- Email: [email protected]
Adaptive Control of Raw Material Mix in Cement Plants
Copyright © IFAC Control of Industrial Systems. Belfort, France, 1997
ADAPTIVE CONTROL OF RAW MATERIAL MIX IN CEMENT PLANTS
Sergio Bittanti·, Andrea Franchini··, Marco Lovera·, Renato Manigrasso··
• Dipanimento di Elettronica e Injormazione •• Dipartimento di Elettrotecnica Politecnico di Milano Piazza Leonardo do Vinci 32 20133 Milano, Italy Tel. +39-2-23993543, email: [email protected]
Abstract: The problem of controlling the lime saturation factor of the clinker in cement plant automation is analyzed; a detailed model for the process is developed and two different control strategies are compared in a simulation study. Adaptive control is proposed as a way of improving process performance and solving a problem connected with the limitations of conventional PlO control. Ce papier analyse le probleme du contr61e du "lime saturation factor" du clinker, faisant partie du probleme de l'automation dans l'industrie du ciment. Un modele du proces a ete mis au point et deux techniques de commande ont ete comparees. En particulier, l'application d'une methode de commande adaptative perrnet d'ameliorer la performance du systeme par rapport a la commande PlO. Keywords: Adaptive control, Recursive estimation, Process control.
I. INTRODUCTION
Lime saturation factor:
The production process for cement manufacturing aims at the achievement of the desired chemical properties for the final product. However, the starting point for the process is the mining, grinding and mixing of raw materials, the composition of which is never exactly known. More precisely, it is of great importance that the intermediate product of the process, called clinker, from which cement is subsequently obtained, satisfies some desired ratios which define its chemical characteristics and, as a consequence, the chemical properties of cement. Such ratios, known in the cement industry as cement moduli, are defined in terms of the proportion of limestone (CaO), silica (Si0 2), iron (Fe203) and bauxite (AI 20 3) as follows:
1269
LSF=
CaO
(1)
2,8Si02 + 1,18Ab03 + O,65Fez03
Hydraulic modulus:
MI =
CaO SiOz + Alz03 + Fez03
(2)
Silica modulus: (3)
Alumina modulus:
(4)
The reason why different raw materials, with different proportions of the various chemicals, are mixed in the production process is that it would be very difficult, if not impossible, to find a single raw material with the proportion of limestone, silica, iron and bauxite required to obtained the desired values for all of the moduli. Furthermore, as the composition of the raw materials is never exactly known, and never perfectly constant, it is very difficult to achieve and maintain a mix of raw materials capable of ensuring that the desired values for the cement moduli are obtained.
only, that is by the set point of one of the two feeders; furthermore the (fast) dynamics of the feeders have been neglected. The grinder is described by the following transfer function (Hulliger, et al., 1984; Franchini, 1995):
M(s) =
-'t'mS
e
(1 + sTI)(1 + ST2)
(5)
which relates the concentrations of the mix at the input of the grinder to the concentrations of the grinder output. Typical values for the two time constants and the delay are given by:
Various methods for raw materials mix control have been proposed in the literature (Swain, 1995); in this paper the application of adaptive techniques is proposed for the control of the lime saturation factor, and the results of a simulation study are presented. The paper is organized as follows: Section 2 is dedicated to the description of the cement production process and the presentation of a model for such a process, which has been used in the simulation study; Section 3 will then present the results obtained in controlling the system by means of a digital PlO controller, while the adaptive control problem will be discussed in Section 4.
K
't'm
=
6
min.
T.
=
6
min.
T2
=
30
min.
An additional delay due to transportation of the mix from the feeders to the grinder has been included, so that the overall delay has a value of about 8 minutes. At the output of the grinder, the measurement of the composition of the product is performed, and the lime saturation factor is computed. Introducing the following shorthand notation for the concentrations:
2. PLANT DESCRIPTION AND MODELLING
and indicating with q J and q2 the set points for the flow of the feeders (with the constraint that q2 = 1- q,), one has that the concentrations in the material mix (CmU> Smw A mw Imu) are derived from the nominal concentrations in the raw materials (C" S" Ab I J and C2• S2' A 2• 12 ) as follows:
The first part of the so-called dry production process for cement manufacturing consists of the following phases: •
proportioning and mixing of the raw materials;
•
feeding of the mix to the grinder;
•
grinding of the mix;
•
blending;
• •
C mix =qjC 1 +(1-ql)c2
(6)
Smix =qjSI +(1-ql)s2
(7)
kiln burning;
A mix =q1A 1 +(1-ql)A 2
(8)
storage of the clinker;
l mix = qlI 1 +(1-ql)I 2
(9)
For the purpose of the present analysis, only the first four phases in the process have been considered, and they have been modelled as follows: the plant works with two raw materials, so that, if the total material flow fed to the grinder is fixed, the composition of the mix is completely defined by one input variable
By taking into account the transfer function of the grinder (equation (5», the concentrations at the output of the grinder (C"" S"" A"" Im ) can be written as:
1270
= M(s)Cmix(s) Sm(s) = M(s)Smix(s)
(11 )
= M(s)Amix(s)
(12)
Cm(S)
Am(s) Im(s)
= M(s)lmix(s)
(10)
(21)
(13) (22)
from which the lime saturation factor (which is the output of the model) can be computed. As the lime saturation factor (LSF) is a nonlinear function of the concentrations of limestone, silica, iron and bauxite in the grinder output, in order to obtain a linear model for the plant a linearization around the values for the (unknown) concentrations in the raw materials is necessary. The linear part of the model can be written in terms of perturbations as: L1C m(S)
=(Cl -
L1S m(s)
= (SI -
Mm(s)
= (AI -
&m(S)
= (1 1 -
C 2)M(s)L1qj(s) S2)M(s)L1ql (s) A 2)M(s)L1QI(s)
12)M(s)dQI (s)
(23)
(24)
(14) Equation (19) is the process model which has been used for the design of the control systems: the interesting feature of this model is that only the gain ps depends on the concentrations of the raw materials, while the other model parameters are known.
(15) (16) (17)
and by linearizing the expression for LSF (equation (1)): 3. PID CONTROLLER DESIGN On the basis of the presented model, a digital PID controller was first designed (Astrom and Hagglund, 1995), with the aim of maintaining the LSF close to the desired value of 0.92. First an analog design was performed, by canceling the poles of the process model and then ensuring a phase margin of 80°. The obtained analog controller was then converted to a digital one by making use of Tustin's bilinear transformation, with a sampling period of 15 minutes.
(18) one obtains the final expression for the plant transfer function from perturbations in the set point of the first feeder to perturbations in the lime saturation factor: &SF(s)
= psM(s)L1QI (s)
The performance of such a digital PID is demonstrated in Figure 1, where a typical diagram of the output of the uncontrolled process is compared with the output of the PID controlled process:
(19)
where
(20)
and
1271
094.------,----.-----~---,__-__,
1.935 . __ •. __
:
_
:.. __ .__
18.-----,---.------,---------,
-:. __ .............••••......
,: ./[\,:£' • • j : : ~I\\i/r~<\,; 1.905
' j ; \.,
. ;
1.7
,
,
,
1.6
:
,
:
1.5
,
,
,...............
14
,
,
,........... ..,
.
'.3
,
,
,
,
.
1.2
--:._
7············· 7··········· --- -~_
.
1.1
•••••• _•• _•••• ~ •••••••••••••••
~
~
... ,L: . ' \
.;•••••......
/..
0.9
090~---;-----:,':-0 - ---:'':-5----:20':----'
_.. _
\
~
.::;
!._-_. _
· ~
~\
, _
..
.
.
i-··············~l~····--
j'"T\ ! ~ \ /
.
.
:
)
"'./
! .~
\
\.
.
..
080~---:-------,1':-0 - --'':-5------,20-::-----'
Figure 1. LSF of the clinker in the storage silos for the cases of the uncontrolled (dashed line) and PlO controlled (solid line) processes.
Figure 2. LSF of the clinker for the uncontrolled (dashed line) and PID controlled (solid line) processes. in the case of maferials inversion.
In general. the results obtained by PID control are satisfactory. However. one situation exists in which this controller is not capable of providing good results. This may occur when the chemical compositions of the two raw materials are very similar to each other and. due to random fluctuations in their characteristics. a so-called inversion phenomenon occurs, i.e.• by indicating with LSF j and LSF2 the LSFs of the raw materials, one goes from a situation when
4. ADAPTIVE CONTROLLER DESIGN In order to obviate this problem. an adaptive controller was designed, based on the estimation of the concentrations of limestone. silica. iron and bauxite in the raw materials from the measurements of the feed flows at the input of the grinder and of the same concentrations at the output of the grinder. The estimation is performed by applying the Recursive Least Squares algorithm in the formulation of (Astrom and Wittenmark, 1989) to equations (6) to (9). Such equations do not account for the phase delay introduced by the dynamics of the grinder, so the clinker concentrations have to be prefiltered with an approximate inverse of the grinder model.
LSF1 < 1 LSFz to a situation when
LSF\ > 1. LSFz
Once the composition of the raw materials has been estimated. simple algebra permits the computation of the optimal value to be applied to the feeder flow ql in order to achieve a desired value for the lime saturation factor. In particular. if one indicates by x the proportion of the first material relative to the second, one can write equations (6)-(9) as:
A simulation of such an occurrence is shown in Figure 2, where PID control leads to divergence.
= XCI +C z
C
x+l
m
= xS J +Sz
S m
= xA\ +A z
A m
1272
x+ 1 x+l
(25)
(26)
(27)
Finally, Figure 4 demonstrates how the adaptive controller is capable of handling the situation of an inversion in the characteristics of the raw materials:
(28)
1.8,---...,.----.----...,.--------,
and by replacing such expressions for the output concentrations in the definition of LSF (equation (1)) one obtains:
LSF=
17
16
__ _ _ _ _ _.. .:.X.:. .:C:. . !I_+_C . .: . . :. 2 -:-_ 2.8(xS I +S2)+1.18(xA I +A 2)+0.65(x1. +1 2)
,.•........
~
l
/.~
::r:'/<••,• /
:
13
(29)
12 ..............::.,
C2 - LSF(2.8S 2 + 1.18A 2 + 0.65F2) (2.8S 1 +1.18A I +0.65F;)LSF-C.
;
1.1
··············r···············~··/·r
:
)
;
/
/
r'( .
~
.
_
~._.
.
__.. _._-
Y'
~
08,oL-----.1----:':10---,
(30)
~ .•.•.•••••.
//
~.: .
:
so that by equating (29) with the desired value for LSF (indicated with LSF), one finds the required proportion of raw materials as follows: X=
; :
20
Figure 4. LSF of the clinker for the Pill controlled (dashed line) and adaptively controlled (solid line) processes, in the case of materials inversion.
From the computed value for x it is then possible to obtain the set point ql for the flow feeder as: (31)
5. CONCLUDING REMARKS Equations (30) and (31) constitute the adopted controller; the unknown values of materials (Cb Sj, Ab 11 and C2, S2, A 2, 12 have been replaced by their estimates obtained via RLS.
The problem of controlling the lime saturation factor of the clinker in cement plant automation has been analyzed; a detailed model for the process is developed and two different control strategies are compared in a simulation study. Adaptive control is proposed as a way of improving process performance and solving a problem connected with the limitation of conventional PID control.
Figure 3 offers a comparison between the performance of the adaptive controller and the PID controller. C93ir-~--.--~----,--,----,--,-----;'l
6. ACKNOWLEDGEMENTS
092
f..... •~ ..~\\ 'H1\•..... ~.. ! \{
1
':-. . 'I
This work has been partially supported by MURST (Ministero dell'Universita' e della Ricerca Scientifica e Tecnologica and by CNR (Consiglio Nazionale delle Ricerche).
'~.'" '. '" :'>,.----.,..; / ......\ i \ / - •
REFERENCES Astrom, KJ. and B. Wittenmark (1989). Adaptive Control. Addison-Wesley. v9.,
5
10
15
20
25
30
35
40
Astrom, KJ. and T. Hagglund (1995). PID Controllers: Theory, Design and Tuning. ISA.
45
Figure 3. LSF of the clinker for the Pill controlled (dashed line) and adaptively controlled (solid line) processes.
Franchini, A. (1995). Automazione dei Cementifici: Controllo Automatico della Qualita' della Farina Cruda da Cemento. Degree Thesis, Politecnico di Milano.
1273
Hulliger, Kohler, Santos (1984). Automatisation de la Production du Cru a la Cimenterie de la SCC Elepens. EPFL Institut d'automatique, 1984. Swain, A.K. (1995). Material mix control in cement plant automation. IEEE Control Systems Magazine.
1274
ADAPTIVE CONTROL OF RAW MATERIAL MIX IN CEMENT PLANTS
Sergio Bittanti·, Andrea Franchini··, Marco Lovera·, Renato Manigrasso··
• Dipanimento di Elettronica e Injormazione •• Dipartimento di Elettrotecnica Politecnico di Milano Piazza Leonardo do Vinci 32 20133 Milano, Italy Tel. +39-2-23993543, email: [email protected]
Abstract: The problem of controlling the lime saturation factor of the clinker in cement plant automation is analyzed; a detailed model for the process is developed and two different control strategies are compared in a simulation study. Adaptive control is proposed as a way of improving process performance and solving a problem connected with the limitations of conventional PlO control. Ce papier analyse le probleme du contr61e du "lime saturation factor" du clinker, faisant partie du probleme de l'automation dans l'industrie du ciment. Un modele du proces a ete mis au point et deux techniques de commande ont ete comparees. En particulier, l'application d'une methode de commande adaptative perrnet d'ameliorer la performance du systeme par rapport a la commande PlO. Keywords: Adaptive control, Recursive estimation, Process control.
I. INTRODUCTION
Lime saturation factor:
The production process for cement manufacturing aims at the achievement of the desired chemical properties for the final product. However, the starting point for the process is the mining, grinding and mixing of raw materials, the composition of which is never exactly known. More precisely, it is of great importance that the intermediate product of the process, called clinker, from which cement is subsequently obtained, satisfies some desired ratios which define its chemical characteristics and, as a consequence, the chemical properties of cement. Such ratios, known in the cement industry as cement moduli, are defined in terms of the proportion of limestone (CaO), silica (Si0 2), iron (Fe203) and bauxite (AI 20 3) as follows:
1269
LSF=
CaO
(1)
2,8Si02 + 1,18Ab03 + O,65Fez03
Hydraulic modulus:
MI =
CaO SiOz + Alz03 + Fez03
(2)
Silica modulus: (3)
Alumina modulus:
(4)
The reason why different raw materials, with different proportions of the various chemicals, are mixed in the production process is that it would be very difficult, if not impossible, to find a single raw material with the proportion of limestone, silica, iron and bauxite required to obtained the desired values for all of the moduli. Furthermore, as the composition of the raw materials is never exactly known, and never perfectly constant, it is very difficult to achieve and maintain a mix of raw materials capable of ensuring that the desired values for the cement moduli are obtained.
only, that is by the set point of one of the two feeders; furthermore the (fast) dynamics of the feeders have been neglected. The grinder is described by the following transfer function (Hulliger, et al., 1984; Franchini, 1995):
M(s) =
-'t'mS
e
(1 + sTI)(1 + ST2)
(5)
which relates the concentrations of the mix at the input of the grinder to the concentrations of the grinder output. Typical values for the two time constants and the delay are given by:
Various methods for raw materials mix control have been proposed in the literature (Swain, 1995); in this paper the application of adaptive techniques is proposed for the control of the lime saturation factor, and the results of a simulation study are presented. The paper is organized as follows: Section 2 is dedicated to the description of the cement production process and the presentation of a model for such a process, which has been used in the simulation study; Section 3 will then present the results obtained in controlling the system by means of a digital PlO controller, while the adaptive control problem will be discussed in Section 4.
K
't'm
=
6
min.
T.
=
6
min.
T2
=
30
min.
An additional delay due to transportation of the mix from the feeders to the grinder has been included, so that the overall delay has a value of about 8 minutes. At the output of the grinder, the measurement of the composition of the product is performed, and the lime saturation factor is computed. Introducing the following shorthand notation for the concentrations:
2. PLANT DESCRIPTION AND MODELLING
and indicating with q J and q2 the set points for the flow of the feeders (with the constraint that q2 = 1- q,), one has that the concentrations in the material mix (CmU> Smw A mw Imu) are derived from the nominal concentrations in the raw materials (C" S" Ab I J and C2• S2' A 2• 12 ) as follows:
The first part of the so-called dry production process for cement manufacturing consists of the following phases: •
proportioning and mixing of the raw materials;
•
feeding of the mix to the grinder;
•
grinding of the mix;
•
blending;
• •
C mix =qjC 1 +(1-ql)c2
(6)
Smix =qjSI +(1-ql)s2
(7)
kiln burning;
A mix =q1A 1 +(1-ql)A 2
(8)
storage of the clinker;
l mix = qlI 1 +(1-ql)I 2
(9)
For the purpose of the present analysis, only the first four phases in the process have been considered, and they have been modelled as follows: the plant works with two raw materials, so that, if the total material flow fed to the grinder is fixed, the composition of the mix is completely defined by one input variable
By taking into account the transfer function of the grinder (equation (5», the concentrations at the output of the grinder (C"" S"" A"" Im ) can be written as:
1270
= M(s)Cmix(s) Sm(s) = M(s)Smix(s)
(11 )
= M(s)Amix(s)
(12)
Cm(S)
Am(s) Im(s)
= M(s)lmix(s)
(10)
(21)
(13) (22)
from which the lime saturation factor (which is the output of the model) can be computed. As the lime saturation factor (LSF) is a nonlinear function of the concentrations of limestone, silica, iron and bauxite in the grinder output, in order to obtain a linear model for the plant a linearization around the values for the (unknown) concentrations in the raw materials is necessary. The linear part of the model can be written in terms of perturbations as: L1C m(S)
=(Cl -
L1S m(s)
= (SI -
Mm(s)
= (AI -
&m(S)
= (1 1 -
C 2)M(s)L1qj(s) S2)M(s)L1ql (s) A 2)M(s)L1QI(s)
12)M(s)dQI (s)
(23)
(24)
(14) Equation (19) is the process model which has been used for the design of the control systems: the interesting feature of this model is that only the gain ps depends on the concentrations of the raw materials, while the other model parameters are known.
(15) (16) (17)
and by linearizing the expression for LSF (equation (1)): 3. PID CONTROLLER DESIGN On the basis of the presented model, a digital PID controller was first designed (Astrom and Hagglund, 1995), with the aim of maintaining the LSF close to the desired value of 0.92. First an analog design was performed, by canceling the poles of the process model and then ensuring a phase margin of 80°. The obtained analog controller was then converted to a digital one by making use of Tustin's bilinear transformation, with a sampling period of 15 minutes.
(18) one obtains the final expression for the plant transfer function from perturbations in the set point of the first feeder to perturbations in the lime saturation factor: &SF(s)
= psM(s)L1QI (s)
The performance of such a digital PID is demonstrated in Figure 1, where a typical diagram of the output of the uncontrolled process is compared with the output of the PID controlled process:
(19)
where
(20)
and
1271
094.------,----.-----~---,__-__,
1.935 . __ •. __
:
_
:.. __ .__
18.-----,---.------,---------,
-:. __ .............••••......
,: ./[\,:£' • • j : : ~I\\i/r~<\,; 1.905
' j ; \.,
. ;
1.7
,
,
,
1.6
:
,
:
1.5
,
,
,...............
14
,
,
,........... ..,
.
'.3
,
,
,
,
.
1.2
--:._
7············· 7··········· --- -~_
.
1.1
•••••• _•• _•••• ~ •••••••••••••••
~
~
... ,L: . ' \
.;•••••......
/..
0.9
090~---;-----:,':-0 - ---:'':-5----:20':----'
_.. _
\
~
.::;
!._-_. _
· ~
~\
, _
..
.
.
i-··············~l~····--
j'"T\ ! ~ \ /
.
.
:
)
"'./
! .~
\
\.
.
..
080~---:-------,1':-0 - --'':-5------,20-::-----'
Figure 1. LSF of the clinker in the storage silos for the cases of the uncontrolled (dashed line) and PlO controlled (solid line) processes.
Figure 2. LSF of the clinker for the uncontrolled (dashed line) and PID controlled (solid line) processes. in the case of maferials inversion.
In general. the results obtained by PID control are satisfactory. However. one situation exists in which this controller is not capable of providing good results. This may occur when the chemical compositions of the two raw materials are very similar to each other and. due to random fluctuations in their characteristics. a so-called inversion phenomenon occurs, i.e.• by indicating with LSF j and LSF2 the LSFs of the raw materials, one goes from a situation when
4. ADAPTIVE CONTROLLER DESIGN In order to obviate this problem. an adaptive controller was designed, based on the estimation of the concentrations of limestone. silica. iron and bauxite in the raw materials from the measurements of the feed flows at the input of the grinder and of the same concentrations at the output of the grinder. The estimation is performed by applying the Recursive Least Squares algorithm in the formulation of (Astrom and Wittenmark, 1989) to equations (6) to (9). Such equations do not account for the phase delay introduced by the dynamics of the grinder, so the clinker concentrations have to be prefiltered with an approximate inverse of the grinder model.
LSF1 < 1 LSFz to a situation when
LSF\ > 1. LSFz
Once the composition of the raw materials has been estimated. simple algebra permits the computation of the optimal value to be applied to the feeder flow ql in order to achieve a desired value for the lime saturation factor. In particular. if one indicates by x the proportion of the first material relative to the second, one can write equations (6)-(9) as:
A simulation of such an occurrence is shown in Figure 2, where PID control leads to divergence.
= XCI +C z
C
x+l
m
= xS J +Sz
S m
= xA\ +A z
A m
1272
x+ 1 x+l
(25)
(26)
(27)
Finally, Figure 4 demonstrates how the adaptive controller is capable of handling the situation of an inversion in the characteristics of the raw materials:
(28)
1.8,---...,.----.----...,.--------,
and by replacing such expressions for the output concentrations in the definition of LSF (equation (1)) one obtains:
LSF=
17
16
__ _ _ _ _ _.. .:.X.:. .:C:. . !I_+_C . .: . . :. 2 -:-_ 2.8(xS I +S2)+1.18(xA I +A 2)+0.65(x1. +1 2)
,.•........
~
l
/.~
::r:'/<••,• /
:
13
(29)
12 ..............::.,
C2 - LSF(2.8S 2 + 1.18A 2 + 0.65F2) (2.8S 1 +1.18A I +0.65F;)LSF-C.
;
1.1
··············r···············~··/·r
:
)
;
/
/
r'( .
~
.
_
~._.
.
__.. _._-
Y'
~
08,oL-----.1----:':10---,
(30)
~ .•.•.•••••.
//
~.: .
:
so that by equating (29) with the desired value for LSF (indicated with LSF), one finds the required proportion of raw materials as follows: X=
; :
20
Figure 4. LSF of the clinker for the Pill controlled (dashed line) and adaptively controlled (solid line) processes, in the case of materials inversion.
From the computed value for x it is then possible to obtain the set point ql for the flow feeder as: (31)
5. CONCLUDING REMARKS Equations (30) and (31) constitute the adopted controller; the unknown values of materials (Cb Sj, Ab 11 and C2, S2, A 2, 12 have been replaced by their estimates obtained via RLS.
The problem of controlling the lime saturation factor of the clinker in cement plant automation has been analyzed; a detailed model for the process is developed and two different control strategies are compared in a simulation study. Adaptive control is proposed as a way of improving process performance and solving a problem connected with the limitation of conventional PID control.
Figure 3 offers a comparison between the performance of the adaptive controller and the PID controller. C93ir-~--.--~----,--,----,--,-----;'l
6. ACKNOWLEDGEMENTS
092
f..... •~ ..~\\ 'H1\•..... ~.. ! \{
1
':-. . 'I
This work has been partially supported by MURST (Ministero dell'Universita' e della Ricerca Scientifica e Tecnologica and by CNR (Consiglio Nazionale delle Ricerche).
'~.'" '. '" :'>,.----.,..; / ......\ i \ / - •
REFERENCES Astrom, KJ. and B. Wittenmark (1989). Adaptive Control. Addison-Wesley. v9.,
5
10
15
20
25
30
35
40
Astrom, KJ. and T. Hagglund (1995). PID Controllers: Theory, Design and Tuning. ISA.
45
Figure 3. LSF of the clinker for the Pill controlled (dashed line) and adaptively controlled (solid line) processes.
Franchini, A. (1995). Automazione dei Cementifici: Controllo Automatico della Qualita' della Farina Cruda da Cemento. Degree Thesis, Politecnico di Milano.
1273
Hulliger, Kohler, Santos (1984). Automatisation de la Production du Cru a la Cimenterie de la SCC Elepens. EPFL Institut d'automatique, 1984. Swain, A.K. (1995). Material mix control in cement plant automation. IEEE Control Systems Magazine.
1274