Dynamics and control of incineration processes · © Davide Manca –Dynamics and Control of...

© Davide Manca – Dynamics and Control of Chemical Processes – Master Degree in ChemEng – Politecnico di Milano 1L2—

Dynamics and control of incineration processes

Davide Manca

Lesson 2 of “Dynamics and Control of Chemical Processes” – Master Degree in Chemical Engineering


Table of contents

Implementation and validation of a detailed first-principles

dynamic model of the combustion section of an incineration plant

Analysis of a multivariable MPC control system

Model reduction

Synthesis of a non-linear MPC control system

Identification of an ARX linear model

Synthesis of a linear MPC control system and comparison with

the non-linear counterpart


Hot section of an incineration plant

Primary kiln

Economizer

Superheater

Boiler

Postcombustion chamber


Grate kiln


Boiler and turbine


Fabric filter and exhaust gas washing


DeNOx and Catox


Layout of an incineration plant


Primary combustion chamber



Primary kiln – Modeling scheme

1

2

2.1

2.2

2.3

2.4

2.5

3.1 3.2 3.3 3.4

4

Homogenous combustion zone

Heterogeneous combustion zone


i,RIF

OUT

i,RIF

IN

i,RIF

i,RIFRFF

dt

dM

Solid Phase

Gas Phase

0 OUT

i,kk

rif

i,RIFOUT

i,k WxPM

RW

NGiNCk ,1,1

OUT

i,RIFFIN

i,RIFF

OUT

i,kW

IN

i,kW

i-th grate

NGi ,1

Primary kiln – Material bal. on the grates


OHkm

Nxy

NOxpSOkHClnCONClOSHCi

iykqpmn

iO

22222

,2

yx i,NOi

1

3150

25001

2

2

100

out

i,OG

%

i,NOG

i,NO

i,NO

W)T/exp(T

W

Combustion reaction in the solid phase

(Bowman, 1975)

2 2

1CO O CO

2

2 2

1 1N O NO

2 2

Combution reactions in the gas phase

Kinetics


, , , ,( , , , )sc i p i i waste i inerts iA f d M M

)exp(11

,

iCG

i

Nisciisc AA ,

*

,

2

2

, , *

, ,

,

x i O i

waste i sc i waste

O i

k xR A PM

Corrective factor with adaptive parameters

),,,,( ,,,, TxWdfk ikiariaiipix Solid granular bed

Kinetic determining step: O2 diffusion

,

2 ,O i see L2–18 eq. (8)

Primary kiln – Combustion kinetics


x

h

b

wastem x b h

Grate schematization


Fw

aste (t

) [k

g/s]

0

Ot

Ot

CG

ON

t3600

Time [s]

2

0

22

1 ( ( ))( ) exp

22waste

t tF t m

Δ

Waste pulse schematization


11

11.5

12

12.5

13

13.5

14

14.5

0 0.5 1 1.5 2

Stea

m f

low

rate

[t/

h]

Time [h]

Average value

NT

NT

k

k 1

y

y

S

MEDIA

T

tNT

Valore istantaneo

11.5

12

12.5

13

13.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Avera

ge s

team

flo

wra

te [

t/h

]

Time [h]

1 Min 5 Min

10 Min

• High : delay time

• Low : high oscillations

averaget

Moving average


Manca D., M. Rovaglio, Ind. Eng. Chem. Res. 2005, 44, 3159-3177

Model equations



Model equations



Model equations



Model equations



Model equations



Model equations



Model equations



Model equations



Model equations



Model equations



<

Model equations


Materialbalances

Energy balances

Momentumbalances

Total

Primary kinl

29 2 86

Postcombustion chamber 15 1 26

Heat recoverysection

55

10

6 9 5 20

Grand total = 132 DAE system

Model dimensions in terms of DAEs


Number of feed-strokes [1/h] 40

Inlet waste flowrate [kg/h] 4,000

Number of strokes to the first grate [1/h] 23

Number of strokes to the second grate [1/h] 20

Number of strokes to the third grate [1/h] 13

Number of strokes to the fourth grate [1/h] 23

Primary air flowrate [Nm3/h] 12,500

Secondary air flowrate [Nm3/h] 6,500

Some significant input process variables

Outlet smokes temperature from the primary kiln [°C] 1,035

Outlet smokes temperature from the postcombustion chamber [°C] 1,115

Outlet oxygen molar fraction from the postcombustion chamber [%] 8.5

Outlet CO content from the postcombustion chamber [mg/Nm3] 11

Steam flowrate [t/h] 12

Some significant output process variables


REAL PLANT

6

8

10

12

14

16

0 0.2 0.4 0.6 0.8 1

Ste

am fl

owra

te [

t/h]

Time [h]

MODEL

Model validation


3400

3600

3800

4000

4200

4400

4600

4800

11 12 13 14 15 16 17

Po

rtata

di ri

fiu

to [

kg

/h]

Tempo [h]

3000

3500

4000

4500

5000

5500

6000

6500

11 12 13 14 15 16 17 Po

rtata

di ari

a s

eco

nd

ari

a [

Nm

3/h

]

Tempo [h]

9600

9900

10200

10500

10800

11100

11400

11700

12000

12300

12600

11 12 13 14 15 16 17

Po

rtata

di ari

a a

lle g

rig

lie [

Nm

3/h

]

Tempo [h]

10200

10400

10600

10800

11000

11200

11400

11600

11800

12000

12200

12400

11 12 13 14 15 16 17 Po

tere

calo

rifi

co

del ri

fiu

to [

kJ/k

g]

Tempo [h]

9

10

11

12

13

14

15

16

11 12 13 14 15 16 17

Po

rta

ta v

ap

ore

[t/

h]

Tempo [h]

REAL INPUTS

SIMULATED OUTPUT

DYNAMIC SIMULATOR

Model validation


9

10

11

12

13

14

15

16

11 12 13 14 15 16 17

Ste

am

flo

wra

te

[t/h

]

Time [h]

Experimental data Simulated values

ModelReal plant

Model validation


Experimental data

Simulated values

940

960

980

1000

1020

1040

1060

1080

1100

1120

1140

1160

11 12 13 14 15 16 17

Prim

ary

kiln tem

pera

ture

[°C

]

Time [h]

5

6

7

8

9

10

11

11 12 13 14 15 16 17

Time [h]

Postc

om

bustion o

xygen m

ola

r fr

action [%

]

960

980

1000

1020

1040

1060

1080

1100

1120

11 12 13 14 15 16 17

Experimental data Simulated values

Postc

om

bustion tem

pera

ture

[°C

]

Time [h]

Experimental data

Simulated values

On line model validation


600

700

800

900

1000

1100

1200

1300

1400

1500

1600

11 12 13 14 15 16 17

HCl

PCI

Wa

ste

he

at o

f co

mb

us

tion

[kJ/k

g]

HC

l c

on

ten

t [

mg

/Nm

3]

Time [h]

10200

10400

10600

10800

11000

11200

11400

11600

11800

12000

12200

12400

13000

14000

15000

16000

17000

18000

19000

11 12 13 14 15 16 17

To

tal

air

flo

wra

te [

Nm

3/h

]

Time [h]

Inferred waste heat of combustion

Experimental trend of the total air flowrate

Inference of heat of combustion and HCl


6

8

10

12

14

16

0 0.2 0.4 0.6 0.8 1

Stea

m f

low

rate

[t

/h]

Time [h]

Dynamic response to different forcing actions

6

8

10

14

16

0 0.2 0.4 0.6 0.8 1

Stea

m f

low

rate

[t/

h]

Time [h]

12

3 x N

1 x 3N


Multivariable model based

control


Implementation and validation of a detailed first-principles

dynamic model of the combustion section of an incineration plant

Analysis of a multivariable MPC control system

Model reduction

Synthesis of a non-linear MPC control system

Identification of an ARX linear model

Synthesis of a linear MPC control system and comparison with

the non-linear counterpart

Table of contents


Use of a model for predictive pursposes

sety

+

Model+

Constraints

Optimizer

Model

Process

+

-

+

-

-

d

y

y

y

u

u

MPC – Implementation scheme


ˆ ˆ( ).... ( 1)min

cobj

u k u k hf

1

2 2

1

ˆ ˆ( ) ( ) ( ) ( )p pk h k h

obj y y y u u

j k i k

f e j PF j u i PF i

Δ

22

ˆ

ˆ)(ˆ,0min

ˆ

ˆ)(ˆ,0max)(

MIN

MIN

MAX

MAXu

u

uiu

u

uiuiPF

)(ˆ)()(;

)(ˆ

)(ˆ)()(ˆ)(ˆ kykyk

jy

jykjyje

SET

SETy

)1(ˆ

)1(ˆ)(ˆ)(ˆ

iu

iuiuiu

Optimization problem to be solved:

22

ˆ

ˆ)(ˆ,0min

ˆ

ˆ)(ˆ,0max)(

MIN

MIN

MAX

MAXy

y

yjy

y

yjyjPF

MPC – Objective function


CONTROLLED VARIABLES (CV)

Steam flowrate (set point)

Primary kiln temperature (upper bound)

Postcombustion chamber temperature (upper bound)

Postcombustion chamber temperature(lower bound)

Volumetric O2 fraction in the postcombustion chamber (lower bound)

CO content in the postcombustion chamber (upper bound)

MPC – Controlled variables (CV)


MANIPULATED VARIABLES (MV)

Strokes number to the feed grate

Primary air flowrate (to the grates)

Secondary air flowrate to the kiln

Strokes number to the first moving grate

Strokes number to the second moving grate

MPC – Manipulated variables (MV)


NON-LINEAR MPC LINEAR MPC

Controlmodel

Detailedmodel(DAE)

Linearizedidentified

model(ARX)

MPC – Control model


11

11.5

12

12.5

13

13.5

14

14.5

0 0.5 1 1.5 2 S

team

flo

wra

te

[t/h

]

Time [ h ]

Continuous model 132 DAE Continuous model 68 DAE

Average value of the discontinuous model

3600

2

0

22

( ( ))1exp( )

22

3600

oCG

o

tN

t

waste

CG

t t

F m

N

ΔAveraged flowrate

Same simulated average values but significantly reduced CPU times

Continuous model(132 DAE)

10% disturbance onthe waste flowrate

Discontinuous model(132 DAE) 6.02 s

2.26 s

CPU time for a 1 min simulation interval

Simplified continuous model (68 DAE)

0.54 s

NL MPC – Continuous simplified model


14.5

Time [h]

11

11.5

12

12.5

13

13.5

14

0 0.2 0.4 0.6 0.8 1

Stea

m f

low

rate

[t/

h]

(CV

)

Average valueInstantaneous value

Set point

3900

4000

4100

4200

4300

4400

4500

4600

0 0.2 0.4 0.6 0.8 1

Wa

ste

flo

wra

te [

kg/h

] (M

V)

Time [h]

Time [h]

12600

12750

12900

13050

13200

13350

13500

0 0.2 0.4 0.6 0.8 1

Air

flo

wra

te t

o t

he

gra

tes

[Nm

3 /h

] (M

V)

5700

5800

5900

6000

6100

6200

6300

6400

6500

6600

6700

6800

0 0.2 0.4 0.6 0.8 1

Seco

nd

ary

air

flo

wra

te [

Nm

3 /h

] (M

V)

Time [h]

NL MPC – Servo problem


11.5

12

12.5

13

13.5

14

14.5

0 0.5 1 1.5 2 2.5 3

Avera

ge s

team

flo

wra

te [

t/h

] (C

V)

Time [h]

NL MPC PI

Set point

3600

3800

4000

4200

4400

4600

4800

5000

0 0.5 1 1.5 2 2.5 3

Waste

flo

wra

te

[kg

/h]

(MV

)

Time [h]

NL MPC

PI

MPC Controller

Faster control action

Reduced oscillations of both the controlled and manipulated variables

NL MPC – Comparison with PI controller


3900

4000

4100

4200

4300

4400

4500

0 0.2 0.4 0.6 0.8 1

waste

flo

wra

te [

kg

/h]

(MV

)

Time [h]

11

11.2

11.4

11.6

11.8

12

12.2

12.4

12.6

0 0.2 0.4 0.6 0.8 1

Ste

am

flo

wra

te [

t/h

] (C

V)

Time [h]

Averaged value Intstantaneous value

Set point

Time [h]

5200

5400

5600

5800

6000

6200

6400

6600

0 0.2 0.4 0.6 0.8 1 Seco

nd

ary

air

flo

wra

te [

Nm

3/h

] (M

V)

12600 12750 12900 13050 13200 13350 13500

13650 13800

13950 14100

0 0.2 0.4 0.6 0.8 1 Air

flo

wra

te t

o t

he g

rate

s [

Nm

3/h

] (M

V)

Time [h]

NL MPC – Regulator problem


)( tu

Plant )( ty

ARX (Auto Regressive Model with Exogenous Input )

nbknbkknaknakkk ubububyayayay 22112211

Matrix of NY·NY output parameters at time (k-i)

iky NY output vector at time (k-i)

jku NU input vector at time (k-j)

ia

jb Matrix of NY·NU input parameters at time (k-j)

na Model order respect to the outputs

nb Model order respect to the inputs

Linear MPC – ARX model


0 200 400 600 800 1000 1200 1400 1600 1800 2000 -1

-0.5

0

0.5

1

1.5

Time

Ou

tpu

t

Input and output signals

0 200 400 600 800 1000 1200 1400 1600 1800 2000 -0.04

-0.02

0

0.02

Time

Inp

ut

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 -1

-0.5

0

0.5

1

1.5

Time

Measured and simulated model output

PRBS Input (Pseudo Random Binary Sequence)

MATLABSYSTEM

IDENTIFICATIONTOOLBOX

LINEAR MODELARX

Linear MPC – Identification procedure


12

12.5

13

13.5

0 0.5 1 1.5 2

Time [h]

Continuous model Linear model

Ste

am

flo

wra

te [

t/h

]

Similar trends within theprediction horizon

CPU times getsignificantly reduced

hp

Linear model (ARX)

10% disturbance on thewaste flowrate

Simplified continuousmodel (68 DAE)

0.54s

4.E-5s

CPU time for a 1 min simulation interval

Linear MPC – Models comparison


11

11.5

12

12.5

13

13.5

14

0 0.2 0.4 0.6 0.8 1

Avera

ge s

team

flo

wra

te [

t/h

] (C

V)

Time [h]

Linear MPC Set point

Non-linear MPC

Comparison between linear and non-linear MPC

The non-linear MPCreaches the

setpoint faster

Linear MPC – Servo problem


11.4

11.6

11.8

12

12.2

12.4

0 0.2 0.4 0.6 0.8 1

Avera

ge s

team

flo

wra

te [

t/h

] (C

V)

Time [h]

Linear MPC Set point

Non-linear MPC

Linear MPC – Regulator problem

Comparison between linear and non-linear MPC

The non-linear MPCshows a smallerdeviation from

the setpoint


CPU time for a

20 min

simulation of

the whole plant

CPU time of the

optimization

procedure

(600 Fobj calls)

Non-linear

MPC0.65 [s] 390. [s]

Linear MPC 7.E-4 [s] 0.45 [s]

11

11.5

12

12.5

13

13.5

14

0 0.2 0.4 0.6 0.8 1

Po

rtata

vap

ore

med

ia [

t/h

] (C

V)

Tempo [h]

MPC lineare Set point

MPC non lineare

The control efficiency is comparable

The CPU time is shorter than the

control time only for the linear MPC

Higher robustness for the linear

MPC

Optimization CPU time <ct

The implementation of thelinear MPC on the real plant is viable

Conclusions


12

12.5

13

13.5

14

0 0.2 0.4 0.6 0.8 1

Av

era

ge

ste

am

frl

ow

rate

[t/

h]

(CV

)

Time [h]

HP = 20 HP = 10 HP = 40

Set point Prediction horizon, hp:

short: reduced predictive capability

long: the prediction becomesless realistic

Linear MPC – Effect of varying hp


11

11.5

12

12.5

13

13.5

14

0 0.2 0.4 0.6 0.8 1

Ste

am

flo

wra

te [

t/h

] (C

V)

Time [h]

Average value Instantaneous value

Set point

4000

4500

5000

5500

6000

6500

7000

0 0.2 0.4 0.6 0.8 1 Se

co

nd

ary

air

flo

wra

te [

Nm

3/h

] (M

V)

Time [h]

3800

3850

3900

3950

4000

4050

4100

4150

4200

4250

4300

0 0.2 0.4 0.6 0.8 1 W

aste

flo

wra

te [

kg

/h]

(MV

) Time [h]

12000

12600

13200

13800

14400

15000

15600

16200

16800

17400

18000

0 0.2 0.4 0.6 0.8 1

Gra

tes

air

flo

wra

te [

Nm

3/h

] (M

V)

Time [h]

hc = 3

Control horizon, hc:

short: Few degrees offreedom.Bolder actions frommanipulated variables

long: Longer CPU time, Smoother controlaction

Linear MPC – Effect of varying hc


Small weighs ( )

on the

manipulated

variables11

11.2

11.4

11.6

11.8

12

12.2

12.4

12.6

12.8

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Ste

am

flo

wra

te [

t/h

] (C

V)

Time [h]

Average value Istantaneous value

Set point

4000

4200

4400

4600

4800

5000

5200

5400

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Wa

ste

flo

wra

te [

kg

/h]

(MV

)

Time [h]

12000

12150

12300

12450

12600

12750

12900

13050

13200

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Gra

tes

air

flo

wra

te [

Nm

3/h

] (M

V)

Time [h]

5600

5800

6000

6200

6400

6600

0 0.2 0.4 0.6 0.8 1 1.2 1.4 Se

co

nd

ary

air

flo

wra

te [

Nm

3/h

] (M

V)

Time [h]

18

20

22

24

26

28

30

0 0.2 0.4 0.6 0.8 1 1.2 1.4 Fir

st

gra

te s

tro

kes

[S

tro

kes

/h]

(MV

)

Time [h]

18

20

22

24

26

28

30

0 0.2 0.4 0.6 0.8 1 1.2 1.4 S

ec

on

d g

rate

str

ok

es

[S

tro

ke

s/h

] (M

V)

Time [h]

u

The controller becomesnervous.

We can observe aRINGING trend

Linear MPC – Ringing


k 1 chk phk

Co

ntr

olle

dva

ria

ble

(CV

)M

an

ipu

late

dva

ria

ble

(MV

)

Time

Time

pc hh

ph high:

• High predictive

capability

• Significant role

played by the

model error

ch high :

• High number of

d.o.f.

• Smoother control

actionsThis is the effective action that is implemented in the plantct

ct Control time:

Shorter than 1/10 of the characteristic time

Linear MPC – Prediction and control horizon


dt

11

11.5

12

12.5

13

13.5

14

14.5

0 0.5 1 1.5 2

Ste

am

flo

wra

te [

t/h

] (C

V)

Time [h]

3800

3900

4000

4100

4200

4300

4400

4500

4600

0 0.5 1 1.5 2

Waste

flo

wra

te [

kg

/h]

(MV

)

Time [h]

y

x

p

min40 tdp

ct

ph

ch

= 1 min

= 20

= 1

MPC – Selection of the controller parameters


940

950

960

970

980

990

1000

1010

0 0.2 0.4 0.6 0.8 1

Po

stc

om

bu

sti

on

tem

pera

ture

[°C

] (C

V)

Time [h]

No constraint With constraint Law constraint

10.4

10.6

10.8

11

11.2

11.4

11.6

11.8

12

0 0.2 0.4 0.6 0.8 1

Ste

am

flo

wra

te [

t/h

] (C

V)

Time [h]

No constraint With constraint

Set point

Setpoint step changeof –10%

Law constraint on theoutlet temperature from the

postcombustion chamber:

T > 950 °C

NL MPC – Constraints


11

11.2

11.4

11.6

11.8

12

12.2

12.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Ste

am

flo

wra

te [

t/h

] (C

V)

Time [h]

No switch Set point

Switch

11

11.2

11.4

11.6

11.8

12

12.2

12.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Ste

am

flo

wra

te [

t/h

] (C

V)

Time [h]

No prediction Set point

Prediction

“Switch” between two ARX models identified

according to two different waste heats

of combustion

The waste heat of combustion is an input

value of the ARX model

Linear MPC – Heat of combustion

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