, rCq+di_i] , s nb- l , b , rCq+dl-i]

¢~r(k) = [U 1 (k), ~'0T(k), W(k)U I (k), w(k)(~oT (k)] u2(k) w(k)_

Conmder Eq (15), a model for parameter ldentffication, which corresponds to the afore-mentioned plant model Eq (6)

D(z-1)~l(k) = O T ( k ) ¢ ( k - dl),

where el (k) and 0(k) are the estimates correspondmg to el(k) and O(k) m Eq (6), respectively

! /,

z ('==..Bz(z ',k) B~iz'.k) z f=" °~ Clz ,k) B,(z '.k) / I g¢ h~(Z'.k)











Fig 3 Structure of adaptive control system including external dmturbance compensation clrcmt

S Matsumura et al


Here, the identification error signal e*(k) defined belo~ is introduced

e*(~) -:-- D(z -1) {el(k ) - ~1(]¢)} =



By using e*(k), the parameter adjustment law 1s obtained as follows D ( z - 1 ) e l ( k ) - 0T(k - 1)/(k - dl) e*(k) =

1 +

_ dl)r(k



1)C(k - dl)

0(k) = 0(k - 1) + r ( k - 1)~(k - dl)e*(k)


1 ( F ( k - 1)r(k)_ l(k) A2(k)F(k - 1)((k - d l ) / T ( k - dl)r(k - 1) A-~ ~ A~~--d l - - ~ - - 1 ) - ' ~ : ~/]-) } '(19) where 0 < Al(k)_< 1. 0_< A2(k) < 2 F ( 0 ) > r I ( 7 > O) As the parameter updating algorithm the constant-trace method advocated by Landau and Tomlzuka (1991), which gives fast convergence to varying parameters, is employed In the constanttrace method, At(k) and A2(k) in Eq (18) are chosen so that trF(k) = const and Al(k) = A2(k)

4 CONSIDERATION ON ROBUSTNESS In the apphcatlon of the control theory to an actual plant, it is important to consider various means that assure safe plant operation, besides the improvement of the control performance The following are some of the measures adopted in the proposed adaptive controller As illustrated in Figure 2, the adaptive controllers are installed in parallel with the conventional PID control system When unexpected malfunction or disorder takes place m the adaptive control system, the control signals from the adaptive controller are lmme&ately bypassed or limited to Its threshold value leaving the plant under the ordinary PID control

Table 1

The samphng period for system ldentfficatlon and control is varied depending upon the magnitude of the plant load m other words the sampling period is larger for a lighter plant load where the plant dynamic is sluggish whereas it is smaller for heavier plant load where process output vanables respond to the boiler input variables rather quickly With the flexible sampling scheme, controller design that covers a large range of the plant loads becomes easier In the computation of the gain matrix P(k) which is used for updating parameter estimation at every control period the U T D U factorizatlon method (U is a umt-upper-tnangular matrix and D is a diagonal matrix) is used (Nm, et al 1992), m order to avoid the deterioration of the positivedefiniteness and symmetrical properties of the gain matrix due to the accumulation of round-up errors during the recurslve computation procedure When the PE (Persistent Excitation) condition seems to be insufficient l e the amplitudes or rates of change of the input signals for parameter estimation remain in a small range for a certain duration of time, the parameter estimation scheme is tentatively suspended by bypassing its computation loop 5 FIELD T E S T RESULTS The proposed adaptive control system was applied m January, 1992 to a 375MW, Nlshl-Nagoya No 3 drum-type boiler unit and In May, 1993 to a 375MW, Owase-Mlta No 1 drum-type umt both of which are owned by Chubu Electric Power C o , Inc The specfficatlons of these two umts are as follows Nlshl-Nagoya No 3 Umt (Boiler) Babcock-Hitachi Evaporation rate 12lOT~H, Mare steam press 140 ~ 169kg/cm 2 Main steam temp 566 °C Reheated steam temp 530 -,- 538 °C oil-fired (Turbine) 375MW 3600rpm MHI

Comparison of control performance for ramp-wise MWD change

Plant Load rate 15 MW/MIN 210---*350MW 350~210MW 210.--,270MW

squared control error(°C " sec) control slgnal(%)MAX-MIN PID AC • PAI_D_q._c . PID AC SHT 2732 987 0 36 SH spray 21 4 19 5 RHT 4360 515 0 12 GD opemng 12 0 11 4 SHT 12739 3342 0 26 SH spray 19 5 19 4 RHT 7521 807 0 11 GD opemng 13 9 14 1 SHT 10113 4612 0 46 SH spray 14 2 17 8 RHT 2423 849 0 35 GD opening 72 80

(s~[nso~[ ~s~,L plo~eI) oou~tuaojaod [oaluo D .Io uos[a~dtuoE) f, ~eI lO.nuo 0 = A n d e p y



~ H : ~ j ~ t S tosmooa~ght~y=TOOT



lo.rmoD Gld

G. ,T Z. . . .



Izl , , *v

I=lg 1 ~





nt oo





OT T~ 9T



OT Tg gT

gc ~

ss 9E ix


Gg 91, OT

gg 9 g OT


01) tat o'~

.t-t O'e


- Tt ca


,~1~ 9T UT

'=it' 9 ~ lOT

g~I' ~Jg ¢AI

gl~ ~











go TT ~T





Tg ~T


,UtS JOj is=am to=u=, = * n d = ~








~\ , L H ~ f




\_/ ~...,...-"








GT TO g ~





TG z z




oN5 TT

g g 9 g 8T


~HP O i




Loot /








TO ~ l



941' OT

G~ 9 g


G~ ~


~t oo



:1 MP40II:








slU~ld 1ottod l~uuog.L ]o o.mle.wdtuo.l, ur~olS


S Matsumuraet al

574 Owase-Mlta No 1 Unit (Boiler) Combustion Engineering Evaporation rate 1225T/H, Main steam press 120 ~- 169kg/cm 2 Main steam temp 571 °C Reheated steam temp 541 ~3 oil-fired (Turbine) 375MW 3600rpm GE

In the field test, steam temperature control performance of the conventional PID control system was compared with that of the adaptive control system under the same load patterns, that IS, the rampwlse load increase and decrease, and the triangular-wise load repetitions Figure 4 shows some results of the field test in which steam temperature deviations of SHT and RHT from their set-point values are illustrated In the figure, the improvement of control performance by adaptive control (right half) is clearly observed when compared with that of the conventional PID control (left), especially for RHT It is also seen that the advantage of the adaptive control over the PID control is evident for rampwme load changes rather than triangular-wise load repetitions In the adaptive control system, control performance is Improved at every repetition when the same type of load pattern is repeatedly Imposed on the plant This IS probably owing to a kind of learning effect that enables the system to adapt to the similar type of changes in boundary conditions As a matter of fact, the results in Fig 4 for rampwise load changes are those obtained after several repetitions of the same kind of rampwlse load changes In the Nlshl-Nagoya No 3 unit, the control performance of the adaptive control for the rampwlse MWD change was numerically compared with that of the PID control for the duration of 30 minutes from the time-point at which the MWD change took place The results are shown in Table 1 As shown in the table, the squared control error of SHT and RHT is remarkably reduced by adopting the adaptive control system, while the amplitude of the control signals remains almost m the same range for both the PID control and adaptive control

6 CONCLUSION The discrete time adaptive control system described in this paper revealed that the proposed system is quite effective for improving the control performance of a nonlinear process like the steam

temperature of a boiler for electric power generatlon plant It was confirmed that, by supplementing the fundamental adaptive control system with some disturbance compensation function, the robustness of the system is increased The identification of loaddependent parameters by means of the first-order algebraic equation and Its use in the compensation for process nonlinearity was found to be quite effective to improve control performance The future problem to be solved is to find a proper measure against fast changes m process behavlour which are mostly caused by variable-pressure operation of the plant The proposed adaptive control system has been under trial operation at the two plants since Its application After its robustness and long-period performance have been confirmed it will be put into routine operation m the near future Acknowledgement The authors would like to express their sincere appreciation to the people of Chubu Electric Power Co , Inc , KBK (Kyokuto Boekl Kalsha) Co, Ltd , for their contribution to the Joint R & D project during the past several years Thanks are especially to Mr S Mlyazuka and Ms Suda for their contribution to the project in the theoretical aspect or in programmg the control algorithm, as well as in implementing the MRACS on site

References ]tkesson, I (1987) Boiler Steam Temperature Control Using A True Adaptive Regulator IEE Conference paper at the 4th workshop of Selflunmg and Adaptive Control, Oxford 22-24 March, 1987 Amm, M , G Y Yasada, B F Womak (1984) Apphcation of Multlvarlable Self-Tuning Controller to A Power Plant Boiler 1984 1EEE Amerncan Control Conference. San Diego, USA, June 1984 /kstrom, K J (1983) Theory and Application of Adaptive Control-A Survey Automatlca Vol 19, pp 471-486 Con, R , and C Maffezzom (1984) Practical Optimal Control of a Drum Boiler Power Plant Automatlca, Vol 20, pp 163-173 Fessl, J (1986) An Application of Multivarlable Self-Tuning Regulators to Drum Boiler Control Automatzca, Vol 22, No 5, pp 581-585 Goodwln, G C , P J Ramadge, and P E Calnes (1980) Discrete Time Multlvarlable Adaptive Control 1EEE Tcansactwns on Automatic Control, Vol AC-25, No 3, pp 449-456 Irving, E , and Dang Van Mien (1981) Discrete Time Model Reference Multi-variable Adaptive

Steam Temperature of Thermal Power Plants Control Apphcatxon to Electric Power Plants IFAC 8th Tr~enmal World Congress, Kyoto, Japan Landau, I D , and M Tormzuka (1981) Theory and Practice of Adaptive Control Systems pp 75-84 (In Japanese), Ohm-sha, Japan Monopoh R V (1974) Model Reference Adaptive Control with an Augmented Error Signal IEEE transactwn on automatzc control, Vol AC-19, No 5, pp 474-484 Narendra,K S , and L S Valavam (1979) Direct and Indirect Model Reference Adaptive Control Automat~ca, Vol 15, pp 653-664 Nakamura, H , and H Akalke (1981) Statistical Identfficatlon for Optimal Control of Supercrltlcal Thermal Power Plants Automatzca, Vol 17, pp 143-155


Nakamura, H , and M Uchlda (1989) Optxmal Regulation for Thermal Power Plants IEEE control systems magaz2ne, Vol 9, NO 1, pp 33-38 Nlu,S , D G Fisher, and D Xlao (1992) An Augmented UD Identfficatlon Algorithm Journal of Control, Vol 56 No 1 pp 199-211 Ogata,K , S Fujn, N Kato, and S Matsumura (1991) Considerations of Adaptwe Control Method of Superheater Temperature m Boiler Plant Transactzon of JSME Ed C, Vol 57, No 539, pp 2277-2284 Surgenor,B W , and J K Proper (1992) An Optimal Multlvanable Controller with Apphcatlon to Steam Temperature Control m a Boder Journal of Dynamzc Systems, Measurement, and Control, Vol 114, pp 733736