Binary separation control in preparative gradient chromatography using iterative learning control

Journal of Chromatography A 1673 (2022) 463078

Contents lists available at ScienceDirect

Journal of Chromatography A
journal homepage: www.elsevier.com/locate/chroma

Binary separation control in preparative gradient chromatography
using iterative learning control
Daniel Espinoza, Niklas Andersson, Bernt Nilsson∗
Department of Chemical Engineering, Lund University, Lund, Sweden

a r t i c l e

i n f o

Article history:
Received 16 February 2022
Revised 7 April 2022
Accepted 19 April 2022
Available online 22 April 2022
Keywords:
Preparative chromatography
Ion-exchange
Separation control
Iterative learning control
Feed-forward control
Model-based control

a b s t r a c t
Purification of biopharmaceuticals has shifted toward continuous and integrated processes, in turn bringing along a need for monitoring and control to maintain a desired separation between the target pharmaceutical and any impurities it may carry. In this study, a cycle-to-cycle control of the retention volumes of

two compounds in a chromatographic, ion exchange purification step was developed, allowing the process
to maintain the desired retention volumes in the separation. The controller made use of a model-based,
multivariate iterative learning control (ILC) algorithm that used a quadratic-criterion objective function
for optimal set point control, along with feed-forward control based on direct model inversion for preemptive control of set point changes. The model was calibrated using 3 experiments, allowing for fast
setup. The controller was tested by introducing three different disturbances to a sequence of otherwise
identical ion exchange separation processes: a change in the salt concentration of the elution buffer, a
change in set point, and a change in the pH of the elution buffer. It was capable of correcting for all
disturbances within at most 3 cycles, proving its efficacy. The successful application of ILC for separation
control in biopharmaceutical purification paves the way for the development of further ILC-based control
strategies within the field, as well as combination with other control strategies.
© 2022 The Author(s). Published by Elsevier B.V.
This is an open access article under the CC BY license ( />
1. Introduction
In the field of biopharmaceutical production, there has been a
paradigm shift from batch production towards integrated and continuous production processes. This shift has been primarily motivated by a societal pressure to reduce the cost of pharmaceuticals,
improved process productivity and more consistent product quality
[1], as well as by a need to make processes more flexible and capable of switching between different pharmaceuticals as the need
arises, both in small and large scale production [2,3].
The shift towards continuous processing has given rise to a
need for automation in monitoring and control. Applying automatic control based on measurements taken online during a
continuous process operation reduces the need for human intervention in the process and, by extension, any unwanted process
downtime or variation in the end product. This is critical if the
benefits of continuous manufacture are to be fully taken advantage
of. Fully integrated and continuous processes for biopharmaceutical production consist of several different process operations, from
reactors and membranes to chromatographic separation steps, and

∗

Corresponding author.
E-mail address: (B. Nilsson).

each unit operates at different time scales and has its own set of
physical properties, which can sometimes be difficult to determine
due to limitations in data availability. For robust, process-wide control of the fully integrated process chain to be possible, this limitation needs to be overcome [4,5].
In particular, chromatographic downstream processing poses
some challenges for process control. Since the performance of a
chromatographic separation step is measured after the separation has taken place, information for use in automatic control is
unavailable before the biopharmaceutical has passed through. A
few different strategies for automatic control of chromatographic
downstream processing have been applied in the past. For example, Dünnerbier, et al. [6] used modeling, simulation, and optimization of a chromatographic separation to control the desired
purity in the product, with the model parameters continuously updating before each optimization to improve the simulation fit to
the experiments. In a similar fashion, Grossmann, et al. [7] applied model-based control of product specifications in a chromatographic multi-column solvent gradient purification (MCSGP)
process for monoclonal antibody (mAb) purification. Some examples of process-wide control in continuous and integrated biopharmaceutical processes include Gomis-Fons, et al. [8], who employed a process with control of the utilization of the chromatography resin in the capture step of a continuous mAb purification

/>0021-9673/© 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( />

D. Espinoza, N. Andersson and B. Nilsson

Journal of Chromatography A 1673 (2022) 463078

process, as well as purity control of the subsequent ion exchange
(IEX) polishing step by means of parallel simulation for adaptive
pooling. Feidl, et al. [9] applied a layered control system to a similar mAb production process, in which a supervisory, process-wide
control layer supervised several regulatory, local control loops tied
to different process units. These local control loops were applied
to the perfusion bioreactor, the subsequent CaptureSMB step, and
the virus inactivation step, while the supervisory layer handled
scheduling and fed set points to the different units. Finally, Löfgren, et al. [10] performed cycle-to-cycle control of loading in a
periodic counter-current chromatography (PCC) process to prevent
overloading of the columns using an iterative learning control approach based on a simple, linear model.

Iterative learning control (ILC) is a control strategy with the
purpose of improving the operation of repetitive processes based
on information from previous process runs. With roots in robotics
engineering, the technique has been adjusted and developed for
chemical engineering applications, with Lee, et al. [11] deriving
and applying a model-predictive ILC strategy to temperature control of a batch reactor and achieving promising results. Furthermore, Holmqvist and Sellberg [12] employed an online, singleinput-single-output (SISO), model-based ILC strategy to control the
retention time of a single component in an IEX chromatography
column by manipulating the time duration of a linear salt gradient. Their controller was based on direct inversion of a model of
the retention time as a function of the gradient time duration.
Since chromatography applications in continuous downstream
processes often operate in a cyclic fashion [3], ILC provides a
promising framework for process control: each individual cycle can
be viewed as a batch, and each cycle provides information that can
be used to make decisions in the next cycle. ILC is dependent on
the process returning to its initial conditions between each batch,
and on the errors in the process being deterministic in nature [13].
Chromatography in continuous applications fulfils both these criteria, as columns are regenerated and equilibrated before each new
cycle, and the whole purpose of continuous operation is to ensure
consistent product quality, thus reducing random or unidentified
errors in each cycle.
To the authors’ knowledge, the current extent of research on
ILC for continuous chromatographic downstream processing of biopharmaceuticals does not go beyond SISO control. The SISO ILC
that has been applied to these processes used the retention time of
one compound as its set point. In a separation between a desired
product and an impurity (for example, a monomer antibody and
its aggregates), it would be useful to control the retention times of
both. Control of these two outputs could, in turn, be enabled by
allowing additional process parameters to be manipulated by the
controller.
The purpose of this study was to develop a control strategy

for a separation of two proteins in the IEX chromatography purification step of a continuous biopharmaceutical production platform. A model-based controller that allowed for tracking of multiple process output parameters, while also requiring minimal work
in model calibration, was developed. The suggested multiple-inputmultiple-output (MIMO) ILC strategy used a simple, linear model
that required 3 experiments to compute. The model itself mapped
the initial and final salt fractions of a linear gradient to the retention time of two compounds. Particularly, the algorithm suggested in this study combined ILC with a quadratic-criterion objective function that took both changes in the process inputs and
errors in the process outputs into account, allowing for robust control while only requiring the tuning of one single parameter. The
controller was also fitted with feed-forward control functionality,
the purpose of which was to allow preemptive control of changes
to the process set points. The resulting controller was then applied
and tested in three case studies: (i) control after a change in the

salt concentration of the elution buffer was applied; (ii) control of
a change in desired retention times; and (iii) control after a change
in pH of the elution buffer was applied. The controller was capable of restoring the retention times to their desired values within,
at most, 3 cycles of the changes being applied, proving its efficacy.
2. Theory
2.1. Formulating the model
Purification by ion exchange chromatography with linear salt
gradient elution can be performed as a five-phase process, illustrated in Fig. 1. In the first phase, the sample containing the product as well as impurities from the upstream process is loaded
onto the column. In a cation exchanger, any positively charged
molecules in the sample adsorb to the negatively charged ligands
on the column packing. In the following phase, called the wash
phase, any non-adsorbed substances are washed out of the column with an equilibration buffer, hereafter referred to as buffer A.
Buffer A has a low ionic strength to stabilize the molecules without
interfering with the adsorption, and commonly consists of buffering salts in low concentrations to counteract any changes in pH
that may occur in the process.
The wash phase is followed by the elution phase, in which
the salt concentration of the mobile phase is increased linearly
over time. This is achieved by mixing buffer A with an elution
buffer, buffer B, which has a high ionic strength and adsorbs more
strongly to the column than the molecules in the sample. This

causes the sample molecules bound to the column to be replaced
by the salt in buffer B, commonly NaCl, and elute out of the column to be measured by means of a UV detector. To achieve a linear
salt gradient, the proportion of buffer B to buffer A in the mixture
is increased linearly over time. Depending on the charge of the
molecules bound to the column, they will elute at different salt
concentrations which results in them being retained in the column
for different durations of time. The time each compound spends
inside the column, i.e., the retention time, is measured via UV absorption after the column outlet. If desired, the retention time can
be expressed in terms of retention volume using the unit column
volume, or CV, instead. The retention volume is independent of the
flowrate of the liquid and the dimensions of the column – as opposed to the retention time, which changes based on these factors
– and has benefits when scaling up a chromatography process.
After the elution phase, the regeneration phase is introduced.
During this phase, the proportion of buffer B to buffer A is increased to 100% to elute any remaining molecules not eluted during the elution phase. Finally, the regeneration phase is followed by
the equilibration phase, during which the column is washed with
100% buffer A to restore it to its initial conditions before the next
sample is loaded onto the column and the process can repeat.
The elution phase is crucial for the purification since the properties of the linear salt gradient determine the residence time of
the compounds in the column as well as the degree to which the
product is separated from the impurities. This is particularly significant in cases where the impurity is poorly resolved from the
product and there is a maximum impurity requirement, since the
amount of peak overlap will restrict the amount of product that is
possible to recover, i.e., the yield. In addition, the residence time
of the product in the column determines the time duration of the
process and thus its overall productivity [14]. This makes the gradient is a prime candidate for manipulation by a controller. By setting a fixed time duration of the elution phase, the slope and intercept of the linear gradient can be controlled by adjusting the
proportion of buffer B at the start (xB,i ) and at the end (xB, f ) of the
elution phase. In turn, the retention volumes of the product and
an impurity of interest can be easily detected at the outlet of the
2

D. Espinoza, N. Andersson and B. Nilsson

Journal of Chromatography A 1673 (2022) 463078

Fig. 1. A chromatogram illustrating the five-step chromatography process. If the time duration of the elution phase, during which the proteins are released from the column,
is set to a constant, the slope of the gradient can be manipulated by adjusting the fractions of buffer B at the beginning (xB,i ) and end (xB, f ) of the elution phase. The
retention volumes of the chromatography peaks, vret,1 and vret,2 , can be measured at the outlet of the column by means of a UV detector. Thus, it is possible to create a
controller with the control signals u = [u1 u2 ] = [xB,i xB, f ] to control the measurement signals y = [y1 y2 ] = [vret,1 vret,2 ].

column and thus serve as good candidates for measurement signals in a control setup. The controller inputs, u1 and u2 , can be
set to xB,i and xB, f , while the outputs, y1 and y2 , can be set to the
retention volumes, vret,1 and vret,2 , as shown in Fig. 1.
The process inputs and outputs can be expressed as the vectors u and y. Then, a map from the inputs to the outputs can be
expressed as a multivariate, non-linear, vector-valued function, F
(Eq. (1)).

y = F (u )

Given a desired point of operation yd and its corresponding set
of operating parameters ud , it is possible to approximate the Jacobian matrix by means of numeric finite-difference linear derivatives (Eq. (6)). This is done by adding a small perturbation ε to
each of u1 and u2 . The smaller the perturbation, the more accurate
the approximation becomes around the point of operation.
y1

Jest =

(1)

vret,1

vret,2

y=

y1
=
y2

u=

u1
xB,i
=
u2
xB, f

(2)

ud =

(3)

One expected property of Eq. (1) is that the retention volumes
are coupled, i.e., a change in only one of the elements of u will
result in a change in both retention volumes.

y2

(
(

)
)

(
(

)−y1 (ud )
)

u pert,1 −y1 (ud )

y1 u pert.2

u pert,1 −y2 (ud )

y2 u pert,2 −y2 (ud )

ε
ε

ε

(6)

ε

u1,d
u2,d

(7)

u pert,1 =

u1,d + ε
u2,d

(8)

u pert,2 =

u1,d
u2,d + ε

(9)

2.2. Estimating model parameters
This means that by running three experiments, one with the
nominal parameters ud and one for each set of perturbed parameters u pert,1 and u pert,2 , it is possible to obtain a model of the system around the nominal point. In essence, Jest is a linearized model
of F around the point (ud , yd ) and G = Jest can be substituted into
Eq. (4).

Given a set of retention volumes, yd , that are achieved by a set
of operating parameters, ud , F can be linearized around yd . The
result is a matrix G that transforms u into y around the point yd .

y = Gu

(4)

Assuming that F is approximately linear in a zone around yd ,
the matrix G can provide a relatively accurate prediction of y in
that zone given a new set of operating parameters u. With this
assumption in mind, the gradient of F describes y relatively well
around yd . The gradient of a multivariate, vector-valued function,
i.e., the Jacobian matrix, J, is defined according to Eq. (5).

J=

∂ F (u )
=
∂u

∂ y1
∂ u1
∂ y2
∂ u1

∂ y1
∂ u2
∂ y2
∂ u2

2.3. Iterative learning control algorithm
The iterative learning control algorithm used in this work was
proposed by Arimoto, et al. [15] and uses the control input signal
u as well as the control error e at batch k to compute the input
signal at batch k + 1. This is done by means of a learning filter,
K, which is a mapping of the control error to the input correction

(5)
3


D. Espinoza, N. Andersson and B. Nilsson

Journal of Chromatography A 1673 (2022) 463078

uk+1 [16].

uk+1 = Kek

(10)

uk+1 = uk+1 − uk

(11)

by the relative gain array (RGA) of G, which becomes the identity
matrix for a diagonal G [17]. If G is not diagonal, it can be made
diagonal by means of multiplication with a decoupling matrix, D.
[18]

T = GD =

ek = yd − yk

(12)

D11

D21

D12
T
= 11
D22
0

y = Gu = GDm = Tm

y = Gu

(13)

ek+1 2Q

+

uk+1 2R

uk+1 = Dmk+1

−1

GT Q

(16)

(17)

(18)

A common choice of D, known as simplified decoupling, is the
following. [18]

D=

1
21
− GG22

− GG12
11
1

(19)

Since this work regards control of the output of a cyclic process between cycles, the elements in G (and by extension, D) are
constants and thus this can be regarded as a form of steady-state
decoupling [17].

(14)

In Eq. (14), Q and R are positive-definite matrices. Larger values
in Q result in a larger penalty on the process error and more aggressive control action, whereas larger values in R result in a larger
penalty on the process input changes and thus dampen them. In
other words, Q and R can be regarded as weighting matrices on
the process error and the process input change, respectively. The
fact that the process input change uk+1 = uk+1 − uk is penalized
means that the algorithm obtains integral action with regards to

the batch number k. Taking the partial derivative of Eq. (14) with
regards to the input u results in the following analytical expression
for the learning filter. [16]

K = GT QG + R

0
T22

The learning filter K described in Eq. (15) is then calculated using T instead of G. The resulting controller described in
Eq. (10) then returns mk+1 which can be converted back into the
real control variables u as follows.

Given a perfect process model and zero noise and disturbances
in the measurement signals, this inverse-model approach would
eliminate the error at batch k completely in batch k + 1. However,
noise and disturbances are to be expected and thus an inversemodel learning filter may be overly sensitive to small errors if applied to a real system, leading to overcorrection by means of a disproportionately large control action. This means that a method to
reduce the controller’s sensitivity to noise is required. One such
method is the use of a quadratic-criterion objective function that
penalizes changes in process input on top of the process error, also
known as Q-ILC, as described by Eq. (14) [16].
uk+1

G12
G22

This operation essentially leads to a change from control of the
original process variables u to control of a set of decoupled process
variables, m. The controller manipulates the decoupled variables
and can thus be designed to fit the decoupled, diagonal system.

Eq. (13) can be rearranged into the following.

Here, yd and yk represent the desired and the actual process
output at batch k, respectively. While there are multiple ways to
design the learning filter, model-based approaches historically tend
to rely on an inverse-model learning filter K = G−1 , where G denotes a model that translates the process input to its output [16].

min Jk+1 =

G11
G21

2.5. Feed-forward of set point changes
For a process to be able to correct for changes in its desired set
points preemptively, some form of feed-forward of the set point
change is necessary. This can be achieved by using direct inversion
of the decoupled process model T, the decoupling matrix D, the
decoupled set of control variables mk , as well as the difference in
process set point yd , according to Eq. (20).

uk = D T−1 yd + mk

(15)

yd = yd,k − yd,k−1

Given a process input-output model G as well as the weighting matrices Q and R, the controller learning filter can be computed using Eq. (15). The choice of Q can be done by letting Q1/2
be scaled to the process outputs, whereas R can be chosen as an
identity matrix multiplied by a scalar value that in turn can be adjusted to the fit the process [11]. Alternatively, the process outputs
can be scaled to lie in a range 0 < y < 1 and Q can be chosen to

be an identity matrix, resulting in a similar effect. In this case, R
can be chosen as rI, where r is a scalar value. Worth noting is that
choosing r = 0 causes Eq. (15) to collapse into K = G−1 , i.e., a direct
inversion controller.

(20)
(21)

One weakness of direct-inversion feed-forward control is that it
relies on the model, T, being stable, as well as that all disturbances
are known, which is an unrealistic expectation [19]. However, any
over- or under-compensations by the feed-forward controller can
be corrected by the ILC.
3. Materials and methods
3.1. Experimental setup
A chromatographic separation process was set up on an ÄKTATM
Pure chromatography system from Cytiva (Uppsala, Sweden). A
1 ml HiTrapTM Capto SP ImpRes ion exchange column from Cytiva
was used for the separation. Four buffers were needed for the experiments: an equilibration buffer, an elution buffer, and two disturbance buffers. A sodium phosphate buffer system was used to
allow for a pH of 6.8 in the equilibration and elution buffers, as
well as in the first disturbance buffer. All buffers had a total phosphate concentration of 20 mM. The equilibration buffer was a solution of only phosphate buffer at 20 mM and pH 6.8. The elution buffer had a NaCl concentration of 500 mM in addition to the
phosphate buffer. The first disturbance buffer had a concentration
of NaCl of 750 mM. The second disturbance buffer had a concentration of NaCl of 500 mM and a total phosphate concentration of

2.4. Decoupling
When designing a multivariable controller, it is important to
take cross-coupling between input and output signals into account.
As mentioned in Section 2.1, linear gradient elution with initial and
final elution buffer proportions as control signals results in coupling between the retention volumes, i.e., the measurement signals. It is easier to control a multivariable process when its system
matrix G is triangular or diagonal, as this makes it possible to design the controller using a similar approach to what one would

use for a single-input, single-output controller for each individual
row in G. The degree to which G is cross-coupled can be quantified
4


D. Espinoza, N. Andersson and B. Nilsson

Journal of Chromatography A 1673 (2022) 463078

The chromatography process consisted of five phases: a loading phase of 1 CV during which the protein sample was loaded
onto the column; a washing phase lasting 5 CV during which the
system was flushed with equilibration buffer to wash out any nonadsorbing substances; an elution phase of 40 CV where the proteins bound to the column were eluted with a linear gradient
consisting of both equilibration buffer and elution buffer; a regeneration phase of 10 CV where the system was flushed with pure
elution buffer to elute any adsorbed substances that did not elute
during the elution phase; and finally, an equilibration phase during
which the system was restored to its initial conditions by flushing it with equilibration buffer for 10 CV. All phases were run at a
flowrate of 1 ml/min.
3.2. Process and controller implementation
Control of the chromatography process was implemented using
the Orbit software developed at the department of Chemical Engineering of Lund University [20]. This software connects to the
UNICORNTM software used to control the ÄKTATM system and allows for pre-scripting and implementation of advanced control via
Python programming [21]. A Python function that executed sequential control of the chromatography phases was written, and
then called upon several times in succession, simulating the cyclic
nature of a process step in a continuous downstream process. The
absorbance was measured at the column outlet at a wavelength of
280 nm, and the resulting absorbance data was acquired from the
Orbit software and analyzed for peaks automatically. This yielded
the retention volumes of each component, which were then passed
to the control algorithm for computation of the gradient inputs for
the following cycle. The disturbances were applied to the sequence

between cycles by either switching from the elution buffers to one
of the disturbance buffers, or by changing the process set points.
Three case studies were performed, where one type of disturbance was applied to each. In case 1, a disturbance to the process
input was applied by switching the elution buffer for the disturbance buffer with a higher salt concentration between cycles in the
sequence. The ILC was then allowed to compensate for the disturbance. Two versions of this case were performed: one with direct
inversion control, and one using the quadratic-criterion objective
function. A value of the diagonal elements of the process input
change penalty matrix, R, was obtained from the second version,
with the desired property of removing oscillations in the measurement signals while also achieving fast control action. This value, r,
was used in the subsequent case studies.
Case 2 involved control of a change in the process set points,
i.e., the desired values of the measurement signals, between cycles in the sequence. First, the desired set point of one peak was
changed, and after a few cycles the same was done for the other
peak. The feed-forward controller was allowed to preemptively adjust the control signals to compensate for the set point change, and
the ILC compensated for any errors in the feed-forward control action on the following cycles.
Finally, case 3 was a study of the controller’s ability to compensate for changes in pH. The disturbance buffer with a higher pH
was applied between cycles, and the corresponding action taken
by the ILC was studied.

Fig. 2. Diagram of the chromatography process, set up on an ÄKTATM Pure system. The two pumps, A and B, were used to drive the equilibration and elution
buffers, respectively. The protein sample (red) was loaded automatically via a super
loop, which was followed by the ion exchange column (IEX) and a train of detectors
(UV, conductivity and pH) before being collected in the waste. The loop and column
valves both allowed for bypass of the super loop and column.

20 mM, but a heightened pH of 7.5. The protein sample consisted
of 1 g/l of cytochrome C from equine heart, and 1 g/l of lysozyme
from chicken egg, dissolved in the elution buffer (20 mM phosphate buffer, pH 6.8), both acquired from Sigma-Aldrich (St. Louis,
MO, USA).
The ÄKTATM Pure system was set up with two pumps, pump A

and pump B, each with its own inlet valve. Pump A was used for
the equilibration buffer A, and pump B was used for the elution
buffer B as well as for the disturbance buffers. The protein sample
was kept in a super loop connected to a loop valve for automatic
loading onto the column, which was connected to a column valve.
Both the loop and column valves allowed for a bypass of the super
loop and column. Following the column valve was a set of detectors: UV, conductivity, and pH detectors, in that order. After the
detectors, the flow path led to a waste collection. A full diagram of
the process is presented in Fig. 2.

3.3. Peak detection
For the purposes of this study, the retention volume of a compound was defined as the number of CVs at which the compound
peak reached its maximum absorbance value at the column outlet,
measured from the beginning of a process cycle. Automatic detection of peaks between cycles was implemented by analyzing the
first and second order derivatives of the UV data received from the
5


D. Espinoza, N. Andersson and B. Nilsson

Journal of Chromatography A 1673 (2022) 463078

Fig. 3. The control configuration used in all experiments. At cycle k, the proportions of elution buffer, or the inputs uk , are sent to the chromatography process, here
denoted as G, and results in the retention volumes of the two peaks, the outputs yk . The process error ek is calculated as the difference between the process set point,
yd,k and yk , and the input for the following cycle, uk+1 , is computed using the iterative learning controller, K. The cycle number is updated, and the process repeats. The
feed-forward control of set point changes, FF, works by updating the current cycle’s inputs, uk , using the difference between the set points of the current and previous
cycles, yd = yd,k − yd,k−1 .

detectors. The numeric first order derivative was computed as the
discrete difference of the UV values divided by the discrete difference of the time values, converted to CVs, while the second order derivative was computed by dividing the discrete difference of

the first order derivative by the discrete difference of the CV values. A minimum UV level was defined, identifying the required absorbance value for a UV reading to be considered part of a peak.
This level was set to 5 mAU. The criteria for a reading to be considered a peak were as follows: (i) the second order derivative of the
absorbance was lesser than 0; (ii) the UV reading was greater than
the minimum peak UV level; (iii) the first order derivative of the
reading was equal to or lesser than 0; (iv) the first order derivative
of the previous reading was greater than 0. The reading was considered a peak if, and only if, all of the above criteria were met, in
which case the corresponding CV value was recorded as the retention volume of the peak.
In order to identify which of the detected peaks were the peaks
of interest, the area of the peak was calculated by integrating the
UV between the start and the end times of the peaks. The peak
areas were then sorted in order of descending peak area, and
the two largest peaks were identified as the cytochrome C and
lysozyme peaks due to their high concentration in the sample. The
start of a peak was defined in two ways, depending on if the peaks
overlapped or not. To identify a peak starting with no peak overlap, the first time to the left of the identified peak retention time
at which the absorbance reading exceeded the minimum UV level
was used. The same condition was used to detect the end of a peak
where no overlap took place.
For a peak that overlapped with another on its left, the time
to the left of the identified peak maximum, at which the following criteria were satisfied, was used: (i) the second order derivative was greater than 0; (ii) the first order derivative was equal to
or greater than 0; (iii) the first order derivative of the reading to
its right was greater than 0. For detecting the end of a peak with
overlap to its right, the same conditions (i) and (ii) were applied,
with a change to (iii) the first order derivative of the reading to its
left was less than 0.

control of changes in set point. Three types of disturbances were
identified throughout the experiments: disturbances to the control
signals, changes in the process dynamics, and disturbances to the
measurement signals, symbolized by du , dG and dy , respectively.

The disturbances to the control signals, du , were adjusted for by
the ILC algorithm and encompass changes to the elution buffer,
such as changing salt concentration or pH. These were tested in
case 1 and case 3, respectively. Disturbances to the process dynamics, dG , result from ambient conditions such as temperature,
which can affect the equilibria in the column, as well as long term
changes to the column such as degradation of its binding capacity. The ILC was able to compensate for the changes in dynamics
that were seen in this study, as they were consistent and slow acting over the course of the experiments. However, the ILC could be
even further improved by updating the process model, G, either
between each cycle or before each controlled sequence, as will be
discussed in Section 4.6. Finally, disturbances to the measurement
signal, dy , stem from inaccuracies in the peak detection due to irregularities in the UV measurements, such as noise. It was primarily in correcting these disturbances that the damping introduced
by the quadratic-criterion objective function proved most useful,
since these disturbances were stochastic in nature and could thus
not be captured by the process model.
The control configuration was programmed in such a way that
it could be switched from quadratic-criterion optimal ILC to direct
inversion control by changing the value of r to 0, allowing both to
be studied and compared.

4.2. Estimating the process model parameters
The model matrix G was estimated using a finite-difference
linear Jacobian around the point ub = [ 20 40 ]T . This combination of control signals yielded the retention volumes yd =
[ 32.6 39.9 ]T CV, which in turn were set to the process set
points. The Jacobian matrix was estimated with a perturbation of
ε = 3 (Eq. (6)). The input and output signals were scaled to ensure that the values of the signals fed to the controller always
fell between 0 and 1. The input signals were scaled by a factor
1
100 as they could range from 0 to 100, while the output signals
1
were scaled by a factor 50

as 50 was the number of CV from the
start of a cycle to the end of its elution phase, the frame within
which the peaks were expected to elute. The control signal values u = [ 20 40 ]T were used for cycle 1 in every controlled
sequence for all three cases.

4. Results and discussion
4.1. Control configuration
The final control system configuration, illustrated in Fig. 3, included two types of control: ILC of deviations in the measurement
signals yk from the set points yd,k at cycle k, and feed-forward
6


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Journal of Chromatography A 1673 (2022) 463078

Fig. 4. Chromatograms from the model parameter estimation experiments. The nominal case was run first, followed by a run with perturbed xB,i and, finally, a run with
perturbed xB, f . The resulting effects on the retention volumes of both peaks is apparent in how they shift. This indicates that the process outputs are coupled, meaning that
a change in one of the process inputs results in a significant change in both process outputs.

The three experiments for process model parameter estimation
resulted in the chromatograms presented in Fig. 4.
The resulting estimated model matrix, G, exhibited the coupling
that was suspected during model formulation, as seen in Fig. 4,
where a perturbation in one of the inputs shifts the retention volumes of both peaks. The suspicion was further confirmed by computing a relative gain array based on G, a measure of the degree
of coupling between the different control signals in the process. To
remedy this, simplified decoupling was applied to G and the decoupled process model, T, was computed. A comparison between
the original and decoupled process model matrices is shown in 22.

G=

−0.022
−0.021

−0.010
−9.2 · 10−3
, T=
−0.017
−5.2 · 10−19

0
−7.4 · 10−3

onward, the retention volumes never settled on the set point and
instead oscillated around it. Corresponding effects can be seen in
the control signals, where particularly the oscillations on cycle 4
and onward can be seen in the oscillations of xB, f . That the controller drifted from cycle 1 to cycle 2 despite no applied disturbance implies that the conversion from a process error to its corresponding control action is exaggerated when r = 0 and informs
the implementation of some damping in upcoming applications,
as do the oscillations of the retention volumes after cycle 3. It is
highly likely that stochastic errors in the peak detection contribute
to this behavior. For example, the data available for estimation of
the derivatives in the peak detection is discrete and limited to the
sampling frequency of the equipment, which means that the distance between samples becomes the highest possible precision in
peak detection. Thus, small deviations from the expected retention
volume can be expected, and the direct inversion controller overcompensates for these small deviations. This can be remedied by
damping, results of which are presented in Fig. 6.
The results of the Q-ILC damping method displayed smoother
control action than the direct inversion method: a smaller change
in control signals was made in response to the disturbance. With a
value of r = 0.02 the controller approached the set points with first

an undershoot on cycle 4 and an overshoot on cycle 5, settling on
the set point on cycle 6 and maintaining the set point values stably
on the remaining cycles. The oscillating behavior potentially caused
by stochastic disturbances was eliminated, with consequently less
aggressive control action when correcting for the disturbance of
cycle 3. This illustrates the compromise needed when designing
the controller: how much control action speed can be sacrificed
in exchange for a less sensitive controller. Increasing r would reduce the overshoot on cycle 5, but also increase the undershoot on
cycle 4, making the controller slower. The choice of r depends on
the desired behavior, whether it is preferred to undershoot more
or if it is acceptable to have some degree of overshoot before settling on the set points. It is unlikely that a disturbance of the size

(22)

The off-diagonal elements of T are equal to or very close to
zero, making it approximately diagonal and thus decoupled and
suitable for controller design. This new process model matrix was
used in all subsequent controller tests.
4.3. Case 1 – salt disturbance
The results from the direct inversion sequence are visualized in
Fig. 5. Chromatograms of cycles 2, 3 and 4 highlight the effects
of the disturbance buffer and the resulting controller action, seen
in the smaller retention volumes of cycle 3 and the reduced control signals on cycle 4, which resulted in almost restored retention volumes. The corresponding effect can be seen in the measurement signals, where both retention volumes drop drastically
on cycle 3 as a result of the disturbance buffer. The oscillations
of the measurement signals are also clearly seen. First, on cycle 2,
the measurement signals drifted slightly over the set point, indicating that the controller had already compensated for something
despite no disturbance having been applied. Second, after the controller had compensated for the disturbance buffer on cycles 4 and
7

D. Espinoza, N. Andersson and B. Nilsson

Journal of Chromatography A 1673 (2022) 463078

Fig. 5. Direct inversion control results. (A) Chromatograms from cycles before, during and after the implementation of the disturbance buffer. Cycle 2 (dashed-dotted) was
followed by cycle 3 (dashed), which had much shorter retention volumes as a consequence of the higher salt concentration in the disturbance buffer. On cycle 3 (solid),
the controller had compensated for the difference in retention volumes by reducing both control signals (gray) significantly. Of note is that second peak of cycle 4 overshot
the mark slightly, landing on a retention volume over 40 CV. (B) The measurement signals from the sequence. The retention volumes were on the set point on cycle 1, but
deviated slightly on cycle 2 despite the lack of a disturbance. On cycle 3, the effects of the disturbance buffer were clearly seen, as were the effects of the controller on
cycle 4, including the overshoot seen in the chromatogram. From cycle 4 and onward, the retention volumes were close to the set point, but never really settled, instead
oscillating around it. (C) The control signals from the sequence. Mirroring the measurement signals, the controller compensated for deviations from the process set point no
matter how small they were, resulting in the drifting from the set point seen on cycle 2. The controller compensation for the disturbance buffer were clearly seen on cycle
4 as a decrease in both control signals, and the measurement signals’ oscillations around the set point from cycle 4 and onwards were reflected in the oscillations in xB, f . Of
particular interest is that no corresponding oscillations in xB,i were discernable.

applied in case 1 would appear in a production setting. Instead, it
is the smaller, stochastic disturbances, or small deviations in salt
concentration when a buffer is exchanged, that would be of interest for control of a continuous downstream process. Thus, it would
be more beneficial to have a slightly more conservative controller
in these cases, such as a dampened Q-ILC.

The feed-forward controller was based on direct model inversion which, as demonstrated in case 1, leads to very aggressive and
sensitive control. However, the “error” in the feed-forward controller is the change in set point, i.e., not a measured value but
a value provided by the user. Thus, stochasticity in the measurement becomes a non-issue. Instead, the coupling behavior along
with possible changes to the column characteristics that invalidate
the model estimation G become the main sources of error in the
control action. This is discussed further in Section 4.6.

4.4. Case 2 – set point change
Feed-forward control of set point changes, the results of which

are displayed in Fig. 7, showed an effective preemptive correction
of the retention volume of the peak. The control action based on
the first set point change resulted in a less steep gradient, since
xB,i increased and xB, f decreased. The higher initial salt concentration worked to accelerate the elution of the first peak, while
the decreased gradient slope delayed the elution of both peaks.
Fig. 7 makes it apparent that some coupling interactions remained
despite the decoupling: when the set point of the first peak
was adjusted for on cycle 6, the second peak’s retention volume
changed as well, deviating from the set point and requiring correction in the following cycle. Interestingly, the effect was much
smaller in the retention volume of the first peak on cycle 10, where
the controller adjusted for the set point change in the second peak.
The difference in magnitude between these two undesired changes
in retention volume further indicates remaining coupling behavior.

4.5. Case 3 – pH disturbance
Fig. 8 showcases the effects that a change in pH from 6.8 to
7.5 had on the process, and the controller’s corresponding action.
Since the net charge of a protein is affected by the pH of its surrounding solution [22], it was expected that the retention volume
would also change, and thus that it would be possible to obtain
the desired retention volume again by adjusting the salt gradient. However, the degree to which the retention volumes change
is dependent on the properties of each individual protein. It is
visible from cycle 3 that the change in retention volumes of either protein was different for the same change in pH, indicating
that the charge of the proteins and, consequently, their binding to
the column were different for the same change in pH. This means
that, at different values of pH, the proteins can be expected to
8


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Journal of Chromatography A 1673 (2022) 463078

Fig. 6. Dampened control results (r = 0.02). (A) Chromatograms from cycles before, during and after the disturbance buffer was applied. The retention volumes changed
drastically from cycle 2 (dotted) to cycle 3 (dashed-dotted) after the application of the disturbance buffer. They then undershot the mark slightly on cycle 4 (dashed) as a
consequence of the damping and overshot the mark on cycle 5 (solid). (B) The measurement signals from the sequence. Following the effect of the disturbance on cycle 3,
the controller undershot both set points on cycle 4 and overshot them on cycle 5, landing on them on cycle 6 and maintaining them on the consequent cycles. Of particular
note is the deviation from the set points on cycle 1 compared to the direct inversion control in Fig. 5, which was corrected for in cycle 2. (C) The control signals from the
sequence. The adjustment from cycle 1 to cycle 2 is clearly visible, as is the compensation for the disturbance buffer.

dissociate from the column at different salt concentrations and
thus the model of retention volume as a function of gradient inputs, G, could change properties as well. However, as seen in Fig. 8,
the controller managed to restore the process to its set points with
the same G by manipulating the salt gradient, even with the elution buffer at a different pH, and maintained the set points in a
stable manner from cycle 4 and onwards.
It is noteworthy that in a production setting, the pH of the
product may be a critical quality parameter and thus a disturbance
to the pH may lead to product loss, despite the controller keeping the retention volumes constant. Set point control of the buffer
pH between gradient chromatography cycles may be possible, but
it may be more useful to adjust the pH of the pooled product in a
different process step.

tion volumes to their set points. This is indicative of a systematic change in process dynamics, possibly caused by degradation
of the column packing, and can result in less robust control as
the column’s physical properties increasingly deviate from the initial estimation of the process model G. The feed-forward control
is also affected by this, as it is based on direct inversion of the
process model: the deviations from the set point seen in Fig. 7, cycles 6 and 10 can be expected to become even greater as the process dynamics change further. To account for this, the controller
can be adapted to continuously update the model G during process runs and using the newest G when determining the control
action, as in the linear time-varying model estimation employed
by Xiong and Zhang [23]. Alternatively, a new linear model estimation using the proposed three-experiment calibration can be
scheduled to be performed with regular intervals during a process

run.
The volume of protein loaded in this study, 1 g/l of each protein, is relatively small compared to the binding capacity of the
packing material reported by the manufacturer, which is 70 g/l for
lysozyme, for example. In a production setting, maximum utilization of the column packing material is desired and thus the protein load volume is set as close to overloading as possible. Consequently, the non-linear adsorption dynamics at high protein concentrations become an issue, as the retention times’ dependence
on the mobile phase composition change from the low-load case
to the overloaded case [22]. This can potentially become an issue
for the ILC if the model G was computed for a very low protein
load while the process is run at much higher loads. However, since
a hypothetical integrated and continuous process with ILC would

4.6. Additional observations
Despite that the same combination of input signals, u =
[ 20 40 ]T , was used in all sequences, it was clear that the
resulting retention volumes were quite varied on cycle 1 of each
controlled sequence. For example, the direct inversion sequence,
shown in Fig. 5, had retention volumes exactly on the set points
on cycle 1. As the subsequent experiments were performed, both
of the retention volumes on cycle 1 drifted downwards, meaning that the proteins released from the column at incrementally
lower salt concentrations as time passed. This is most visible when
comparing cycle 1 in Fig. 5, the very first experiment performed,
with that of Fig. 7, the last. In the latter case, it took 2 cycles
after cycle 1 for the quadratic-criterion ILC to return the reten9


D. Espinoza, N. Andersson and B. Nilsson

Journal of Chromatography A 1673 (2022) 463078

Fig. 7. Control of set point changes (r = 0.02). (A) Chromatograms from cycle 5 (dotted), before the set point change of the first peak; cycle 6 (dashed-dotted), where the
set point change and the feed-forward control action took place; cycle 9 (dashed), before the set point change of the second peak; and cycle 10 (solid), where the set point

change was adjusted for. (B) The measurement signals from the sequence. The feed-forward controller managed to correct for both set point changes on cycles 6 and 10.
However, the correction led to a drift in the retention volume of the second peak on cycle 6. The correction on cycle 10, on the other hand, showed a much smaller drift of
the retention volume of the first peak. (C) The control signals from the sequence. The controller correction took place on the same cycle as the set point change due to the
feed-forward control.

be designed with this loading capacity in mind, this issue is solved
by simply estimating G at the intended load.
However, one issue that may arise from varying concentrations
is that of automatic peak detection. The peak detection method
applied in this work relies on the peaks in the chromatogram being well-resolved enough to allow for discernible differences in the
first and second order derivatives to be detectable. If a disturbance
causes the peaks to become so poorly resolved that no such differences in derivatives can be detected between them, the peak detection method would result in a single peak detected. Such disturbances would have a greater effect if the ratio of concentration between the product and impurity is large, in which case the
larger peak would cause the smaller to appear as a tail or front.
An example of this can be seen in the pooling results reported by
Gomis-Fons, et al. [8], in which purification of a monoclonal antibody from its aggregates is performed in an ion exchange step. The
aggregate is present in such small quantities that it shows up as a
small tail in the product peak in the chromatogram, making it undetectable by the used peak detection algorithm. To address this,
a more advanced automatic peak detection algorithm is needed.
In this study, both proteins used were present at equal concentrations and absorb the specified UV wavelength to such an extent
that their respective peaks were clearly distinguishable, bypassing
this issue.
The proposed control setup made use of the proportion of
buffer A to buffer B as its manipulated variables, since these resulted in straightforward control of the individual retention volumes after decoupling. However, one could easily imagine other
combinations of control signals to control the retention times.

One possible addition to or substitution for the current control
signals is the liquid flowrate during the elution phase, as it affects the resolution of product and impurity. If a method to estimate the resolution robustly and automatically is available, resolution control by means of gradient and flowrate manipulation
could potentially be used to obtained. Flowrate control could be
easily implemented in combination with retention volume control of one or both peaks, due to the controller being expressed
in volume instead of time. As long as the desired combination of input and output signals results in a linearizable process

model, the three-experiment model calibration described in this
work can be applied. As for very non-linear processes, a different
model calibration method may need to be applied, e.g., continuously updating process models as described above, or the application of different process models for different areas of the control
space.
Mechanistic models for the prediction of the retention volumes
as functions of the linear gradient in ion exchange chromatography
are available, in which a number of parameters pertaining to the
column and the sample compounds are required [24]. It is possible
to formulate model-based ILC using these models, in which case
the experiments for Jacobian matrix estimation can be replaced by
experiments for estimation of mechanistic model parameters. The
resulting controller may have an even more precise prediction of
the retention volumes and may even be used for estimation of the
resolution, allowing for more advance measurement signals. However, for the control of only the retention volumes, it is expected
that the control action would not differ significantly from that of
the proposed controller.
10


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Journal of Chromatography A 1673 (2022) 463078

Fig. 8. Control of a pH disturbance (r = 0.02). (A) Chromatograms from cycles before, during and after the disturbance buffer was applied. The retention volume dropped
from cycle 2 (dashed-dotted) to cycle 3 (dashed) as a consequence of the higher pH in the elution buffer and was restored to the set point values in cycle 4 (solid). A very
small change in the gradient (gray) was required to restore the process to its set points. (B) The measurement signals from the sequence. Noteworthy is that the process
maintained the set point values in a very stable manner after the correction of the disturbance on cycle 4. The effect of the pH disturbance on the retention volume of the
first peak was smaller than that of the second peak. (C) The control signals from the sequence. The minor changes in control signal required to correct for the disturbance,
as was seen in the chromatograms, is reflected here.

5. Concluding remarks

et al. [8]. In summary, the proposed control approach shows potential in improving consistency in product quality and aligns with
the goals of continuous biopharmaceutical production.

In this study, a control strategy for the retention volumes of two
substances in an ion exchange chromatography process was developed. The controller was an iterative learning controller based on
a linearized, multivariate model of the retention volumes of two
proteins as functions of the beginning and ending elution buffer
proportions of a linear salt gradient. It was able to compensate for
errors to the process inputs, outputs, and to changes in the process
dynamics. A model-based feed-forward control strategy was also
successfully implemented to allow for control of set point changes.
The linear model was computed using finite-difference derivatives
and required a total of 3 experiments to compute. The model can
be improved to account for systematic changes in process dynamics by self-updating during process runs or by scheduled recalibration at regular intervals.
The choice of control signals is in line with the idea of a layered, plant-wide control system in the sense that they are specific to the ion exchange step and thus do not change the behavior
of other process units. The controller is thus locally acting, which
makes it flexible and capable of being used in combination with
other control systems. For example, it is compatible with the regulatory control layer described by Feidl, et al. [9]. The feed-forward
control of set point changes becomes a particular advantage here,
as changes to the process set points dictated by a supervisory control layer can be managed while minimizing process errors. Another potential application is product yield control in chromatographic polishing of mAbs, especially in combination with the purity control by means of adaptive pooling explored by Gomis-Fons,

Declaration of Competing Interest
The authors declare that no commercial or financial conflict of
interest exists with regards to this work.
CRediT authorship contribution statement
Daniel Espinoza: Conceptualization, Methodology, Validation,
Investigation, Writing – original draft, Writing – review & editing, Visualization. Niklas Andersson: Software, Writing – review &
editing, Supervision. Bernt Nilsson: Conceptualization, Resources,

Writing – review & editing, Supervision, Project administration,
Funding acquisition.
Acknowledgments
The authors acknowledge that this research is part of the AutoPilot project, which is funded by the Swedish Agency of Innovation, VINNOVA (Grant No.: 2019-05314).
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