Dynamics and control of

(1)

Dynamics and control of incineration processes

Davide Manca

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

(2)

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

(3)

Hot section of an incineration plant

Primary kiln

Economizer Superheater

Boiler

Postcombustion chamber

(4)

Grate kiln

(5)

Boiler and turbine

(6)

Fabric filter and exhaust gas

washing

(7)

DeNOx and Catox

(8)

Layout of an incineration plant

(9)

Primary combustion chamber

(10)

(11)

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

(12)

i , RIF OUT

i , RIF IN

i , RIF i

,

RIF F F R

dt

dM   

Solid Phase

Gas Phase

 0





 _k _k ^OUT _, _i

rif i , RIF OUT

i ,

k x W

PM W R

NG i

NC

k  1 ,  1 ,

OUT i ,

F RIF IN

i ,

F RIF

OUT i ,

W k

IN i ,

W k

i-th grate

NG i  1 ,

Primary kiln – Material bal. on the grates

(13)

O k H

N m x NO y

x pSO

kHCl nCO

N Cl O S H

C _n _m _p _q _k _y

^O ⁱ

₂ _i ⁱ ₂ ₂

2 2

2,

    





 

 ^

y x _i   _NO _, _i 

1 3150

1 2500

2

100 







 



out i , O G

% i , NO G i

, NO i

, NO

W ) T / exp(

T

W



Combustion reaction in the solid phase

(Bowman, 1975)

2 2

CO 1 O CO

  2  1 ₂ 1 ₂

N O NO

2    2 

Combution reactions in the gas phase

Kinetics

(14)

, ( , , , , , , )

sc i p i i waste i inerts i

A  f d  M M

 

 



  







 1 1 exp( ^, )

  ^CG ⁱ

i

N

i sc i

i

sc A

A ^* _,    _,

2

, , *

, ,

,

x i O i

waste i sc i waste

O i

k x

R A PM



   

Corrective factor with adaptive parameters

) , ,

, ,

( _, _, _,

, f d W x T

k _x _i  _p _i  _i _aria _i _k _i Solid granular bed

Kinetic determining step: O

₂

diffusion



 ,

2,



O i

see L2–18 eq. (8)

Primary kiln – Combustion kinetics

(15)

 x

h

b

waste

m  x b h

    

Grate schematization

(16)

F w ast e (t) [kg /s]

0 t

_O

t

_O

 

CG

O

N

t  3600

Time [s]

2 0

2 2

1 ( ( ))

( ) exp

2 2

waste

t t

F t m 

  

   

 Δ          

Waste pulse schematization

(17)

11 11.5 12 12.5 13 13.5 14 14.5

0 0.5 1 1.5 2

St eam flo wrat e [t /h ]

Time [h]

Average value

NT

k



k



¹

y y

S MEDIA

T NT  t

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

Ave rage s tea m f low rate [t /h]

Time [h]

1 Min 5 Min 10 Min

• High : delay time

• Low : high oscillations

average

t

Moving average

(18)

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

Model equations

(19)

Model equations

(20)

Model equations

(21)

Model equations

(22)

Model equations

(23)

Model equations

(24)

Model equations

(25)

Model equations

(26)

Model equations

(27)

Model equations

(28)

<

Model equations

(29)

Material balances

Energy balances

Momentum balances

Total

Primary kinl

29 2 86

Postcombustion

chamber 15 1 26

Heat recovery section

55

10 6 9 5 20

Grand total = 132 DAE system

Model dimensions in terms of DAEs

(30)

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

Some significant output process variables

(31)

REAL PLANT

6 8 10 12 14 16

0 0.2 0.4 0.6 0.8 1

Steam flo w rate [ t/h ]

Time [h]

MODEL

Model validation

(32)

3400 3600 3800 4000 4200 4400 4600 4800

11 12 13 14 15 16 17

Portata di rifiuto [kg/h]

Tempo [h]

3000 3500 4000 4500 5000 5500 6000 6500

11 12 13 14 15 16 17

Portata di aria secondaria [Nm3/h]

Tempo [h]

9600 9900 10200 10500 10800 11100 11400 11700 12000 12300 12600

11 12 13 14 15 16 17

Portata di aria alle griglie [Nm3/h]

Tempo [h]

10200 10400 10600 10800 11000 11200 11400 11600 11800 12000 12200 12400

11 12 13 14 15 16 17

Potere calorifico del rifiuto [kJ/kg]

Tempo [h]

9 10 11 12 13 14 15 16

11 12 13 14 15 16 17

Portata vapore [t/h]

REAL INPUTS

DYNAMIC SIMULATOR

Model validation

(33)

9 10 11 12 13 14 15 16

11 12 13 14 15 16 17

S tea m f low rate [t /h]

Time [h]

Experimental data Simulated values

Model Real plant

Model validation

(34)

Experimental data Simulated values

940 960 980 1000 1020 1040 1060 1080 1100 1120 1140 1160

11 12 13 14 15 16 17

Primary kiln temperature [°C]

Time [h]

5 6 7 8 9 10 11

11 12 13 14 15 16 17

Time [h]

Postcombustion oxygen molar fraction [%]

960 980 1000 1020 1040 1060 1080 1100 1120

Postcombustion temperature [°C]

On line model validation

(35)

600 700 800 900 1000 1100 1200 1300 1400 1500 1600

11 12 13 14 15 16 17

HCl

PCI Waste heat of combustion [kJ/kg]

HCl content [mg/Nm3]

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

Total air flowrate [Nm3/h]

Time [h]

Inferred waste heat of combustion

Experimental trend of the total air flowrate

Inference of heat of combustion and HCl

(36)

6 8 10 12 14 16

0 0.2 0.4 0.6 0.8 1

Steam flowrate [t/h]

Time [h]

Dynamic response to different forcing actions

8 10 14 16

Steam flowrate [t/h]

12

3 x N

1 x 3N

(37)

Multivariable model based

control

(38)

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

Use of a model for predictive pursposes

y

set

+

Model Constraints +

Optimizer

Model Process

+

-

+ - -

d

yˆ

y

yˆ u

u

MPC – Implementation scheme

(40)

ˆ( ).... (

min

ˆ 1)

c

u k u k h

f

obj

 

 

² ¹

^ ^

²

1

ˆ ( ) ( ) ˆ ( ) ( )

p p

k h k h

obj y y y u u

j k i k

f

^

 e j PF j

^ ^

 u i PF i

  

 

     

               ^Δ     

2 2

ˆ ) ˆ ˆ ( , 0 ˆ min

) ˆ ˆ ( , 0 max )

( 

 





 

 



 



 



 



 

 

 





 

 



 



 



 



 



MIN MIN MAX

MAX

u u

u i

u u

u i

i u PF

 

) ˆ ( ) ( )

( ) ;

ˆ (

) ˆ (

) ( )

ˆ ( )

ˆ ( k y k y k

j y

k j

j y e

SET

y    

  

) 1 ˆ (

) ˆ ( ) ˆ (



 

 u i

i u i

i u u

Optimization problem to be solved:

2 2

ˆ ) ˆ ˆ ( , 0 ˆ min

) ˆ ˆ ( , 0 max )

( 

 





 

 



 



  

 



 

 

 





 

 



 



  

 



 



MIN MIN MAX

MAX

y y

y j

y y

y j

j y PF

MPC – Objective function

(41)

CONTROLLED VARIABLES (CV)

Steam flowrate (set point)

Primary kiln temperature (upper bound)

Postcombustion chamber temperature (upper bound) Postcombustion chamber temperature(lower bound)

Volumetric O ₂ fraction in the postcombustion chamber (lower bound) CO content in the postcombustion chamber (upper bound)

MPC – Controlled variables (CV)

(42)

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)

(43)

NON-LINEAR MPC LINEAR MPC

Control model

Detailed model

(DAE)

Linearized identified

model (ARX)

MPC – Control model

(44)

11 11.5 12 12.5 13 13.5 14 14.5

0 0.5 1 1.5 2

S tea m f low rate [t /h]

Time [ h ]

Continuous model 132 DAE Continuous model 68 DAE Average value of the discontinuous model

3600

2 0 2 2

( ( ))

1 exp( )

2 2

3600

o CG

o

t N

t waste

CG

t t

F m

N



  



   

  

  

Averaged flowrate Δ

Same simulated average values but significantly reduced CPU times

Continuous model (132 DAE)

10% disturbance on the 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

(45)

14.5

Time [h]

11 11.5 12 12.5 13 13.5 14

0 0.2 0.4 0.6 0.8 1

Steam flowrate [t/h] (CV)

Average value Instantaneous value Set point

3900 4000 4100 4200 4300 4400 4500 4600

0 0.2 0.4 0.6 0.8 1

Waste flowrate [kg/h] (MV)

Time [h]

12600 12750 12900 13050 13200 13350 13500

0 0.2 0.4 0.6 0.8 1

Air flowrate to the grates[Nm3/h] (MV)

5700 5800 5900 6000 6100 6200 6300 6400 6500 6600 6700 6800

0 0.2 0.4 0.6 0.8 1

Secondaryair flowrate [Nm3/h] (MV)

Time [h]

NL MPC – Servo problem

(46)

11.5 12 12.5 13 13.5 14 14.5

0 0.5 1 1.5 2 2.5 3

Average steam flowrate [t/h] (CV)

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 flowrate [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

(47)

3900 4000 4100 4200 4300 4400 4500

0 0.2 0.4 0.6 0.8 1

waste flowrate [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

Steam flowrate [t/h] (CV)

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

Secondary air flowrate [Nm3/h] (MV)

12600 12750 12900 13050 13200 13350 13500 13650 13800 13950 14100

0 0.2 0.4 0.6 0.8 1

Air flowrate to the grates [Nm3/h] (MV)

Time [h]

NL MPC – Regulator problem

(48)

) (t u

Plant

) ( t y

ARX (Auto Regressive Model with Exogenous Input )

nb k nb k

k na

k na k

k

 a  y

_

 a  y

_

    a  y

_

 b  u

_

 b  u

_

    b  u

_

y

₁ ₁ ₂ ₂ ₁ ₁ ₂ ₂

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

i

y

k 

NY output vector at time (k-i)

j

u

k 

NU input vector at time (k-j)

a

i

b

j

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

(49)

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

-0.5 0 0.5 1 1.5

Time

Output

Input and output signals

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

-0.02 0 0.02

Time

Input

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)

MATLAB SYSTEM IDENTIFICATION

TOOLBOX

LINEAR MODEL ARX

Linear MPC – Identification procedure

(50)

12 12.5 13 13.5

0 0.5 1 1.5 2

Time [h]

Continuous model Linear model

Steam flowrate [t/h]

Similar trends within the prediction horizon

CPU times get significantly reduced

h

_p

Linear model (ARX)

10% disturbance on the waste flowrate

Simplified continuous

model (68 DAE) 0.54s

4.E-5s CPU time for a 1 min

simulation interval

Linear MPC – Models comparison

(51)

11.5 12 12.5 13 13.5 14

0 0.2 0.4 0.6 0.8 1

Ave rage s tea m f low rate [t /h] ( CV )

Time [h]

Linear MPC Set point Non-linear MPC

Comparison between linear and non-linear MPC

The non-linear MPC reaches the setpoint faster

Linear MPC – Servo problem

(52)

11.4 11.6 11.8 12 12.2 12.4

0 0.2 0.4 0.6 0.8 1

Ave rage s tea m f low rate [t /h] ( CV )

Linear MPC Set point Non-linear MPC

Linear MPC – Regulator problem

Comparison between linear and non-linear MPC

The non-linear MPC shows a smaller

deviation from

the setpoint

(53)

CPU time for a 20 min

simulation of the whole plant

CPU time of the optimization procedure (600 F

_obj

calls) Non-linear

MPC

0.65 [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 rta ta v a p o re m e d ia [t/ h ] (C V)

Tempo [h]

MPClineare 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 < t _c

The implementation of the

linear MPC on the real plant is viable

Conclusions

(54)

12 12.5 13 13.5 14

0 0.2 0.4 0.6 0.8 1

Ave rage s tea m f rlow rate [t /h] ( CV )

Time [h]

HP = 20 HP = 10 HP = 40 Set point

Prediction horizon, h _p :

short: reduced predictive capability

long: the prediction becomes less realistic

Linear MPC – Effect of varying h _p

(55)

11.5 12 12.5 13 13.5 14

0 0.2 0.4 0.6 0.8 1

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

Secondary air flowrate [Nm3/h] (MV)

Time [h]

3800 3850 3900 3950 4000 4050 4100 4150 4200 4250 4300

0 0.2 0.4 0.6 0.8 1

Waste flowrate [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

Grates air flowrate [Nm3/h] (MV)

Time [h]

h _c = 3

Control horizon, h _c :

short:

Few degrees of freedom.

Bolder actions from manipulated variables long:

Longer CPU time, Smoother control action

Linear MPC – Effect of varying h _c

(56)

Small weighs ( ) on the

manipulated

variables

¹¹

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

Steam flowrate [t/h] (CV)

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

Waste flowrate [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

Grates air flowrate [Nm3/h] (MV)

Time [h]

5600 5800 6000 6200 6400 6600

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Secondary air flowrate [Nm3/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

First grate strokes [Strokes/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

Second grate strokes [Strokes/h] (MV)

Time [h]

 u

The controller becomes nervous.

We can observe a RINGING trend

Linear MPC – Ringing

(57)

k k



h

_c 1

k  h

p

Co n tro lled va ria bl e (CV) M an ipu lat ed va ria b le (M V)

Time Time

p

c h

h  h p _high:

• High predictive capability

• Significant role played by the model error

h c high :

• High number of d.o.f.

• Smoother control actions

This is the effective action that is implemented in the plant

t c

t c Control time:

Shorter than 1/10 of the characteristic time

Linear MPC – Prediction and control horizon

(58)

t

d 11

11.5 12 12.5 13 13.5 14 14.5

0 0.5 1 1.5 2

Steam flowrate [t/h] (CV)

Time [h]

3800 3900 4000 4100 4200 4300 4400 4500 4600

0 0.5 1 1.5 2

Waste flowrate [kg/h] (MV)

 y

 x



p

min 40

t _d

p  



t c

h p

h c

= 1 min

= 20

= 1

MPC – Selection of the controller parameters

(59)

940 950 960 970 980 990 1000 1010

0 0.2 0.4 0.6 0.8 1

Postcombustion temperature [°C] (CV)

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

Time [h]

No constraint With constraint Set point

Setpoint step change of –10%

Law constraint on the outlet temperature from the

postcombustion chamber:

T > 950 °C

NL MPC – Constraints

(60)

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

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

Time [h]

No prediction Set point Prediction

Dynamics and control of