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202 IEEE TRANS.4CTIONS Oh AUTOMATIC CONTROL, VOL. AC-18, NO . 3, J U K E 1973

Design and Analysis of Boiler-Turbine-GeneratorControls Using Optimal Linear Regulator Theory

JOHN P. McDOKALD AND HARRY G. KWATNY

Abstract-The demand for improved dynamic response of fossil-fired power plants has motivated a comprehensive program of controlsystem design and analysis. Previous papers have reported th e de-velopment of a nonlinear mathematical model of a drum-type, twinfurnace, reheat boiler-turbine-generator (RBTG) system which issuitable for control system analysis a nd has been extensively verifiedby field test . On th e basis of t his model, local stability, observability,and controllability have been examined over th e load range, usinglinearization and modal analysis. An approach to control system de-sign has been developed based on optimal linear regulator theory an dwhich recognizes the limita tion of an imperfect model. This approachproduces integral-type action which guarantees zero steady- stateerrors. The controller do es not require complete st at e feedback. Im-proved performance has been demonstrated by comparison with theexisting control structure through simulation using th e nonlinearprocess model.

TI. IKTRODUCTION

HE CON TINUISG increase in demand for electricpower, una.nticipa.t.ed delays in new generat,ing ca-

pacity addit,ions, and the trend toward larger ge ne ra hgstations and larger interconnections are among the manyfactors which have magnified the importance of individualunit response capability to he pon-er system operatingobjective of providing reliable and efficient. electric service.

During normal operation, .good unit response capability isessent.ia1 for stable implementation of the megawatt dis-patch system oad control concept 1 . In emergency sit ua-ti om , responsive generation can be coordinated for loadpickup or rejection in order o avoid or minimize casmdingof system disturbances [2]. It. is essent,ial that generatingunits have a sufficiently high degree of stability to be ableto stick with the system through an emergency situat ionni th ou t unreasonable risk. Should solation become nec-essary, th e unit must be capable of controlled rejection ofgenerat,ion without complete shutdown in order to servicei ts local loads and to beavailable for system restoration 3].

These system operating requirements conflict with th eobvious desire t o maximize th e life and t o avoid damage ofenormously expensive and complex primary equipment.This is a particularlyimportant concernat the present timewhen replacement generation is frequent l- not available orat best. involves extremely high operating costs. In recentyears? new information concerning turbine metal fatiguedue to cyclic thermal stress [4], [5 ] has made this a major

Paper recommended by J. Peschon, Past Chairman of the IEEElianuscript received September 1, 19i2; revised January 26 , 19i3.

S-CS Uti lity S-stems Committee.

Electric Company, 2301 JIarket Street, Philadelphia, Pa. 19101.J. P. 1IcDonald is with the Research Division, Philadelphia

H. G. Kaatny is n7it.h the College of Engineering, Ihesel Uni-versity, Philadeiphia, Pa . 19104.

consideration in operating generating stat,ions. Neverthe-less, numerous reports [6]-[SI suggest, on t.he basis of t,estexperience, that, the primary equipment itself oes not. im-pose a serious inherent limitation on oad change capabilhyand that, with suitably designed automatic controls, theobjectives of system operation an bemet-consistent. nithunit safety a.nd life requirements.

I n [SI, Durrant and Vollnler suggest a variety of alterna-tive operating and control strategies for boiler-t.urbine-generator systems t o meet different, system operating ob -jectives. Among these are nonstandard automatic controlprocedures such as using attemperating sprays to generatesteam in the superheater or assisting load pickup, mariipu-lating gas flow for control of temperatures, incorporatingvariable steam pressure operation o regulate t,urbine rotortemperature variations, and relaxing throttle temperaturetolerances, also to obtain better control of rotor t,empera-ture.Theynote hat he operating objectives are fre-quen tly conflicting with respect t o a given procedure andsuggest further investigation to clarify t he implications ofthese alt ernatives or specific applications.

Optimization and simulation prolqde a framework par-ticularly n-ell suited to t he identification and evaluationof alternative control strategies. There have been someprevious attempts to apply optimal control t.heory to th econtrol of a power boiler. Notable among hese are theworks of Sicholson [9]- [111 and Anderson [12]. Xcho l-sons use of an oversimplified boiler model has made hispositive esults essentially meaningless for large powerboiler applications. Xndersons work! on the other hand,follon-ed an extensive effort of model development. [13].In E121 -4nderson concludes that nteg rated optimal con- *tro l schemes do not significantly improve th e performanceof th e unit considered.

-4ndersons conclusions are c0ntra.r- t o the optimism

generated for coordinated control schemes by test experi-ence and are also subject, to question on the basis that. themodel used is still not an adequate characterization of atypical power boiler. In the work reported herein, everyeffort has been made to avoid such criticism. The modelused in hese tudies has beenused to simulate hePhiladelphia Electric Companys Cromby Xumber 2 unit,and has been subjected o extensive comparisons nithclosed-loop steady-state and open-loop transient, field tes ts[14], [16]. The model is nonlinear, and all manipulatedvariables normally considered for automated operation areincluded. Several rather subtle details which have been

previously overlooked but which are crit ical to wide-rangeunitoperation havebeen epresented, such asmultiple

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M C DONALD AND KWATNY: BOILER-TLTRBINE-GENERATQR CONTROL 203

HIGH LOW

BOILERFEED PUMP/FEEDWATERALVE

MULTIPLE PRESSURE PRESSURETHROTTLE TURBINE TURBINE

SUPERHEATER

I I

Fig. 1. Schematic diagram of Cromby Number 2 unit.

regulating valves, burner positions, and multiple feed-pumps.

From the out,set, of the study, the object-ive has been t ogobeyond idenntification and evaluation of a1t.ernativecontzol strategies and t,o provide feedback controller de-sign suitable or implementat.ion should t be warranted onthe basis of simulation results. To achieve thi s end, thecont,roller design methodology described in det.ail in [ l S ]has been ut.ilized. This procedure s based on optimal linearregulator theory but circumvent,s the practical eficienciesof standard results. In particula.r, the design incorporatesa practical met,hod of state reconstruction when there are alimited number of essentia.lly noise-free outputs , retainsthe advanta ge of classical proportional integral (PI) con-trollers tha t st.eady-state accuracy is guaranteed even inthe presence of immeasurable consta.nt, disturbances, andis not dependent upon unreasonable odel precision.

In Section 11, theplant, t,s nonlinear nlat11emat.ica.lmodel, and some resul ts of local linear analysis are dis-cussed. Formulat.ion of the overall control problem and adescription of t,he current control system are inc1ude.d inSection 111. In Section IV, he design algorithm is de-scribed in t,he context f t he present a.pplication, and com-puter simulation results are iscussed in Sect,ion V .

11. MATHEMATICAL M O D EL

The aforementioned Cromby Kumber 2 unit is typicalof a. large class of power generating stations and has beenused as the object of analysis for the studies reported inthis paper. Cromby Number 2 is a 200-MW boiler-tur-binegenerator system which ncludes a. pulverized coal-fired, twin urnace, rum-type, cont.rolled circulat.ion,single reheat boiler. I n l s ] , t.he syst.ern (shown sche-matically n Fig. 1) was partit.ioned nto subsections, t oeach of which were applied t.he requisit,e laws governingthe transfer of energy and mass and the equat.ions f statedescribing mat,erial properties. The resulting nlathemat,icalmodel onsists of 14 first-order onlinear differentialequa,tions and 70 non1inea.r algebraic equations describingth e variables of int,erwt, many f which may be suppressedif desired. All plant parameters used in t,he model were ob-tained from physical data or calculat.ed from acceptance

test, data.

TABLE ISTATE ARIABLES

1 ) Superheat furnace metal temperature.2 ) Reheat furnace metal temperature.

4) Drum stea m density.3 ) Drum water volume.

6 ) Secondary su perhea ter st.eam densit.y.5 ) Primary superheater steam density.

7) Reheater steam density.8) Primary superheater enthalpy.9) Average secondary superheater enthalpy.

IO) Secondary superheater outlet enthalpy.11) Average reheat.er enthalpy .12) Reheater outlet ent,halpy.13) Mas s of coal in crusher zone of mill.14) Fraction of tota l mill volume occupied by coal.

TABLE I1

COXTROL NPUTS

1) Feedwater valve area.a2 ) Governing valve area.*3) Mill feeder stxoke.84)

Superheat spray flow.5 ) Reheat spray flow.6 ) Air fl0w.a7 ) Superheat furnace burner tilts.88) Reheat furnace burner tilts."

a Used by existing control system.

TABLE I11OUTPUT V~RIABLES PARTIAL IST)

Generation.*Throtkle flow.8Throttle pressure.*Throttle temperature.8

Reheater outlet. f l o a . ~Rehea ter outlet. pressure.Reheater out,let temperature.^Drum pressure.Gas flow.Impuls e chamber pressure.Impulse chamber temperature.Primary superheater outlet flow.Primary superh eater outlet pressure.Primary superheater outlet temperature.Rehea ter inlet (cold rehe at) pressure.Rehea ter inlet. (cold reheat.) tempera ture.Coal flow rate.

Feedwat.er flow.8Drum level.8

Average secondary superh eater tempe rature.Average reheater temperat,ure.

Used by existing cont,rol system.

The mathemat.ica1 model is described by the equations

where z is the 14-dimensional state vector, u s the 8-di-nlensional cont.ro1 vector , and y is the 70-dimensional out-put vect,or as defined in Tables 1-111.

Local properties of t he nonlinear system have been ex-amined o ~ e r he process load ra.nge by genemting approxi -rnat.e linear models at the desired steady-st,at.e operating

points in theollowing form:

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204 IEEE TRANSACTIONS ON AUTOMATTC COXTROL, JUNE 1973

? = A X + B U Y = C X + D U (2)

where (x,y,u) in (2) represent, deviations from th e st,eady-state operating values xo,yo,uo).

The varia tion of t he linear model eigenvalues with loadalong a t.ypica1 steady-state operating profile is shorn-n inFig. 2 . Illustrated are 13 of the 14 eigenvalues. The remain-ing eigenvalue is lva ys zero. The arrow points n the irec-

tion of decreasing load. The seemingly errat,ic behal-ior oft.he eigenvalues is a result of t he highly nonlinear valvecharacteristic. Examination of th e eigenvectors leads t o afew general observations. he zero eigenvalue is associat,edwith the dr um wat,er volume. Drum water volume is af-fected by every mode which is consistent ni th th e knon-1-edge that water level requires tight regula,tion. There isgenerally a very high degree of coupling bet,meen t.he st atevariables. Tw o modes are clearly identifiable with the milldynamics.

Local observability and controllability havebeen ex-amined. If feeder stroke is not available as control input,

th en the wo mill modes are uncontrollable. The system iscont,rollable, however, even xhen superheat and eheatsprays are not used as control inputs. Drum evel must bemeasured in order to have an observable situat,ion. Other-wise, almost any selection of output s will suffice.

111. OPERATING OBJECTIVES ND EXISTING OATROLS

The principal operat.ing objectives an be summarized nth e following st,atement

Thecontrol system should provide formaximum rate ofchange of generator output from th e initial state to an as-signed target stat,e without exceeding specified imits on

process variables.Th e 1imit.s currently specified for Cromby Kumber 2 onth e key out.put variables are given n Table V.

There is a serious need for a basic evaluat ion of whatconstit.ut es tolerable variations of these process variables.If t.he constraints are set too oose, then the risk of equip-ment damage is great,; and, f they are set. too tight , a lo^value of th e maximum ra te of change of generation nil1 bedetermined for he unit.. It. s obvious t.hat. scessive1)- highpressures constitute a safety hazard and that excessive orwidely varying steam temperatures should be avoided be-cause of the close clearances in the turbine and the gossi-

bility of metal fatigue due o cyclic thermal stress.However, th e precise specification of accept able limitsisperlmps somen-hat arbitrary. For example, the re hasbeen considerable discussion within the ind ust ry of vari-able pressure operat.ion [17] in which case operating pres-sures as much as 400 psia below nominal are advocated,and the lant is normally operated at ow load v i t 11 as muchas a 100F drop in throttle temperature. Such practicescontradict the limits of -50 psia on thro ttle pressure and-10F on t,hrottle emperature. The emergency lowerlimit on emperature (-200F) ismore ealistic. How-ever, these constraints have been set and. until a convinc-ing evaluation is made hich s ho ~ - s ustifica.tion for chang-ing them, they must be adhered t o in any coritrol design.

. .003

' .002

.

d '

.001 5

0 :I 1

II

- -DO1

--.ooz

~ -.003

-IO. -I. - -01 -.001 -.0001R E A L

Fig. 2. Root. locus for RBTG system. Dot represents high load;arrow represents low load.

DeviationsNominal

Values Normal Emergency

Throttle pressure 1825 psia =t50 psia f 7 5 psiaThrottle temperature 1000F , f 10F +20"F

Reheat temperature 1000F 5 1 0 F +20"P-200F

Excess oxygenDrum level

- 00F4 . 4 5

0 in f 3 n f 4 n2-57c 1.5-676

TABLE 1'C R O M B Y C N B E R UNIT COSTROL XPCTCOSSTRSIKTS

Feedwater valve normalized area 0 1Governing valve normalized area 0 8Normalized feeder stroke 0 1Superheat spray flow 0 60 klbjhReheat. spray flow 0 60 klb/hA ir flow IS0 1b:s 600 lb?sSuperheat, burner tilts - 0" + 3 0 Reheat burner tilts - 0" + 3 0

The control const.raints are tabulated in Table 1'. Theseconstraints are based on physical imits of trave l for valve 'actuators or on maximum equipment capacity. The mini-mum value for air flow insures safe furnace conditions at.lou- load.

Both sprays and tilts are provided for temperature con-t rol. Sprays arc sed t o supplement the tilt s n-hich normallyare the primary means of temperature control. This ad-ditional capability t o prevent temperatures from becomingtoo high is consistent with th e concern over excessive ther-mal stress and close turbine clearances.

The existing Cromb?- Sumber 2 unit control system iscomposed of five distinct. control loops. These include: h epower generation control oop, Fig. 3 ; the fuel controlloop, Fig. 4; he air control loop, Fig. 5; the steam tem-peraturr control loop, Fig. G (there are actually two identi-cal controllers-one for supe rheat. he other for eheat.temperatures); and the drum level control oop, Fig. 7.The mathema.tical characterizations s h o ~ n re. of course,

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N C DONALD AND KWATNY: BOILER-TURBINE-GENERATOR CONTROL 205

LIMITYNAMICS

MEGAWATT L1-l

OUTPUT

Fig. 3. Power generation control loop model, Cromby Number 2unit. P = 0.03; I = 0.4; and 7 = 10.

M A G N I T U D EL I M I T

ME ASURE D

T H R O T T L E R E S S U R E

Fig. 4. Fuel control loop model, Cromby Number 2 unit.P = 0.001; I = 0.003; D = 120.

+,,,,IRI MAGNITUDEAG

L IMIT

BIASADJUSTMENT

Fig. 5. Air flow control loop model, Cromby Number 2 unit,.P = 1238.26; 7 = 10.

T E M P E R AT U R E B U R N E R

S E TO I N T +

>b30 T I LT

P O S I T I O NI I I M A G N I T U D E

M E A S U R E D

T E M P E R AT U R E

Fig. 6 . Steam tempe rature cont,rol loop model, Crom by Numbe r 2unit.. P = 1.5; I = 0.01.

MEASUREDT HROT T L E

FLOW 1

FEEDWATERMEASURED FEEDWATERV A LVE AREA

FLOW I \

DRUM WATERVOLUME

LIMIT DYNAMICS

SE T OINT-

D RU M WATERMEASURED

VOLUME'J

Fig. i . Threeelement feedwater control loop model, Cromby Kum-ber 2 unit. PI = 10; Pn = 0.OOi; Pa = 0.01323; I = 5; 7 = 10.

idealizat,ions of the ac tual ontrols. Closed-loop simulationshows, however, th at th e ystem is a very good representa-tion of the actual unit .

IV . CONTROLLER ESIGN

Conventional power generation control systems haveevolved with time a.nd have independent feedba.ck control

of key process variables. These regulators were designedto hold the process variables at a fixed desired value.Today it is recognized th at such control syst.ems are in-adequate for oad tracking, a.nd manufacturers are nowincluding feedforward feat.ures hich will change set pointsas a function of demand input. Even th e most advancedof t,hese conventionally designed control systems cannothandle this highly interactive process under rapid oadcha.nge n a satisfact,ory manner.

Modern control t,heory provides the t,echniques for thedesign of dynamically int,egrated contxol systems for mul-tivariable processes. The met,hodology proposed in [16has been utilized t.0 design a cont.ro1 system fo r th e boiler-turbine-generator system of int,erest. The design process sbriefly described below in somewhat less general .ermsthan provided in [16]. An important featur e of t he proce-dure is th at , by ncluding asimple characterizat.ion ofmodel error, the resultant controller retains he steady-st at e accuracy of classical PI controllers.

The feedback cont.roller is designed on t.he basis of anapproximate linear model obtained a t a preseleded steady-stat e operating point. The model used for design ,akesthe following form:

3i. = A X + BUw = vy = C x + D u + w (3)

where x is an n-dimensional s ta te vector, y is a p-dimen-sional output. vect.or, u is an m-dimensional input. vector,and w s a p-dimensional bias vector. The bias noise Y is awhit enoise process aving ero-mean ,nd ovariance

The random bias vect.or w has been specifically intro-duced to represent model inaccuracies. As th e object,ive ist.he synthesis of an optimal deterministic cont,roller, th elimiting form as V vanishes is of particular int.erest.. Int,his case, t.he bias vector becomes a. cons tant, but a prioriunknown, bias.

The objective is t o st.eer t.he system so t,hat y tracks aconst,ant desired value g while u varies moderately aboutsome nominal value. To obtain an a.ppropr iate cost func-t.iona1, consider 2 ~ ' o be a constant. In thi s case, the follow-ing st,eady-state conditions on ( x , u ) Fvith y = g a.re ob-tained from (3) with 3i. = 0:

T.,6(t).

0 = 8 3 + Bfi , tj = C2 + Df i + W . (4)In th e regulator problem there exists a t least one solu-

tion (2 ,a) foreach ( g , ~ ) .n t.his case, (4) mustconsistof no more th an n + m independent equa.tions. Equations(4) can be arranged in the form

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206 IEEE TIL4NSACTIONS ON AUMYATIC CONTROL, UN E 1973

If, in addition, the oefficient matrix is of full rank (which,in this case, guarant,ees th at th e number of rows are notgreater th an t he number of columns), then a solut.ion for(2,zi) is

[3 [ C D ] { [ C D ] [ C D l } - [ g !? w] )A B A B A B

Upon partitioning t.he olution, 3 and 8 re obt,ained in theform

8 = V(t j - 1.) 3 = X ( 8 - r ) . ( 6 )

A quadrat ic cost functional can be defined as

J T = (Y - ~)Qo(Y - 8)

+ST{y - g)Q(y - 8) + (U - a)R(u - zz)]dt (7)0

where Qo, Q arenonnegative definite and R is positivedefinite. It. s desired to minimize

where Po satisfies the Riccati equation

P&,[I - HG] + [ I - G H I A I P,- Pd1HVV-HA1P~= 0. (15)

The matrix e2 s given by

e2 = [ 3If 9, denotes a mat,rix whose ro-s-s are a set. of n linea,rlyindependent rows of I - H*H an d Al denotes the matxix

All = A , - B l M , (17)

t,hen r4 nda2 are iven byr4 = AnA1&, a2 = A,KIH*. (18)

From the results of [ 1 6 ] t is known that the 272 + peigenvalues of th e closed-loop linear syst,em nclude th ep zero eigenvalues corresponding to the bias variables w,the n stable eigenvalues corresponding t o t.he closed-loop

system matrixA

= A-

B K , and the n stable eigenvaluesof the matrix &Ale2 which are associated with t.he ob-server. Moreover, a prescribed degree of stability CY for th eobserver eigenvalues is atta ined by replacing A , in (14),

In composite form he system (3 ) can be written as (15) by A,+ d . f a is zero and the system matrix A isstable (which is the case for the reheat boiler-turbine-

?i.l = Air1 + B 1 ~ 1 + GV genera,tor (RBTG) syst,em), then Po = 0 and H * an d Ay1 = HZ1 + Dul (8 ) specialize to

where H * = [!j, A, = [ I , 01. (19)Kote tha.t an alternate form of (13) which has certain1 = [ u! 1, u1 = [u - ug1, y1 = y - jx - xg

advantages for applicat-ion is~ 4 1 [o O ] j B1 = [t], G = [e,]0 &= A,A18& + A , B ~ u ~ B nA IH *( yl- D u ~ ) . (20)

H = [C I,].

The optimal controller as obtained in l61 is

ul* = - N P 1 , ,%I [ K ; + K X ]where

K = (DQD + R)-(BS + DQC)and S satisfies the Riccat.i equation

0 = { A- B(DQD + R)-DQC) S+ S ( A - B(DQD + R ) - ~ D Q c )- SB(DQD + R)-BS+ {CQC - CQD(DQD +R ) lDQC}

(9) This alloxs t.he estimator t o use the actual appl ied controlinputs, which is particularly important when t.he sgst.emcontrols sat,urate. For the ase Po = 0, (20) specializes t o

( 10).$ = A $ + Bul. (2 1)

To apply t.his controller to the ctual nonlinear process,(I1) the steady-stat .e process outputs and contro ls are charac-

terized as unctions of the mega1vat.t denland (RIWD).Then, the linear feedforward elements can be replaced bythe actual onlinear relationships

8 = g(l\lWD) i = j(3IWD). (22)

(12)The resultant. controller is illustrated in ig. 8.

Th etate est.imate tl s obtainedrom V. COMPUTERIMULATIONESULTSp 1 = H* ( y l - D U I )+ e& Theontrol designethodologyescribedbove hasf = r& + 4 ( y l - D u J been developed into a convenient and flexible digit.al com-(13) puter program. This program is used in conjunction with

where thearametersre defined below. the BTGinearnalysisrogra,mndheBTG non-linear simulation program to design and analyze RBTGcontrols. A typical case study can include the followinghe matrix H * is given by

H * = (GV.,G+ P,,AlfjJ,7p-1 (14) steps.

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M C DONALD AND KWATNY: BOILER-TURBINE-GENERATOR CONTROL 207

1

Step I : Specify a desired steady- state proiile. (This canbe done with t.he aid f t,he simulation program.)

Step 2: Specifynominal operating oad level forcontxoller design. Use th e linear analysis program .0 obtainthe A , B , C, and D mat.rices.

Step 3: Specify which controls and out put s are to beused.

Step Q: Specify cost functional weighting matrices andobserver degree of stability.

Step 5: Execute controller design program.Step 6: Execute simulation program.Current p h t operating pra.ctice is t o use the steady-

state profile reported in [14]. However, superheat, and re-heat burner tilts .re positioned at their positive imit aboveapproximat,ely 200 MW, and consequently it is not possi-ble to regulate temperature. This difficulty can be circum-vented by adjusting the xcess air flow. This has been doneto develop ast.eady-st.ate operating profle for the load

range 130-230 MW , which provides for superheat and re-heat. stea,m temperat.ures of 1000F with burner tilt posi-tions suit,ably interior to their constraints. Of particularn0t.e is th e nonlinear chara.ct.eristic of the governing valvesas shown in ig. 9.

The control inputs and rocess 0utput.s used in the xist-ing control system were used in the design of the optimal

, control syst.em. The control nputs are: 1) feedwat.er valvearea; 2) governing valve area; 3) mill feeder stroke; 4)superheat furnace burner tilts; 5) reheat furnace burnert,ilts; and 6) air flow. The process 0utput.s used for controlare: 1) generat.ion; 2) t,hr ott le flow minus feedwater flow

minus (coefficient) drum level error; 3) throthle pressure; 4)throttle temperahre; and ) reheater outlet temperahre.The first case study was made with all weightings set o

unity, and bhe weightings were hen adjust,ed y observingthe abilit,y of th e control system t o keep the process out-puts Tvithin the specified constraints. The optimal controlsystem which is used in th e ollowing comparison with t,heexisting control system is defined by the set of weightingsgiven in Table VI.

The convent,ional control system, he st at e ariable feed-back system, and the state estimat,or system were simu-hted. The &ate aria.ble feedback system was investigatedt o establish the ultimate otent.ia1 for improvement.

Figs. l(r12 compare the response of t,he t,hree control

i " 130 150 170 190 210 23 0t.EGA*hIl DEUAW

Fig. 9. Cromby Number 2 unit steady-state proiile for governingvalves.

TABLE VIO p m x . 4 ~CONTROL YSTEN EIGHTIKGS

Variableeightingalue

Feedwateralverea 0 . 2Governingalverea 4 x 10-10Milleedertroke 0.15Superheaturnerilts 0.2

Reheat burner tiltsAir flow - 0.0220Generation 4000Throttle flow minus feedaater flow minus (0.28)

drum levelrror 1Thro ttle pressure 6000Throt,tleemperature 400Reheaterutletemperature 100

systems t o a. lO-MW ste p decrease in the megawatt de-mand. Fig. 13 compares .he response for a 25-XiW ste pdecrease.

V I. CONCLUSIOSS

This paper reports t,he evelopment of a methodology forth e design and analysis of mult.ivariable process controlsand it s application to the control of conventional, drm-t.ype, fossil-fired, single reheat, &earn power plants. he de-sign met,hodology s ba.sed on opt.imal linear control theory,incorporates feedforward, provides a method of stat.e re-construction, retains t.he steady-stat,e accuracy advantageof classical PI cont.rollers, and is not dependent upon un-reasonable model recision.

The application t,o t,he design and analysis of RBTG sys-te m control has been successful, a nd the que sti on as towhether or not. the applica.t.ion of modern control theorycan improve the control of fossil-fired RBTG syst em can

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208 IEEE TRANSACTIONS O N AUMMATIC CONTROL, JUNE 1973

w0

2 0 5

0 4 8 I2 !6 2 0 0 4 8 12 16 20

TIME - MIN TIME-MIN

Fig. 10. Thrott,le pressure and feeder stroke response to a IO-MW Fig. 11. Generation and governing valve response to a 10-MW stepstep decrease. Solid line denotes convent.iona1; broken line denotes decrease. Solid line denotes convent,ional; broken line denotes st at e

statestimator; otted line denotes st at e feedback. estimator; dot.ted ineenotes st at e feedback.

o 4 e 1 2 16 20-

- ~

TIME - MI N0 4 8 I 2 16 20

T IME -MlN

Fig. 12. Throttle temperature and superheat burner t.ilt. response to Fig. 13. Throttle pressure and feeder stroke response to a 25-3fWa l O - M W st.ep decrease. Solid line denotes convent.ional; broken st,ep decrease. Solid line denotes conventional; broken line denot,esline denotes state estimator; dotted ine denotes st at e feedback. st,ate estima tor; ot.ted line denotes st at e feedback.

be answered in the affirmat.ive. The improvement in dy-namic response which can be btained is shown to be quitesignificant. Perhaps the most dramatic result is the tightregulation of pressure which is accomplished without sig-nificant, increase in control action. This arises principallythrough coordination of fuel flow! air flow, and burnertil ts. It is interesting to note that the optimal regulatortakes advantage of the natu ral slowness of boiler tempera-t.ure dynamics and manipulates air and burner tilts-nor-mally associated with emperatu re control-to assist inregulating .he faster pressure dynamics before the tem-perature transient becomes significant.

The simulation results ere obt,ained using he nonlinearboiler model and the control system performed well even

in t.he ace of the quite irregular characterist .ics f the mul-tiple governing valves. It should be noted t.hat the plant.characteristic would actually be smoot.her as the simula-tions were run n1t.h no valve overlap, which m-ould not beth e case in the ield.

It. is interest.ing o no te that the ressure responses withthe st ate est imator and s tate feedback systems are quiteclose. whereas there is significant difference between thecorresponding temperature responses. This is t o be ex-pected as the rocess dynamics are irect,ly reflected in th eobserver and he emperatu re dynamics are elativelyslow. By including a degree of st.abilit.y specification forth e observer, hon-ever, the es timato r tracking of th e slowmodes can be sped up to an y desirable rat e so that . per-

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formanee of t he state estimator system approaches hat of H. G. KwatnY, J- McDonald, and J. H- spare, A nonlinearmodel for rehea t boiler-turbine-generator systems, Part II-

th etate feedba,ckystem. Development, in Proc. 12th Joint AutomaticCmtrol Conf.,1971,The approach t o design afforded by modern [16] H. G. Kwatny, Optimal inear cy t. ro l t,heory and a class of

t.heory, exemplified in this paper, makes it particularly PI controllers for process cont.rol, in Proc. 13th Joint Auto-

tions of contro ls and outputs, the effect, of emphasizing th e and sta rtu p of large turbin es n utilit y power plants, in Proc.importance of regulating specific process variables such as Americnn Power Conf., 1971.

first-stage temperatur e), and the effect of restricting theuse of specific control variables.

pp. 227-236.

easy to investigate the effect Of using different [IT] s. W. Lovejoy and W. G. Riess, Variable pressure operationmatic Control Conf., 1972.

ACKNOWLEDGMENT

The authors wish t.o acknowledge th e advice and supportof their colleague L. H. Fink throughout the course of t.hisproject.

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