close

Вход

Забыли?

вход по аккаунту

?

Models of an Industrial Evaporator System for Education and Research in Process Control.

код для вставкиСкачать
Dev. Chem Eng
Mineral Process., lO(i/2),pp.105-127,2002
Models of an Industrial Evaporator System
for Education and Research in Process
Control
Kiew M. Kam”, Prabirkumar Saha’, Moses 0. TadC’*
and G. P. Rangaiah2
‘
Department of Chemical Engineering, Curtin University of
Technology, GPO Box UI987, Perth 6845, Western Australia
Department of Chemical and Environmental Engineering, National
University of Singapore, Singapore I 1 9260
Current affiliation. Chemical & Process Engineering Centre,
National University of Singapore, Singapore I I9260
’
Realistic models of typical industrial processes are essential for effective and
practice-oriented education and research in process control This paper presents two
mechanistic models of an industrialfwe-eflect evaporator system, and also indicates
their potential applications in process control-related research and training
Simulation programs for these models in four diflerent platforms (viz, MAPLE,
M A TLAB, Simulink and C++) are developed Relative merits and applicationspecific usefulness of these four platforms in process control studies are discussed
Introduction
The growth of computer-based training during recent years has been phenomenal in
chemical engineering education [I]. It has emerged as the tool of choice for most
training and development programs due to speed of computation, portability of
software, visual graphic utilities and various other user interfaces (e.g. printer, plotter,
etc.). Particularly in the field of process control applications, the cause and effect of
different control schemes and controller tuning parameters on chemical process
systems are readily demonstrated through visual computer simulations rather than just
“being taught” fiom the textbooks. Furthermore, use of computer models for case
study projects in process control courses allows practical and open-ended problem
solving [2] for the training of graduate students. For example, a single-stage forcedcirculation evaporator of Newell and Lee [3] was implemented in Simulink as the
computer model for the case study project performed in the undergraduate process
control course in the Dept of Chemical Engineering at Curtin University of
*
Authorfor correspondence (email tadem@che curtin edu au)
105
K M.Kam,P. Saha. M . 0 Tad6 and G.P Rangaiah
Technology On completion of the project, students remarked that it has greatly
improved their understanding of the concepts of control system design. Further, they
understood the importance of process identification for optimal controller tuning,
advanced process control concepts (such as feedforward and cascade control) and
process interaction compensation techniques (such as relative gain array for pairing
the variables and decoupling control).
An evaporator was chosen as an exemplary process for the aforementioned
process control course, due to its importance in the chemical and mineral processing
industries Various mechanistic and black box models have been developed for
industrial evaporator systems by researchers in the last decade [e g 4-1 11 Many of
these models were developed for only single or double effect bench scale evaporators.
Although they are suitable for computer simulation and process control studies, they
were not adequate to show a clear picture of an industrial evaporator system, which
are mostly multi-effect in nature. Some of the cited works deal with industrial-scale
evaporators; however complete details of the models are not reported, possibly due to
proprietary reasons.
More recently, Kam and Tad6 [12] presented two mechanistic models of a fiveeffect evaporator system, and used them in control studies. Comprising numerous
state, input and output variables, and having the severe nonlinearity and difficult
dynamic (minimum phase) characteristics, these evaporator models provide a
complete base for extensive nonlinear process control studies. The purpose of the
present work is three-fold:
1. To present and compare two mechanistic models of the five-effect evaporator for
possible application in process control related research and training.
2. To develop simulation programs of these models in four different platforms (viz.
MAPLE, MATLAB, Sirnulink and C++) and compare the merits, dements and
application-specific usefulness of these four platforms in process control studies.
3. To indicate different ways of using the two models for education and research in
process control.
The Evaporator System
The selected evaporator system is the first step in the liquor burning process
associated with the Bayer process for alumina production at an alumina refinery. It
consists of one falling film, three forced-circulation, and a super-concentration
evaporators in series. The main components of each stage are a flash tank (FT), a
flash pot and a heater (HT). A simplified schematic o f the evaporator system is
depicted in Figure 1. Note that the flash pots are not shown in this figure for
simplicity of the schematic. Spent liquor, which is recovered after precipitation of the
alumina from its solution, is fed to the falling film stage (FT #1). The volatile
component, water in this case, is removed under a high recycle rate and the product is
further concentrated through the three forced circulation stages (FT #2 to #4). The
super-concentration stage (FT #5) is used to remove the residual ‘flashing’ of the
concentrated liquor without recycle.
In each of the forced-circulation and super-concentration stages, the spent liquor is
heated through a shell and tube heat exchanger (heater) and water is removed as
Models of an industrial Evaporator System
HT#= heater no
; FTIl =flash tank no ;C = Condenser
I
Figure 1. Simpl@ed schematic of the industrial evaporator system
vapour at lower pressure in the flash tank. The vapour given off is used as the heating
medium in the heaters downstream. Live steam is used as the heating medium for HT
#3, #4 and #5 The flashed vapours from FT #3 and #4 are combined and used in HT
#2, while the vapour fiom FT #2 is used in HT ## 1. The steam condensates 6om the
heaters are collected in the flash pots. Live steam to HT #3 is set in ratio to the
amount of live steam entering HT #4, while the amount of live steam to HT #5 is set
depending on the amount of residual ‘flashing’ to be removed. The cooling water
flow to the contact condenser (C in Figure 1) is set such that all remaining flashed
vapour is condensed. The evaporator system is crucial in the aluminium refinery
operation and is difficult to control using classical controllers due to complex
characteristics such as strong process interactions and nonlinearities.
There are 15 state variables that are of interest. They are the liquor levels in the
the liquor densities (pi, i=l,2,. .S),and temperatures of the
flash tanks (hi, i=1,2,. -3,
product streams leaving each stage (Ti, i=1,2,. ..5). The controlled outputs in the plant
are the liquor levels in the flash tanks (hi, i=1,2,,..5), the product liquor density of
stage 4 (p4), and the product liquor temperature of the super-concentration stage (Ts).
The manipulated inputs are the liquor product flows (Qpi,i=1,2,...5), the steam rate to
HT #4 ( hs4
), and the vapour withdrawal rate from FT #5 ( mv5 ) In the actual plant
situation, all these manipulated inputs and the controlled outputs are measured online.
Additionally, on-line measurements of the product liquor temperatures of the fvst
four stages (TI,
T2, T3, Tq) are available. The product liquor densities of the fust three
stages (p,, pz, p3), however, are not measured on-line.
107
K M. Kam,P.Saha, M . 0 Tad6 and G.P Rangaiah
Models for the Evaporator System
Two mathematical models, M1 and M2, were developed for the industrial evaporator
system using unsteady-state mass and energy balances around the units in Figure 1.
For this modelling only the first four stages of the evaporator system are considered in
order to avoid additional complexities. Each of the models consists of 12 ordinary
differential equations with 5 input and 5 output variables. The state, input and output
variables for the two evaporator models are summarized in Table 1 It should be noted
that, due to proprietary issues, the actual values of these variables are multiplied with
an arbitrary factor to honour the confidentiality And the reported data do not alter the
basic characteristics of the models It should also be noted that values of state
variables in this table are only approximate steady-state values; exact values depend
on the model(s) selected, and will have to be obtained in each case. All controlled and
manipulated variables (y’s and u’s respectively) were selected according to the actual
plant situation. The differences between M1 and M2 are due to different assumptions
(summarized in Table 2) that were used in their development. These and the model
equations presented below and in the Appendix A, have been reported by Kam and
Tade [12, 131, and are included here for completeness and convenience.
Table 1. State, input and output variables and their nominal values for the
evaporation system
States
T4
XI2
PI
P2
P3
1.5
2.25
2.25
2 25
1.54
66 0
90.6
129
135
1.357
1.422
149
Inputs (u ’s) and Outputs (y s)
QPI
32.736
u2
QP2
27.713
u3
QP3
23.850
u4
QP~
2 1.642
u5
ms4
2.3814
UI
Y4
hl
h2
h3
h4
Ys
P4
Y1
Y2
Y3
1.5
2.25
2.25
2.25
1 54
Model M1
The model equations for the second stage of the evaporator system are presented
below; model equations for other stages can be found in the Appendix A. Further
information on the evaporator model and its derivation are available in 1141.
108
Models of an Industrial Evaporator System
[ ;"
dt
1
1
C O T ~(v2 - h , A 2 )
[
E2 - m v 2
+ Pv2( QPl -QP2
-P W
BPL$ = 102.69~2- 128.82
Table 2. Assumptions usedfor development of evaporator models MI and M2
Additional assumptions for Model M2
Assumptions for both Models MI & M2
1. Dynamics of instrumentation and 8. Liquor boiling point elevation in
each
flash
tank
remains
control valves are very fast and
unchanged.
negligible when compared to the
9 Vapour
pressure-temperature
dynamics of flash tanks.
relation of flashed vapour is
2 . Liquor density and temperature in
linear.
each flash tank are respectively the
same as those of corresponding 10. Latent heat of vaporization of
liquor remains constant.
discharged stream since perfect
mixing is usually achieved in each 11 No accumulation of vapour in the
flash tanks and the steam space in
flash tank.
the
shell side of the heaters
Specific
heat
capacities
of
all
3.
remains unchanged. This means
process streams remain constant.
amount of vapour leaving a FT
4. Effects of falling film on the heat
transfer rate and the dynamics of
(liz, ) is equal to the amount of
heater discharge temperatures are
water vaporisation in that FT (E,),
neglected.
and it can be completely
5 . Liquor in each flash tank is in
condensed in the downstream
equilibrium with the corresponding
heater as per Figure 1 (without
flashed vapour.
being limited by the heat transfer
6 . Heat losses t?om the evaporator
rate such as equation 14).
system are negligible.
7. No flashing of liquor in the heaters.
109
K M. Kam, P. Saha, M . 0 Tadk and G.P Rangaiah
Boiling point elevation (BPE) of the liquor is dependent on the liquor density as
shown in Equation (5). Equation ( 5 ) was determined from the data obtained fiom the
plant.
MP2
p v 2 = R(273.1+ T2 - BPE,)
[
P2 = 0.133exp A -
(7)
C + 2 7 3 l+T2-BPE2
The constants M and R are the molecular mass of water and the gas constant,
respectively, and A, B, C are constants in the Antoine equation for the vapour
pressure-temperaturerelation of water vapour
The flashed vapour from FT #2 is used in HT #l.As such, the amount of vapour
that is drawn fiom FT #2 (i e. m v 2 ) depends on the amount of condensation due to
heat exchange with the liquor in HT #I. The rate of vapour withdrawal t7om FT #2 is
given as:
where the subscripts HF and S refer to heater feed and steam, respectively. The steam
temperature in HT # 1 (i.e. Tsl) is the same as the saturation temperature of the flashed
vapour 6om FT #2:
The liquor density ( p ~ and
~ ~temperature
)
(THFl)in FT # 1 are obtained 6om mass and
energy balances at the mixing point as follows:
PHFI=
110
4
+ Qf
QHFI
Pf
Models of an Industrial EvaporaforSystem
The recycle rate R , is set to a constant.
The evaporation rate E2 in Equation (4) depends on the amount of steam
condensing in HT #2, which is equal to the amount of flashed vapour from FT #3 and
+ m,, ) and is also governed by the rate of heat transfer in HT
FT #4 (i.e. ms2 = kV3
#2 given by:
R2~2T2+ QPI PICITI
THF2 =
QHF2
PHF2 =
P HF 2cHF
2
R2 + QPI P I
QHF 2
Model M2
The additional assumptions (tabulated in Table 2) are used to simplify model M i . The
simplified model is referred to as model M2. The model equations for the second
stage of the evaporator system are given below; model equations for other stages can
be found in the Appendix A Further information on the evaporator model and its
derivation are available in [14].
%=-!---(
dt
COT^
E2 -
4 2
+ pv2
P W
where
1
1.58M
R(273 1 + T2 - B P E 2 ) - (273.1 +pT2
v 2- BPE2)
(21)
111
K M.Kam. P. Saha, M.0 Tad6 and G.P Rangaiah
MP2
p v 2 = R(273.1+ T, - BPE2)
The value of BPEl is constant for model M 2 (viz , 16). The model equations for
the liquor temperature of model M2 in Equations (20) and (21) are considerably
simpler than Equations (3) and ( 8 ) of model M1 The simplification is due to the
additional assumptions that the BPE is independent of the liquor density and that the
vapour pressure-temperature relation of the flashed vapour is linear in Equation (26)
This was obtained by local linearization of Equation (7) at the nominal liquor
temperature. Another noticeable difference between the model equations of the two
models is the steam flow to HT #2 and the vapour withdrawal rate from FT #2 Note
that, instead of depending on the heat transfer in the heater, the vapour withdrawal
rate in model M2 is equal to the rate of evaporation in the FT, i e Equation (24)
Values of constant quantities in the evaporator models are presented in Table 3
Some of the characteristics of the evaporator models are summarised in Appendix B
Table 3. Values of constant quantities in the evaporator models.
3290
BPE3
BPE4
112
1 24.6
I 30.6
kJ/k
"C
OC
Ih
I
3
hV4
I 2243600
1 2243600
Mkg
kJkg
Models of an Industrial Evaporator Sysrem
Implementation of the Evaporator Models
During the course of our research on model-based control of the evaporator system,
models M1 and M2 have been implemented on four computing platforms. Maple,
Matlab, Simulink and C++ These simulation programs for the industrial evaporator
system can be obtained upon request f?om the corresponding author. Comparative
merits of the different computing platforms based on our experience for the
evaporator model simulation are summarized in Table 4, and briefly discussed below.
These are helpful to educators and researchers in choosing a correct programming
platform for their process control studies.
Implementation in MAPLE
MAPLE allows mixed symbolic manipulation and numerical computation that can
achieve greater accuracy and speed in engineering problem solving. The use of
MAPLE in control engineering has received significant attention in the literature [ 1,
151. The evaporator model was implemented easily in Maple as it has useful built-in
mathematical functionality, such as the linulg package that has a collection of
functions for matrix manipulations and evaluations, and the dsolve fknction and
DEtools package for solving a system of ordinary differential equations. The linalg
package is particularly useful in developing design procedures for an analytical
nonlinear controller by using an input-output linearization technique [ 151.
While MAPLE is efficient in symbolic designs in terms of less programming
effort, it is limited for numerical simulation of closed-loop control systems. This is
because the required execution (or clock) time is substantially higher when compared
to other numerical simulation packages such as Simulink. The large execution time
seems to be due to poor use of memory when computing in MAPLE, and the
execution time grows with closed-loop simulation time. For example, memory used
for executing a MAPLE statement is not “reclaimed” for other subsequent executions.
Therefore, as the number of executed statements increases (i.e. the do-while loop in
closed-loop simulation code), the amount of free memory that is available decreases.
This causes the execution time to increase due to less available memory. For this
reason, numerical simulation involving repetitive and iterative computations in Maple
is not viable.
Implementation in Matlab
The use of MATLAB in process control application has received significant attention
in the literature [16]. It allows extensive matrix manipulation and numerical
computation in an “interpreter” form Development of programs for simulating
evaporator models was found to be easy in MATLAB as it has a group of built-in
mathematical functionalities (called toolboxes) such as funfun toolbox that has the
ode45 function for solving a system of ordinary differential equations. For control
applications, there are lmictrl and lmilab (LMIControl Toolbox), &t (QFT Control
Design Toolbox), fizzy (Fuzzy Logic Toolbox), rnpccmds (Model Predictive Control
Toolbox), ncd (Nonlinear Control Design Blockset), m e t (Neural Network Toolbox),
and robust (Robust Control Toolbox). MATLAB is equally efficient in analytical
derivatiodsimplification of fust principle models through its symbolic (Symbolic
Math Toolbox). This is particularly useful in the calculation of Jacobian matrices. All
113
K.M. Karn, P. Saha. M.0 Tade‘and G.P Rangaiah
these toolboxes are quite useful in developing design procedures for linear and
nonlinear controllers
The programming in MATLAB is easy but not so transparent if the toolboxes are
used extensively For this same reason, applications are sometimes restricted due to
limited choice of features in the functional subroutines. The debugging of a program
is quite easy if the problem is not due to the limitation of built-in subroutines such as
those in toolboxes. Also there are graphic utility toolboxes, such as gruphkd (two
dimensional graphs), gruphjld (three dimensional graphs), specgraph (specialized
graphs), graphics (Handle Graphics) and uitools (graphical user interface tools).
These are convenient and sufficient to have a quick online visualization of simulation
results. There are two major demerits of MATLAB simulation First, the program is
always platform dependent Although MATLAB compilers are being used to convert
the code to C/C++ and compile it to form a stand-alone application file, the use is
quite limited. One of the reasons for this is that MATLAB compiler cannot convert a
few commands such as “eval” and “plot”, which are considered to be key commands
in most of the application programs Second, MATLAB simulation is very slow
because it considers all its variables as matrices Even a scalar is taken as a 1x1
matrix in the memory space, which eventually slows down the computations
Implementation in Sirnulink
The use of Simulink in simulation jobs has found wide acceptance due to its user
friendly and menu-driven programming technique It allows the user to draw a flow
diagram of the model calculations, with the help of a few pre-assigned blocks,
sirnulink (Simulink) and blocks (Simulink block library) are the toolboxes containing
various block modules required by the software. Simulink does use the features of
MATLAB functions and subroutines or toolboxes, but in a manner, which is not at all
transparent to the user. It is definitely easy to develop a program for the model in
Simulink, and associate it with available control system utility blocks to generate
correct control strategy. However, they have their own limitations in terms of the
specific need of a particular control algorithm In those cases, the use of S-function
facilitates for users developing their own blocks for control and other applications.
The debugging of Simulink programs is the easiest if the problem is not due to the
limitation of subroutine blocks. Switching between two control strategies requires
nothing more than changing the specific controller block in the main program There
are two major demerits of Simulink simulation. First, like MATLAB, the Sirnulink
program is always platform dependent. Unlike MATLAB, compilers are not proved to
be useful to form any stand-alone application file. Second, Sirnulink does not allow
handling of two independent variables in the program. As a result, the control
application requiring two independent variables (such as Model Predictive Control for
nonlinear processes, where a second time variable is needed for calculation of future
prediction of model outputs for optimization purpose) are quite difficult to program.
Implementation in C++
The use of C++ in process simulation and control has become quite popular because
of its general-purpose structured or object-oriented programming technique that is
powerful, efficient and compact. C++ combines the features of a high level language
with the elements of the assembler (in “compiler” form) and thus is close to both man
I14
bl
4
4
Analysis of
program
Program
I Programming
Integration
step size
Open-loop
simulation
Feature
Needs graph utilities that
are easy to use
Requires platform
Quick, simple and
transaarent.
Tedious
requlrement mcreases
and computational speed
decays exponentially.
Need to be specified.
Accuracy depends upon
correct choice of
+
I
Easy on-line plotting
Requires platform
Easy on-line plotting
Requires platform
Easiest
Easy but least transparent
Takes internally, not so
transparent. But at least 10
times faster than MATLAB
Need to be specified.
Equipped wlth
facility for variable
Easy but not
transnarent
Easier
Fastest
Slowest
Faster than Matlab
1
Needs graph utilities;
graphics programming
m C++ IS difficult and
time consuming
Stand-alone EXE file
Depends on
subprograms
developedhsed for
numerical integration.
Tedious and difficult
but transnarent
Most tedious
1
Table 4. Comparisons of different computing platforms for evaporator model simulation.
I
K M . Kam, P Saha, M . 0 Tad6 and G.P Rangaiah
and machine. It has now been implemented on virtually every type of computer, fi-om
micro to macro. Unlike MATLAB/Simulink, developing the program for simulation
of an evaporator model in C++ has been found to be quite time consuming and
tedious, It does not have any built-in mathematical functionality for linear algebra or
numerical computations. Thus for open-loop simulation as well as for control
applications, one needs to develop functional subroutines for everything from ODE
solver to graphic utility.
However, the programming in C++ is most transparent as it is entirely done by the
user. Nevertheless one can take the help of readily available codes for a specific
application [ 171; in fact, there are often several choices of functional subroutines and
the user has to select the most appropriate code. The debugging of programs is the
most tedious out of the four platforms. The greatest advantage of C++ code is that it is
compiled to generate a stand-alone executable file for future application. Thus the
program is platform independent. If needed, it is possible to maintain the
confidentiality of the code.
60
-g
-
50
40
30 20 lo-
.--
. .
*
25
20
I5
10
0
5
0
g
N
c
o
-5
-10
-I5
-20
-25
-30
-35
32
28
24
20
16
12
-
-
8
5
m
4
g
-4
cv
o
-8
0
1
2
3
time (hr)
4
5
0
1
2
3
time (hr)
4
5
12
10
8
6
4
2
o
-2
-4
-6
-12
-16
-20
-24
-28
-a
-10
-12
-14
0
1
2
3
time (hr)
4
5
Legend for all the figures
+20% change in m,4 for M1 model
-20% change in ms4 for MI model
+20% change in m,4 for M 2 model
-20% change in ms4 for M2 model
Figure 2. Open-loop responses of evaporator models A41 and M2 for a change in
from 2 3814 to 2 8577 liquor level in the four flash tanks
116
Models of an Industrial Evaporator System
Comparison and Use of Evaporator Models
Open loop simulation of the two evaporator models subjected to a S O % increase in
the steam flow to HT #4 was performed in each of the four platforms. The results
obtained in all the platforms are identical The open loop responses of the evaporator
models obtained from Simulink are given in Figures 2 to 4. In these figures, outputs
and other state variables are expressed in terms of percentage deviations 60m their
respective nominal steady-state conditions (in Table 1). The responses of the two
models differ significantly from each other In Figure 3, the responses of the liquor
temperatures are in the opposite directions (e.g. T3 of M1 increases while T3 of M2
decreases). In the case of the liquor densities, the ultimate responses of the M1 and
M2 are different indicating uncertainty in the model gains. The effect of steam flow
on the liquor densities of model M2 is larger than those of model MI. Structural
model uncertainties are evident from the difference in the transient responses of the
liquor levels, densities and temperatures. Model mismatch between M1 and M2 was
also shown using closed-loop simulation [12]. All these differences are due to the
additional assumptions for model M2 stated previously
.
. I
50
40
.
I
I
-4
-6
I -20- .
0
1
2
3
4
5
0
1
time (hr)
4
,
-4
-3
-
-6
4
10
1
8
2
3
time (hr)
4
5
6
-
&
n
b
4
2
o
-2
0
1
2
3
time (hr)
4
5
0
I
I
I
I
I
2
3
time (hr)
4
5
Legend for all the figurer
+20% change in ms4 for MI model
-20% change In mS4 for MI model
+20% change in m,4 for M2 model
-20% change in mS4 for M2 model
Figure 3. Open-loop responses of evaporator models MI and M2 for a change in
ms4fiom 2 3814 to 2 8577 liquor temperature in the fourfrash tanks
117
K M.Kam, P,Saha. M . 0 Tad6 and G.P Rangaiah
3
,
10
05
E-
oo
a
-05
-lo
-15
I
......
o....
1 -
0
1
2
3
time (hr)
4
5
0
5
1
2
3
time (hr)
4
5
1
0
-3
-4
0
1
2
3
time (hr)
4
5
*....*
I
I
I
I
I
0
1
2
3
4
5
time (hr)
Legend for all the figures
+20% change in m,4 for MI model
-20% change in ms4 for MI model
4
+20% change in ms4 for M2 model
-20% change in ms4 for M 2 model
Figure 4. Open-loop responses of evaporator models MI and M2 for a change in
ms4from 2 3814 to 2 8577 liquor density in the fourflash tanks
The challenge involved in control studies using models M1 and M2 can easily be
understood by the “process characterisation cube” described by Ogunnaike and Ray
[18]. The three axes of this cube correspond to three process characteristics, viz
degree of dynamic complexity, degree of nonlinearity and degree of interaction.
Having severe nonlinearity and structural complexity (as shown by many equations
above, and open-loop responses in Figures 2 to 4), models M1 and M2 belong to the
most difficult “Category VIII Processes”. Model M 1 is considered relatively more
realistic for the industrial evaporator system than model M2 due to fewer
assumptions. However, fiom a controller design point of view, model M 2 is relatively
viable for nonlinear model-based controller design due t o its simplicity. Furthermore,
118
Models of an Industrial Evaporator System
the control-nonaffine nature of model M1 (i.e. temperature state equations are
nonlinear with respect to the manipulated inputs) and the exponential terms make it
computationally less attractive for nonlinear control system design
Nevertheless, the availability of two models for industrial evaporator systems
allows more rigorous and realistic nonlinear control studies through computer
simulation [ 12, 13, 18, 191 These studies have generally employed model M 1 as the
process and model M2 for controller design. The suggested control techniques for this
kind of system would be a full-scale multivariable, nonlinear, model based control
law with capabilities for handling difficult dynamics, such as Generic Model Control
and Nonlinear Model Predictive Control [30].Apart from this use of models M1 and
M2, they can be used in several other ways in process control research and education.
A few possible ways are:
1. Process identification of either model M1 or M2, and the identified model can
then be used for model-based controller design for the simulated process
2 Either model M1 or M2 can be used as the process for training in classical control
techniques at undergraduate and/or post-graduate level
3 Various evaporator configurations (such as one or a few stages) are possible for
process flexibility and controllability studies This would require the users to set
up relevant model equations from either models MI or M2, and select the input
and output variables.
While the strict validity of both models MI and M2 to the real evaporator system
on-site has not been established, model M2 is considered to satisfactorily represent
the actual plant owing to the success of the implementation trial of geometric
nonlinear control on the evaporator system simulator on-site [21] In the
implementation trial, model M2 was utilised for the geometric nonlinear controller
design. Should model M2 fail to represent the evaporator system satisfactorily, such a
success would not have been possible Being more realistic than model M2 from the
physical point of view, it is understood that model M1 also represents a valid model
to the actual evaporator system.
Several measured andor unmeasured load disturbances may occur during the
operation of the industrial evaporator system. Common disturbances are due to
changes in the feed (such as rate, density and temperature in F in Figure 1) to the
evaporator system, andor changes in the heat transfer coefficient of heaters For
control studies on the evaporator models by researchers and students, the following
disturbances are suggested.
1 . Change in flow rate of feed, F from the nominal value of 37 7 to 39.7 or 35 7.
2. Change in heat transfer coefficient, UA in heaters 1 and 2 from the nominal value
of 1999780 and 965390 to 1699810 and 820580 respectively.
3. Change in density of feed, F from the nominal values of 1.3 10 to 1 245 or 1 376
4. Change in temperature of feed, F from the nominal values of 60 to 54 or 66
5. Change in the set point of product liquor density from FT#4 from the nominal
value of 1.54 to 1.46 or 1 62
Based on our experience, the authors recommend the use of MATLAB and/or
Simulink platforms for performing control studies owing to the availability of various
control system toolboxes. However, the Maple platform is better for easy analysis and
design of analytical nonlinear controllers with its iinarg package C++ platform will
119
K M. Karn, P. Saha, M . 0 Tadk and G.P Rangaiah
be recommended to those who want absolute transparency in the entire simulation
code.
Conclusions
Two different mechanistic models of a complex multistage industrial evaporator
system are presented. The models are significantly different from each other, and they
are useful for training and research in process control at the undergraduate and/or
postgraduate levels. The models are simulated in four different platforms of
programming language/package viz. MAPLE, MATLAB, Simulink and C++. The
merits, demerits and usefulness of these codes are critically analyzed, which will
enable the reader to choose the appropriate programming technique for their
application-specific need.
Nomenclature
Abbreviations
BPE
boiling point elevation
CW
cooling water
D
underflow
F
liquor feed
FT
flashtank
HD
heater discharge
HF
heater feed
HT
heater
HW
hot water
P
product flow
S
steam flow
V
vapour flow
Symbols
C
h
Q
T
U
X
Y
m
P
specific heat capacities
flash tank level
volumetric flow
liquor temperature
manipulated input variable
state variable
controlled output variable
mass flow
liquor density
Subscripts
P
liquor product
v
vapour
S
steam
References
Mackenzie, J G and Allen, M 1998 Mathematical power tools Chem Eng Educ ,32(2), 156
Bequette, B W , Schott, K D , Prasad, V ,Natarajan, V and Rao, R R 1998 Case study projects in an
undergraduate process control course Chem Eng Educ ,32(3), 214
3 Newell, R B and Lee, P L 1989 Applied Process Control A Case Study, Prentice-Hall, New York
4 Montano, A , Silva, G and Hernandez, V 1991 Nonlinear control of a double effect evaporator In
Advanced Control of Chemical Processes, Pergamon Press, New York, 167
5 Allen, R M and Young, B R 1994 Gain scheduled lumped parameter multi-input multi-output models
of a pilot plant climbing film evaporator Control Engineering Practice, 2(2), 219
6 Quaak, P , Vanwijck, M P C M and Vanharan, 3 J 1994 Comparison of process identification and
physical modeling for falling film evaporators Food Control, 5(2), 73
7 Vanwijck, M P C M , Quaak, P and Vanharan, J J 1994 Multivariable supervisoly control of a 4effect falling film evaporator Food Control, 5(2), 83
8 Wang, F Y and Cameron, I T 1994 Control studies on a model evaporation process constrained
state driving with conventional and higher relative degree system Journal of Process Control, 4(2), 59
9 To, L C ,Tadt, M 0 , Kraetzl, M and Le Page, G P 1995 Nonlinear control of a simulated industrial
evaporation process Journal of Process Control, 5(3), 173
10 Young, B R and Allen, R M 1995 MlMO identification of a pilot plant climbing film evaporator
Control Engineering Practice, 3(8), 1067
1
2
-
120
Models of an Industrial Evaporaior System
15
16
17
18
19
20
21
To, L C , Tade, M 0 and Le Page, G P 1997 Implementation of input output linearization control
technique on an industrial evaporative system CHEMECA 1997, Rotorua, New Zealand, PC2d
Kam, K M and Tade, M 0 2000 Simulated control studies of five-effect evaporator models Comput
Chem Eng,23(11-12), 1795
Kam, K M and Tade, M 0 1999 Nonlinear control of a simulated industrial evaporation system using
an input-output linearization technique with a reduced-order observer Ind Eng Chem Res ,38,2995
Kam, K M and Tad6, M 0 1997 Technical Report 1/97 Dynamic Modeling and Differential
Geometric Analysis of an Industrial Multi-stage Evaporation Unit, School of Chemical Engineering,
Curtin University of Technology, Western Australia
Kam, K M , Tade, M 0 , To, L C and Le Page, G P 1999 Implementation of MAPLEprocedures for
simulating an industrial multi-stage evaporator MapleTech, 5(2&3), 27
Henson, M A and Seborg, D E 1997 Nonlinear Process Control, Prentice-Hall Inc ,New Jersey
Press, W H , Teukolsky, S A , Vellerling, W T and Flannery, B P 1997 Numerical Recipes in C The Art of Scientific Computation, Cambridge University Press
Kam, K M Tadt5, M 0 Rangaiah. G P and Tian. Y C 2001 Strategies for enhancing geometric
nonlinear control of an industrial evaporator system Ind Eng Chem Res ,40,656
Rangaiah, G P , Saha, P and Tadt, M 0 2001 Nonlinear model predictive control of an industrial
four-stage evaporator system Chem Eng J . accepted - in press
Ogunnaike, B A and Ray, W H 1994 Process Dynamics, Modelling, and Control, Oxford University
Press, New York
Kam, K M , Implementation and Simulation of Nonlinear Control Systems for Mineral Processes,
Ph D Thesis, Chapter 8, Curtin University of Technology, Western Australia (2000)
.
.
Received 26 January 2001; Accepted after revision. 19 March 2001
Appendix A
Equations for stages 1, 3 and 4 for both models MI and M2 are presented in this
appendix. Further details of the derivation of these equations can be found in [ 141
Model MI
Stage 1
121
K M.Kam. P. Saha, M . 0 Tade' and G.P Rangaiah
where
"'
M4
= R(273.1+ T, - BPE,)
P,=0.133ex
d
A-
C+273 l+TI-BPEI
Stape 3
(A.12)
( A 13)
%=
dt
-[
1
1
C O T ~(P'3 -hy43) (E3 - m ~ 3+ P V ~ Q( P -~ Q P ~ --PE3
w
-q
-&[
- COT3 C0RhO3[
E3(
- 1) - QP2 P P 2 (
I)]
(A.14)
- I))]]
where
(A. 15)
122
Models of an Industrial Evaporator System
hs3 = (5.76 / 2.38)m,4
(A.16)
BPE3 = 102.69~3-128.82
(A.17)
MP3
p v 3 = R(273 1 + T3 - BPE,)
d
P3=0 133ex A -
" 1
(A.19)
C + 273.1 + T3 - BPE3
CoRh03 = -102 69pv3
1
B
(C+273.1+T3-BPE3)2 (273 1+T3-BP&)
(A.21)
(A.22)
mv3 =
1
Stage 4
-
* L[
dt = h4A4 E4[
(A.23)
-1) -Q P ~ P P ~ [ -I ) ]
(A.24)
(A.25)
where
' 3Q P ~~ 4 ~ 4 7 '+4 ms44s4
E4 = Q P ~~ 3 ~ 3 7 Av4
K M. Kam, P. Saha, M . 0 Tad6 and C P Rangaiah
BPE4 = 1 0 2 . 6 9 ~ 4- 128.82
(A.27)
(A.28)
P4 = O 133ex
CoRh04
d
A-
(A.29)
C + 2 7 3 l+Tq-BPE4
= - 102 69pv4
B
1
(A.3 1)
(C+273.1+T4-BPE4)2 (273 1+T4 -BpE4)
Model M2
Stage 1
where
(A.36)
124
Models of an Industrial Evaporator System
(A 37)
(A.38)
MPI
p v l = R(273 1 + T, - BPE,)
COT,= (Vl - Alh,
PVl
0.75M
R(273 1 + T, - BPE1)- (273.1 + ,
'7 - BPEl)
Stape 3
-=-[
dh3
dt
1
A3
QPZ - Q P ~ -P W
dt = -!--[
h3A3 E3(
- I)- Qpz P P ~ (
5 = L(
E3 - k v 3+ py3( Qf.2
dt
CoT3
-Qp3
-I)]
-Pw
where
(A.45)
kv3
(A.46)
= E3
ms3 = (5.76 l2.38)k,,
(A.47)
MP3
p v 3 = R(273.1+ T3 - BPE3)
(A.48)
P3
= 4.09T3
- 410.38
COT, = (V3 - A3h3
(A.49)
4.09M
Pv3
R(273.1+ T3 - BPE3)- (273.1 + T3 - BPE3)
125
K M. Kam, P. Saha. M.0.Tad6 and G.P Rangaiah
Stage 4
-[
dh4 - 1
--
dt
A4
-"I
-
Q P ~ Q P ~
(AS 1)
PW
* 1[ (2
dt
=
h4A4
- 1 ) - Qp3 pp3
E4
(2
-
(A.52)
I)]
(A.53)
where
(A.54)
(A 5 5 )
pV4 =
MP4
R(273.1+ T4 - B P E 4 )
P4 = 4.09q - 434.95
(A 57)
4 09M
Pv4
R(273 1 + T 4 - B P E 4 ) - ( 2 7 3 1 + T 4 - B P E 4 )
Appendix B
Linear models for M1 and M2 models were obtained by performing local
linearization about the steady-state operating conditions given in Table 1. They are
expressed in state space form as:
QP~,ks4IT
and d = [QJ, pfi TAT.The matrices A, Y and r are the Jacobian matrices for state, input
and disturbance variables respectively, and were found by local linearization of the
nonlinear evaporator models
where x = [hi, hz, h3, h4, p4, p i , pz, p3, 7'1, T2,7'3,
126
7'4IT,
u = [QPL
Qp2,
Qp3,
Models of an Industrial Evaporator System
It can be shown that the Eigen values of the linearized models LM 1and LM2 are.
- 8.1757
- 2.4121 k 0.58431'
%hi,
-1.7389
- 1.3465
- 0.5397
=
0.23 17
- 0.1133
- 0 01 12 f 0.0042i
- 0.0025
- 2.5283 k 0.33731-
- 0.9957 k 0.66861'
0.1033 -I 0.0184i
- 0 0169 k 0 0652i
0 1040 x lo-*
0.4095 x
0.2297 x
- 0.3782 x lo-'
0 0015
Some of the Eigen values of both MI and M2 models are positive which imply that
the evaporator models are open loop unstable There are also noticeable differences
between the two sets of Eigen values indicating dissimilarity between the evaporator
models M1 and M2.
127
Документ
Категория
Без категории
Просмотров
0
Размер файла
936 Кб
Теги
process, model, research, industries, evaporated, system, education, control
1/--страниц
Пожаловаться на содержимое документа