MODEL-BASED OPTIMIZATION AND CONTROL OF CHROMATOGRAPHIC PROCESSES
Karsten-Ulrich Klatt ;1 Felix Hanisch Guido Dünnebier Sebastian Engell Process Control Laboratory, Department of Chemical Engineering, University of Dortmund, 44221 Dortmund,
e-mail: [email protected]
Abstract: This contribution presents an integrated approach to the optimal operation and automatic control of
chromatographic separation processes in batch elution mode as well as in continuous SMB operation. The new
approach is based on computationally efficient simulation models and combines techniques from mathematical
optimization, parameter estimation and control theory. The resulting algorithms were implemented in an industrial
standard control system and the capability of the proposed control approach is demonstrated on the separation of
fructose and glucose, both in batch and SMB operation mode.
Keywords: Chromatographic separation, simulated moving bed, process control, dynamic optimization,
parameter estimation.
1. INTRODUCTION
Chromatographic separation processes are an emerging
technology for the separation of Life Science products,
such as pharmaceuticals, food, and fine chemicals. To
improve the economic viability, a countercurrent operation is often desirable, but the real countercurrent of the
solid leads to serious operating problems. Therefore, the
Simulated Moving Bed (SMB) process is an interesting
alternative option to batch chromatography since it provides the advantages of a continuous countercurrent unit
operation while avoiding the technical problems of a true
moving bed.
Both conventional batch and SMB chromatographic processes exhibit complex nonlinear dynamics, and a high
sensitivity in the vicinity of the economic optimum.
Furthermore, concentration measurements are expensive
and can only be installed at the outlet of the separation
columns. Thus the optimal operation and automatic control of chromatographic separation processes is a challenging task. Currently, most processes are controlled
manually. To avoid off-spec production and to ensure
sufficient robustness margins they are operated far from
the optimum. This contribution presents the conceptual
design and technical realization of a model-based optimization and control scheme for batch and continuous
chromatographic separation processes which makes it
possible to exploit their full economic potential.
2. PROCESS DESCRIPTION
Chromatographic separations are usually operated in
batch mode, the elution mode considered in this work
being the most commonly used operation. Here, one
pulse of the mixture which has to be separated is injected
together with a suitable solvent (desorbent) into the column containing the solid adsorbent. Due to the different adsorption affinities, the components have different
1
We thank G. Zimmer and M. Turnu for their valuable contribution
to the parameter estimation and reduced model identification issue,
respectively, and our colleagues from the Chair of Plant Design, especially A. Jupke and A. Epping, for the fruitful cooperation within
our joint chromatography project. The financial support of the Bundesministerium für Bildung und Forschung under the grant number
03D0062B0 is very gratefully acknowledged.
Section I
Desorbent D
Section IV
....
....
Direction of
Port Switching
A+D Extract
....
Section II
-A
-B
Raffinate B+D
....
A+B Feed
Section III
Figure 1. Scheme of a simulated moving bed process
migration velocities and the mixture is thus gradually
separated while moving through the column. The eluting
solvent is analyzed with a suitable detector at the outlet
of the column, and a fractionating valve separates the
mixture into its components.
The major drawbacks of the batch operation mode are
the high demand of eluent and the non-continuous product streams. It would be preferable to have a countercurrent flow of the fluid and the adsorbent. However,
a real countercurrent flow of the solid is difficult to
realize. The invention of the Simulated Moving Bed
process overcame these difficulties (Broughton and Gerhold, 1961). Here the countercurrent movement of the
phases is approximated by sequentially switching the
valves of interconnected columns in the direction of the
liquid flow.
According to the relative position of the columns to the
inlet and outlet nodes the SMB process can be divided
into four different sections (see fig. 1). The separation is
performed in the two central sections where component
B is desorbed and component A is adsorbed. The desorbent is used to desorb component A in the first section to
regenerate the adsorbent, and component B is adsorbed
in the fourth section to regenerate the desorbent. The
net flow rates of the components have different signs in
the central sections II and III, thus components B and A
are transported from the feed inlet upstream to the raffinate outlet with the fluid stream and downstream to the
extract outlet with the ”solid stream”, respectively. The
stationary regime of this process is a cyclic steady state,
in which in each section an identical transient during
the periods between two valve switches takes place. The
cyclic steady state is practically reached after a certain
number of valve switches, but the states of the system are
still varying over time because of the periodic movement
of the inlet and outlet ports along the columns.
egy for the numerical solution of the equations above,
based on Galerkin finite elements for the liquid phase
equations, orthogonal collocation for the solid phase,
and a suitable set of initial and boundary conditions, was
proposed by Gu (Gu, 1995). In this manner, simulation
times far below realtime can be achieved while reproducing experimental results very accurately (Dünnebier
and Klatt, 1999).
3. MATHEMATICAL MODELING AND
SIMULATION
For the modeling of the SMB process, we follow a
modular approach i.e. we build a rigorous model of
the process by connecting dynamic models of the single chromatographic columns and considering the cyclic
port switching. The models consist of two parts: the
node balances to describe the interconnection and the
switching, and the dynamic models of the single chromatographic columns. The node balances are used to
calculate the inlet flows and concentrations for the four
zones of the process (Ruthven and Ching, 1989) and
comprise the mass balances at the respective nodes.
The switching operation can, from a mathematical point
of view, be represented by a shifting of the initial or
boundary conditions for the single columns. Using this
node model, the dynamic models of the single columns
are interconnected. Any type of dynamic model for the
single columns can be incorporated into the SMB model.
In a recent publication (Dünnebier et al., 1998), it was
shown that for processes with linear adsorption equilibrium, the Dispersive Model for Linear Isotherms (DLIModel) provides a very accurate and computationally efficient column model. Assuming that the effects of axial
dispersion and mass transfer resistance can be lumped
into the single parameter Dap; i leads to a quasi-linear
parabolic partial differential equation for each component:
∂ci
∂ci
∂2 ci
+ uL
= Dap; i
:
(1)
γi
∂t
∂x
∂x2
The adsorption equilibrium is described by qi = Ki ci and
the parameter γ is defined as γ = 1 + 1 ε ε Ki , where ε represents the column void fraction. The interstitial velocity
uL is assumed to be constant between two switching
periods. The above PDE was solved by Lapidus and
Amundsen (Lapidus and Amundsen, 1952) for arbitrary
initial and boundary conditions using a double Laplace
transform and the application of this closed form solution to SMB processes is desribed in (Dünnebier et
al., 1998).
For complex nonlinear and coupled adsorption behavior,
a more detailed model is needed. We here use a model
of the most comprehensive General Rate Model (GRModel) type. Assuming no radial distribution of uL and
ci , the differential material balances for each component
result in the following set of equations
4. OPTIMAL OPERATION OF BATCH
CHROMATOGRAPHY
The determination of the optimal operating regime for
batch elution chromatography can be stated as follows:
a certain amount of raw material has to be separated
into the desired components while strictly satisfying the
constraints on purity and recovery. In this optimization
problem there are the following degrees of freedom:
ε) 3 kl ; i
(ci c p; i (r = R p ))
εR p
∂2 ci
∂ci
Dax 2 + uL
=0
(2)
∂x
∂x
∂c p; i
∂c p; i
∂qi
1 ∂
ε p)
+ εp
ε p D p; i 2
r2
= 0:
∂t
∂t
r ∂r
∂r
∂ci
∂t
(1
+
(1
In this model, any type of adsorption equilibrium can
be included. A very efficient spatial discretization strat-
a) The overall throughput, represented by the interstitial velocity uL .
b) The injection period tin j as a measure for the size
of the feed charge.
c) The cycle period tcyc , i.e. the duration from the
beginning of one feed injection to the beginning of
the next one.
d) The switching times of the fractionating valve
τswitch; i .
The product requirements can usually be formulated in
terms of minimum purities, minimum recoveries or maximum losses. In case of a binary separation, all these
constraints can be transformed into each other. In the
sequel, we use the product recovery Reci as a measure
of the product quality. The objective function for the
ṁ
optimization is the productivity Pri = mProduct i . This forAdsorbent
mulation results in the following dynamic optimization
problem:
(3)
max Pr(uL ; tcyc ; tin j ; τswitch; i )
;
s: t : Reci Recmin; i
0 uL umax
L
tin j ; tcyc 0 :
For the solution of (3) we exploit the fact that the
recovery constraints are always active at the optimal
solution and can be considered as dynamic equalities:
Rec = Φ(uL ; tin j ; tcyc ; τswitch; i ) :
(4)
If for a specified recovery the solution of (4) would
explicitly be given in terms of tin j , tcyc and τswitch; i , one
would obtain an equivalent optimization problem with
only one degree of freedom:
(5)
max Pr(uL )
s: t : 0 uL umax
L :
Unfortunately, a closed form solution of eq. (4) is not
available, but the structure of the optimization problem
allows for an online solution by an efficient decomposition strategy. The resulting problem then consists of
two stages: the iterative solution of the dynamic equality
constraints (4) in an inner loop, and the solution of (5)
in an outer loop.
The iterative solution of (4) starts with a dynamic simulation of the process model for the respective value of
uL with initial guesses for tin j and tcyc . By integration
of the resulting elution profiles, a set of switching times
τswitch; i is determined which exactly gives the desired
product recovery. In general, these switching times are
either not feasible because the collecting intervals for the
two fractions overlap, or not optimal, because a fraction
of pure solvent is obtained between the two collecting
intervals. A simple gradient based search converges to
the optimal and feasible solution for tin j and tcyc in a few
steps yielding the solution of the equality constraints for
a given interstitial velocity uL . The optimal interstitial
velocity is then determined in the outer loop using a simple Newton type method. Because the objective function
is unimodal, (5) can be treated as an unconstrained optimization problem with one degree of freedom without
explicitly considering the constraint.
In order to compensate for plant/model mismatch, we
combine the online optimization of the operating parameters with an online parameter estimation strategy. The
large number of parameters and their strong interactions
do generally not allow for the estimation of all parameters from the measured elution profile. Proceeding from
reasonable initial values of the model parameters from
off-line experiments, we thus identify a reduced set of
parameters. The model parameters can in principle be
classified as:
I Kinetic parameters describing the effects of mass
transfer, diffusion and axial dispersion,
II Adsorption parameters describing the thermodynamic equilibrium of adsorption.
Though this classification is only a rough approximation in case of a complex adsorption behavior, it is a
useful means for choosing the dominant parameters.
The effects of the kinetic parameters are additive in a
first approximation, therefore an experimentally determined elution profile can be approximated by fitting
only one kinetic parameter and the adsorption parameters (Golshan-Shirazi and Guiochon, 1992). Simulation
studies for several physical systems led to the conclusion
that for those systems the mass transfer parameters kl ; i
and the isotherm coefficients Ki are the dominant ones
and should be chosen for parameter estimation. In the
reduced online parameter estimation problem e.g. for a
binary separation, 4 parameters have to be estimated.
As soon as the set of peaks resulting from one injected
pulse is eluted, this data is used for adjusting the model
prediction to the measurement signals by a least-squares
type algorithm.
5. OPTIMIZATION AND CONTROL OF SMB
CHROMATOGRAPHY
The online optimization of the complex SMB process
under real-time requirements is currently not possible.
Therefore, we propose a two-layer control architecture
where the optimal operating trajectory is calculated offline by dynamic optimization based on a rigorous process model, the parameters of which are adapted to the
current measurements. The remaining control task is
then to keep the process along the calculated optimal trajectory despite disturbances and plant/model mismatch.
This task is performed in the bottom layer where identification models based on simulation data of the rigorous
process model along the optimal trajectory are combined
with a suitable local controller. The control architecture
is schematically shown in fig. 2 and the concrete realization of the elements is explained below.
Process
SMB-Process
Model-Based
Control
On-Line
Control
Identification of
Local Black-Box
Models
Model-Based
Parameter Estimation
Model-Based
Optimization of
Operating Parameters
Off-Line
Optimization
Figure 2. Control concept for SMB processes
Trajectory optimization and model parameter estimation: The operating regime of a SMB process is a
periodic orbit or cyclic steady state (CSS). The calculation of the optimal operating parameters thus constitutes
a dynamic optimization problem. In case of a given plant
and a pre-specified feed inflow, the cost function can be
reduced to the required desorbent inflow QD . By defining cax; k as the axial concentration profiles at the end of
a switching period (see fig. 3), and by expressing both
the process dynamics between two switching operations
and the switching operation itself by the operator Φ, we
can write the following condition for the CSS:
(6)
cax; k+1 = Φ (cax; k )
kΦ(cax; k ) cax; k k epssteady :
(7)
The purity requirements for the products in the extract
and in the raffinate stream are formulated as inequality
constraints. Besides that, the efficiency and functionality
of most adsorbents is only guaranteed up to a maximum
interstitial velocity, which results in an additional constraint for the flow rate in the first section of the process.
The optimization problem can then be stated as follows:
min QD (Qi ; τswitch )
s.t.
kΦ(cax k )
;
τZ
switch
0
τZ
switch
0
cax; k k
epssteady
cA; Ex (t )
dt
cA; Ex (t ) + cB; Ex (t )
PurEx min
cB; Ra f (t )
dt
cA; Ra f (t ) + cB; Ra f (t )
;
PurRa f
;
(8)
min
Q1 Qmax :
The natural choice of the degrees of freedom are the
desorbent flow rate QD , the extract flow rate QE , the
switching time τswitch and the recycle flow rate QIV .
However, this results in an ill-conditioned optimization
problem. Thus, we replace the ”natural degrees of freedom” QE , QD , QIV and τswitch by the variables βi :
QF
(1 ε)A L
=
QS = ∂g
∂gB
A
τswitch
=β3
β2
∂cA
∂cB
∂gA
∂gB
QE = QS (
β1
β2 )
∂cA
∂cB
∂gA
∂gB
QD = QS (
β1
=β4 )
∂cA
∂cB
∂gB
εb
=β4 +
)
QIV = QS (
∂cB
1 εb
gi = ε p ci + (1 ε p)qi (cA ; cB );
(9)
t1
with respect to γi ; Dap; i (i = A; B) then gives the column specific parameters. Here, ci (x = L; t; γi ; Dap; i ) is
the solution of the PDE (1) with boundary and initial
conditions
ci (x = 0; t; γi ; Dap; i ) = ce; i (t )
(10)
ci (x; t = 0; γi ; Dap; i ) = c0; i (x) :
(11)
Unfortunately, the boundary and initial concentrations
are largely not available from the measurements. Therefore, a special approximation strategy was developed
using the measured concentrations of A and B in the
extract and raffinate outflow in two consecutive switching periods (see (Zimmer et al., 1999) for a detailed
description of this strategy).
Reduced model identification and trajectory control:
Because of the favorable properties of the nonlinear
transformation given by eq. (9), we choose the variables
βi as inputs for the trajectory control loop. With an
appropriate choice of outputs, this nonlinear transformation results in a nearly decoupled system dynamics.
One characteristic indicator for the separation performance of a SMB unit is the axial position of the adsorption and desorption fronts of the two components at a
certain moment, e.g. at the end of a switching period (see
figure 3). Indicators of these front positions are chosen
as the outputs of a reduced model for control. Assuming an on-line concentration measurement at the end
of each of the columns, an approximation of the axial
concentration profile can be obtained by connecting all
measurements of the elution profiles obtained during one
switching period. This representation is here denoted as
the Assembled Elution Profile (AEP).
Several different methods for the determination of
the front positions from the AEP have been evaluated,
trading off the computational requirements for the calculation, the robustness against noise, and the physical meaning of the calculated positions. From this, we
chose a function approximation method using a modified
Gaussian error function. The two parameters of the function are calculated for each front by a least-squares fit to
the available measurements, and the respective inflection
points which serve as the output variables are calculated
analytically afterwards.
The input and output variables of the identification
model represent deviations from the nominal trajectory:
four input variables ∆βi and the deviations of the four
nominal front positions ∆yi as outputs. As a reduced
system model for the dynamics in the vicinity of the
nominal trajectory we use a linear time invariant model
of the MIMO ARX type (Ljung, 1987):
A(q)y(t ) = B(q)u(t ) + e(t ) ;
(12)
F (z)GC (z)
F (z)GC (z)GM (z)
(13)
where A and B are 4 4-Matrices containing polynomial
functions of the discrete time shift operator q in each
element. PRMS signals (Isermann, 1992) were used to
excite the rigorous simulation model in the vicinity of
the optimal operating trajectory. The order of the system
was estimated by evaluation of the step responses and
the performance of the identified model. The necessary
computations were performed using the MATLAB System Identification Toolbox (Ljung, 1995).
After identification of the MIMO ARX model (12), in
principle, any standard linear control design approach
as well as linear model predictive control could be used
to realize a MIMO trajectory controller. However, we
here exploit the fact that due to the particular choice
of the input and output variables, the system dynamics
are only weakly coupled in the vicinity of the optimal
operating trajectory. Therefore, a decentralized trajectory controller can be implemented. For the design of
the discrete time SISO controller in each channel we
applied internal model control as proposed in (Zafiriou
and Morari, 1985). In the conventional feedback representation, the controller is of the form
C(z) =
1
where GC is the internal model controller, designed
by inverting the system model following the guidelines
0.04
Component A
Component B
0.035
Concentration [g/cm3]
where QS is the apparent solid flow rate and qi =
f (cA ; cB ), describes the adsorption equilibrium isotherm.
This nonlinear transformation, which is based on physical considerations, results in a better conditioned optimization problem.
For the solution of the optimization problem (8), a
sequential algorithm was proposed in (Dünnebier et
al., 1999b). The degrees of freedom βi are chosen by
the optimization algorithm in an outer loop and then
transformed back into flow rates and switching times. In
the inner loop, the CSS is calculated by direct dynamic
simulation. The purity constraints are evaluated by integration of the elution profiles. The nonlinear program
in the outer loop can then be solved by a standard SQP
algorithm, while the required gradients are evaluated by
perturbation methods (see (Dünnebier et al., 1999b) for
details of the implementation).
The results of the trajectory optimization illustrated
above essentially depend on a reliable determination of
the model parameters. Because these parameters may be
time varying (e.g. due to aging of the chromatographic
columns), an on-line estimation algorithm should be included. In (Zimmer et al., 1999) such an algorithm was
proposed for systems with linear adsorption isotherms
based on concentration measurement devices located in
the product outlets. Assuming the validity of the DLI
model (1), the system has, in the case of a binary separation, four parameters describing the physical behavior,
which are γi and Dap; i (i = A; B). A linear adsorption
isotherm implies that the components A and B do not
interact. Thus, the two parameter sets (γA , Dap; A ) and
(γB , Dap; B ) can be determined separately.
The measured outlet concentrations ci; meas (x = L; t ) are
compared to the outlet concentrations which are determined by the solution of the simulation model where the
relevant parameters can be freely assigned. Optimizing
a quadratic cost functional
Z t2 2
ci; meas (t ) ci(x = L; t; γi ; Dap; i ) dt
J (γi ; Dap; i ) =
0.03
Desorption front B
0.025
Adsorption front A
Adsorption front B
0.02
Desorption front A
0.015
0.01
0.005
0
−214.4
−160.8
↑ Desorbent
−107.2
↓ Extract
−53.6
0
↑ Feed
53.6
107.2
160.8
↓ Raffinate Length [cm]
214.4
Figure 3. Axial concentration profile of a simulated
moving bed unit
80
78
0
5
10
15
0
5
10
15
20
25
30
Optimal interstitial velocity
35
40 Time [h]
35
40
0.04
0.035
0.03
0.025
Time interval [s]
Interstitial velocity [cm/s]
76
20
25
Switching times
30
Time [h]
2000
1500
Inject. Per. [s]
Cycle Per. [2 s]
1000
0
5
10
15
20
25
30
35
40 Time [h]
Figure 4. Product purities and operating parameters during an experimental run (setpoint change for required purity at approx. 28 hours from 80% to 85%)
suggested in (Zafiriou and Morari, 1985). GM is the
transfer function of the respective model, and F (z) is a
first order filter
z(1 α)
(14)
F (z) =
z α
where α has to be suitably chosen in the range 0 α < 1.
6. IMPLEMENTATION AND RESULTS
In the Process Design Laboratory at the University of
Dortmund there are two chromatographic setups, on
which this theoretical framework can be implemented
and verified. A single chromatographic column, NOVAPREP Preparative HPLC, is used for model validation and separation experiments in batch elution mode,
while a complex SMB plant, a NOVASEP LICOSEP
LAB 12-26, can perform continuous production-like
separations. To work in a realistic process control environment and in order to minimize the implementation
effort, both systems are operated by a commercial process control system.
The control system consists of a decentralized control
system (DCS) of the SIEMENS S7-400-series (CPU S7414-2DP with the corresponding I/O-groups on the
same rack or with further I/O-slaves) and the Windows
Control Center (WinCC) as human machine interface.
Both processes, the batch and the SMB chromatography,
are controlled by the DCS on a bottom level and are
monitored by WinCC. Through its C-script interface,
Global Script, WinCC allows for the integration of userdefined algorithms and programs.
So far the control scheme for optimal batch operation was implemented and was verified experimentally.
The manipulated variables, batch cycle time, injection
time, and feed flow rate, are controlled by the DCS;
the concentrations of each component in the eluent are
measured using the concept proposed in (Altenhöner et
al., 1997). The measuring devices have to be chosen
according to the components in the mixture. In case
of a glucose/fructose separation a density meter and a
−3
5
x 10
step disturbance u1
step disturbance u2
0
CVs
82
−5
−10
0.1
MVs
Component A
Component B
84
0.05
0
−0.05
5
−3
x 10
10
15
20
Periods
25
30 60
70
80
90
Periods
step disturbance u3
step disturbance u4
10
CVs
Purity [%]
86
polarmeter are used. The concentration measurements
are transmitted via industrial ethernet and stored and
monitored in WinCC. By continuously calculating the
gradients for each component, the algorithm detects the
elution of a pair of peaks. The concentration data of
one pair of peaks is collected and, after the second peak
has left the column, transferred to the optimization algorithm together with the corresponding injection data.
While the process is continuously controlled by the low
level DCS, the optimizer updates the process model
based on the measurements and returns new optimal
values for the operating parameters, which are applied
to the process for the next batch.
Figure 4 shows the results of an experimental run where
a mixture containing each 30mg/ml fructose (component
A) and glucose (component B) was separated. The initial
disturbance is rejected, and after about 28 hours the controlled process reaches a steady state. At this point, a set
point change takes place in the product specifications:
purities and recoveries are now required to be 85%.
The control scheme reacts by immediately decreasing
the interstitial velocity and increasing the injection and
cycle intervals. This leads to a better separation of the
two peaks and to the desired increase in purity.
Whilst the implementation for the batch column is finished, this is currently performed for the more complex SMB control architecture. Therefore, we here show
some simulation results for a fructose/glucose separation
on the LICOSEP SMB in an 8-column setting in order
to highlight the capabilities of the proposed control concept.
Figure 5 shows the controlled response to a step disturbance on the plant inputs while operating along the optimized trajectory. In practice, this scenario corresponds
to an irregularity in the pumps or in the piping system,
5
0
0.1
MVs
Resulting purities
0.05
0
−0.05
120
130
140
Periods
150 180
190
200
210
Periods
Figure 5. Step disturbances in the manipulated variables
(∆βi ) and resulting deviations of the front positions
from the optimal values (1: solid, 2: dashed, 3:
dotted, 4: dash-dotted)
well as the application of the approach to pharmaceutical products which show a more complex adsorption
behavior than the sugar separation depicted here.
Change of adsorptions parameters KHA +5%, KHB −5%
−3
10
x 10
CVs
5
0
8. REFERENCES
−5
0.1
MVs
0.05
0
−0.05
−0.1
0
5
10
15
20
Periods
25
30
35
40
Figure 6. Change of feed batch simulated by change
of adsorption parameters at period 5 (1: solid, 2:
dashed, 3: dotted, 4: dash-dotted)
e.g. a faulty pump sealing or a column leakage. Each of
the subplots in figure 5 shows a disturbance in one input
and all resulting MV and CV moves. As can be clearly
seen, the deviations are suppressed quickly and the
closed loop reacts mostly decoupled. In many cases, a
separation process follows prior production steps which
might be continuous or discontinuous, a typical example
in the Life Science context being a fermenter or a batch
reactor. Thus a continuous SMB chromatography has to
face changes in the composition of the feed batch. This
scenario is simulated by changing the characteristic adsorption parameters after five periods by 5% for each
of the components, Glucose and Fructose. The results
are shown in figure 6 and it can be seen that the front
positions are driven back to their nominal values.
7. CONCLUSIONS
In this paper, a new approach for the optimal operation
and advanced control of chromatographic processes both
in batch elution and SMB operation mode was proposed,
which explicitly aims at controlling the processes close
to their economic optimum. In case of the batch operation, the control strategy combines online dynamic
optimization and parameter estimation techniques. Because online optimization is currently not possible for
the complex dynamics of the SMB process, we here suggest a two-layer control structure where in the top layer
the optimal operating trajectory is calculated off-line by
dynamic optimization. The respective model parameters are determined by an online estimation algorithm
which, in addition to providing actual and reliable model
parameters for the trajectory optimization, enables the
online monitoring of the unmeasurable concentration
profile within the separation columns. The task of the
second layer of the control architecture is to keep the
process along the optimized trajectory. The trajectory
control loop comprises a decentralized internal model
controller based on a linear ARX type identification
model.
The control algorithm for the batch column was implemented in a standard industrial control system. The
effectiveness of the approach could be shown for the
separation of fructose and glucose experimentally in a
batch elution chromatography and by simulation studies
for an 8-column SMB setup. The experimental verification on the SMB plant is planned for the near future, as
Altenhöner, U., M. Meurer, J. Strube and H. SchmidtTraub (1997). Parameter estimation for the simulation of liquid chromatography. Journal of Chromatography A 769, 59–69.
Broughton, D.B. and C.G. Gerhold (1961). Continuous
sorption process employing fixed bed of sorbent
and moving inlets and outlets. Technical Report US
Pat. 2985589.
Dünnebier, G. and K.-U. Klatt (1999). Modelling and
simulation of nonlinear chromatographic separation processes: A comparison of different modelling approaches. Chem. Eng. Sc. 55, 373–380.
Dünnebier, G., I. Weirich and K.-U. Klatt (1998). Computationally efficient dynamic modelling and simulation of simulated moving bed chromatographic
processes with linear isotherms. Chem. Eng. Sc.
53(14), 2537–2546.
Dünnebier, G., J. Fricke and K.-U. Klatt (1999b). Optimal design and operation of simulated moving bed
chromatographic reactors. Submitted to Ind. Eng.
Chem. Res.
Golshan-Shirazi, S. and G. Guiochon (1992). Comparison of the various kinetic models of non-linear
chromatography. Journal of Chromatography A
603, 1–11.
Gu, T. (1995). Mathematical Modelling and Scale Up
of Liquid Chromatography. Springer Verlag. New
York.
Isermann, R. (1992). Identifikation dynamischer Systeme. Springer Verlag. Berlin, Heidelberg, New
York.
Lapidus, L. and N.R. Amundsen (1952). Mathematics
of adsorption in beds. IV. The effect of longitudinal diffusion in ion exchange and chromatographic
columns. J. Phys. Chem. 56, 984–988.
Ljung, L. (1987). System Identification - Theory for the
User. Prentice-Hall. New York.
Ljung, L. (1995). MATLAB System Identification Toolbox Handbook. The Mathworks.
Ruthven, D.M. and C.B. Ching (1989). Counter-current
and simulated moving bed adsorption separation
processes. Chem. Eng. Sc. 44, 1011–1038.
Zafiriou, E. and M. Morari (1985). Digital controllers for
SISO systems: A review and a new algorithm. Int.
J. Control 42, 855–876.
Zimmer, G., G. Dünnebier and K.-U. Klatt (1999). Online parameter estimation and process monitoring
of simulated moving bed chromatographic processes. In: Proceedings of the European Control
Conference. Karlsruhe, 1999.