Jl of the Instrum .Soc.

of India 16

M odel P redictive C ontrol of M ulti Input M ulti O utput

(M IM O ) B oiler Turbine System U sing M A TLA B
G . M allikarjuna R ao*,B ikash S w ain and R . S arvesw ara P rasad
D epartm en to f Electro n ics & In stru m en tatio n En g ineerin g ,
Lakired d y B alired dy C o lleg e o f En g in eerin g ,Vijayaw ad a,A n dh ra P rad esh ,In d ia
*E -M ail:m allik_rao@ red iffm ail.co m

A bstract :Th e trad itio n alco ntrolstrateg y b ased on PID con tro llers m ay b e u nsatisfactory
w h en d ealin g w ith p ro cesses w ith larg e tim e delay an d co n strain ts.T his p ap er p resen ts
a m o del p red ictive co n troller (M P C ) fo r a b oiler tu rb in e in p o w er p lan t. W e created 3x4
lin earized m od elfo r o u r system . W e use M P C th eory to design a co ntroller for this b o iler
sy stem to h an d le th o se co n strain ts o n in p u ts to th e p lan t d irectly.Lim itin g larg e
o versho ots is also con sidered in th e design .W e p lo tted drum level,dru m pressu re,steam
tem p eratu re again st tim e in th e b o iler w ith o u t con strain ts an d w ith co n strain ts.
K eyw o rd s :M od elP redictive C o ntro l,P ID co n tro l,b o iler tu rb in e,lin earized m o d el,d ru m
p ressu re,co nstraints, M IM O

IN T R O D U C T IO N y2 :drum pressure (M Pa),

y3 :steam tem perature (0C )
B oiler-turbine unitsconstitute a criticalcom ponentofa co-
generation system . D uring operation, especially the start-up W iththisassum ption the resulting m odelhasthree inputs
operation, these units are subject to high tem perature (u1, u2 and u3) and three outputs (y1, y2 andy3) and one
variationsthat aggravate the stress of the m aterialused in their unm easured disturbance isAir flow rate.T he nom inaloperating
construction and thus anegative effectin theirlifespans.B ecause conditionsare specified as follow :
the boilersystem ism ultivariate and there existsom e constraints
1. T hree utility boilers,tw o C O boilersand tw o O T SG s are
on the inputsto plant,m odelpredictive controltheory is used.
on-line.
For practicalconsideration,the originalcontroller ofthe boiler
system designed for dynam ic perform ance is taken as a pre- 2. T he totalsteam load is 470.77kg/s.
com pensator.Finally,the resulting system isextensively sim ulated
3. T he totalsteam turbine electricaloutputis 145.53M W .
and tested on acom puter,using a sophisticated nonlinear m odel
ofthe boiler system .W e use M PC theory to design a controller A t this operating condition, for each of the three utility
for this boiler system to handle thoseconstraints on inputs to boilers,w e have
the plant directly. O n the other hand, the superheater tubes
w hich connectw ith the boiler are quite sensitive to peak
tem perature, so the steam tem perature should not havelarge
overshoot.Lim iting such overshoots is also considered in the
design. B ecause the system becom es very com plex after pre-
com pensation, the system identification approach is applied w here u40 isU nm easured disturbance
toreduce the orderofthe m odel.
T he linearized m odelhas the follow ing form :
IM P LE M E N TA T IO N O F M P C T O M IM O
S YS TE M
T he inputand outputvariables in this system are
u1 :feed w ater flow (kg/s);
u2 :fuelflow (kg/s),
u3 :attem peratorspray flow (kg/s),
u4 :air flow (kg/s);
y1 :drum level(m ),

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 Jl of the Instrum .Soc.of India 17

w here

LetF have the form

W here U (k)= [u(k/k)T ;:::;(k + N u-1/k)T ]T
Let F have the form F = [F1;F2;:::;FN u;f];
w here each Fihas size q *m ,and fhas q *1.T hus itcan be
w ritten as

B ecause the controlhorizon is N u,w e have

In M A T LA B w e create 3x4 linearizedm odel as show n

below :
B y solving above equations w e have

W here unm easured disturbance A ir flow rate is given by

N ow define
D ue to the physical lim its of actuators, there are exit
constraints on the three inputs: W e can w rite as

0< u1<120 N ow the problem becom es m inim izing the costfunction J

0< u2<7 subject to the inequality constraint. T his is a standard
optim ization problem know n as quadraticprogram m ing (Q P),
0<u3<10 and standard routines are available,e.g.,in M AT LA B .

M P C D E SIG N T he C ostfunction is given by

For the com pensated and reduced plant, w e choose the

follow ing M PC costfunction:

w here y1,y2 and y3 are the predicted outputs

Subjectto the follow ing constraints Exportthism odelin to M PC G raphicalU serInterface in
M AT LA B and define the param eters and N om inalconditions.
um in<u1<um ax
SettheC ontrolhorizon,Prediction horizon and sim ulation
w here w is the reference output,y the predicted output, tim e of 10 seconds
N 2 the outputprediction horizon,N u thecontrolhorizon,Q ;
C reate tw o controllersw ith sam e param etersand sim ulate
R are the w eighting factors,and u is the input change from
the first one norm ally and second controller w ith look ahead
the previous step.
m ode
To solve this constrained optim ization problem ,w e need
to translate input am plitude constraintsinto ones on u.It is SIM U LA TIO N & R E SU L TS
easy to convert constraints on inputs in our plant into the
follow ing form W e can observe that look ahead m ode provides m ore
control over the process and the sim ulation results are as
show n below

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 Jl of the Instrum .Soc.of India 18

0 < u1 < 120 -10 <u1 < 10

0d < u2 < 7 -10 < u2 < 10
0<u3 < 10 -10 < u3 < 10
A dd inputdisturbance and N oise m odelto 4th controller
W e can observe that C onstraints on input variables and
inputvariable rates im proves the speed ofresponse and w hen
w e relaxed the constraint on the C hange in Input,w e observe
thatthe M PC controllertakesadvantage ofthisand increase the
change in inputto reach steadystate faster.

- First controller
- 2n d contro ller w ith loo k ahead

Fig . 1 : Plant outputs w ithout C ontraints

- 3rd controller w ith C onstraints
- 4th controller w ith N oise & D istu rbance
w ith C on straints

Fig . 3 : Plant o utputs w ith C onstraints an d N oise

- first controller
- 2n d contro ller w ith loo k ahead

Fig . 2 : Plant in puts w ithout C on straints

- 3rd controller w ith C onstraints

N ow create tw o m ore controllersw ith sam e param eters by - 4th controller w ith N oise & D istu rbance
w ith C on straints
copying controllersand scenarios.
A dd C onstraints to both ofthem as Fig . 4 : Plant inp uts w ith C ontraints and N oise

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 Jl of the Instrum .Soc.of India 19

M PC C ontroller com pensates for both D isturbance and m ultiple objective functions, an infinite prediction horizon,
N oise m odels and the response is alm ost closer to nom inal nonlinearprocess m odels, better use of m odel uncertainty
response.Boilersystem isdesigned w ith the M PC theory,w hich estim ates,and better handling ofillconditioning.
hasadvantageson handling inputconstraintsand m ulti-variable
system s.T hereforethe plantcan tolerate any type ofD isturbance A C K N O W LE D G E M E N T
and N oise as these factors are com pensated by M odel
Predictive C ontroller. T heauthorsthank the H O D ,D epartm entofEIE,LB R C E
forhissupport.
C O N C L U S IO N S
R E FE R E N C E S
A n im portantobservation isthatindustrialM PC controllers
alm ostalw aysuseem piricaldynam ic m odels identified from test 1. M od el P redictive C ontrol System D esign and
data.T he im pactofidentification theory on processm odeling is Im plem entation using M atlab by Liuping W ang.
perhapscom parable to the im pactofoptim alcontroltheory on 2. M ichaelN ikolaou,M odelpredictive controllers:A critical
m odelpredictive control. It is probably safe to say thatM PC synthesis of theory and industrial needs, A dvances in
practice is one of the largest application areas of system C hem icalEngineering,A cadem ic Press,2001,Volum e 26.
identification.T he currentsuccess ofM PC technology m ay be 3. B equette B .W . Process C ontrol M odelling D esign and
due to carefully designed planttests. Effortstow ards integrating Sim ulation PrenticeH allEdition.
identification andcontroldesign m ay bring significantbenefits 4. B em porad, A ., R educing conservativeness in predictive
to industrialpractice. control of constrained system s w ith disturbances,
T he future of M PC technology is bright,w ith allof the Proceedings of the 37th IEEE C onference D ecision &
vendors surveyed herereporting significant applications in C ontrol,D ec.1998.
progress.N ext-generation M PC technology is likely to include

March 2016 Vol. 46 No. 1