Binary separation control in preparative gradient chromatography using iterative learning control

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.

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Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/chroma

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

Puriﬁcationofbiopharmaceuticalshasshiftedtowardcontinuousandintegratedprocesses,inturn bring-ingalonganeedformonitoringandcontroltomaintainadesiredseparationbetweenthetarget pharma-ceuticalandanyimpuritiesitmaycarry.Inthisstudy,acycle-to-cyclecontroloftheretentionvolumesof twocompoundsinachromatographic,ionexchangepuriﬁcationstepwasdeveloped,allowingtheprocess

tomaintainthedesiredretentionvolumesintheseparation.Thecontrollermadeuseofamodel-based, multivariateiterativelearningcontrol(ILC)algorithmthatusedaquadratic-criterionobjectivefunction foroptimalsetpointcontrol,alongwithfeed-forwardcontrolbasedondirectmodelinversionfor pre-emptivecontrol ofset pointchanges Themodelwas calibratedusing3experiments,allowingforfast setup.Thecontrollerwastestedbyintroducingthreedifferentdisturbancestoasequenceofotherwise identicalionexchangeseparationprocesses:achangeinthe saltconcentrationoftheelutionbuffer,a changeinset point,andachangeinthepH oftheelution buffer.Itwas capableofcorrectingforall disturbanceswithinatmost3cycles,provingitsefficacy.ThesuccessfulapplicationofILCforseparation controlinbiopharmaceuticalpurificationpavesthewayforthedevelopmentoffurtherILC-basedcontrol strategieswithinthefield,aswellascombinationwithothercontrolstrategies

1 Introduction

In the ﬁeld of biopharmaceutical production, there has been a

paradigm shift from batch production towards integrated and con-

tinuous production processes This shift has been primarily moti-

vated 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 ca-

pable 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 au-

tomatic control based on measurements taken online during a

continuous process operation reduces the need for human inter-

vention 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 biopharmaceuti-

cal production consist of several different process operations, from

reactors and membranes to chromatographic separation steps, and

∗ Corresponding author

E-mail address: bernt.nilsson@chemeng.lth.se (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 limi- tation 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 exam- ples 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

https://doi.org/10.1016/j.chroma.2022.463078

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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 sim-

ilar 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, Löf-

gren, 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 ap-

proach 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 con-

trol of a batch reactor and achieving promising results Further-

more, Holmqvist and Sellberg [12] employed an online, single-

input-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 gradi-

ent 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 crite-

ria, 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 bio-

pharmaceuticals 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 pu-

riﬁcation step of a continuous biopharmaceutical production plat-

form A model-based controller that allowed for tracking of multi-

ple process output parameters, while also requiring minimal work

in model calibration, was developed The suggested multiple-input-

multiple-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 re-

tention time of two compounds Particularly, the algorithm sug-

gested in this study combined ILC with a quadratic-criterion ob-

jective function that took both changes in the process inputs and

errors in the process outputs into account, allowing for robust con-

trol 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 capa- ble of restoring the retention times to their desired values within,

at most, 3 cycles of the changes being applied, proving its eﬃcacy

2 Theory

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 buffer- ing 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 ab- sorption 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 op- posed 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 sig- nificant 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 in- tercept of the linear gradient can be controlled by adjusting the proportion of buffer B at the start ( x B,i) and at the end ( x B , 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

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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 ( x B,i ) and end ( x B, f ) of the elution phase The retention volumes of the chromatography peaks, v ret ,1 and v ret ,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 = [ u 1 u 2 ] = [ x B,i x B, f ] to control the measurement signals y = [ y 1 y 2 ] = [ v ret ,1 v ret ,2 ]

column and thus serve as good candidates for measurement sig-

nals in a control setup The controller inputs, u1 and u2, can be

set to x B ,iand x B , f, while the outputs, y1and y2, can be set to the

retention volumes, v ret ,1 and v ret ,2, as shown in Fig.1

The process inputs and outputs can be expressed as the vec-

tors 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=

y1

y2

=

vret,1

vret ,2

(2)

u=

u1

u2

=

x B,i

x B, f

(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

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

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

∂ y1

∂ u2

∂ y2

∂ u1

∂ y2

∂ u2

(5)

Given a desired point of operation yd and its corresponding set

of operating parameters ud, it is possible to approximate the Ja- cobian 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

Jest=

y

1(upert,1)−y1(ud ) ε

y1(upert.2 )−y1(ud ) ε

y2(upert,1)−y2(ud )

ε y2(upert,2)−y2(ud )

ε

(6)

ud=

u1,d

u2,d

(7)

upert ,1=

u1,d+ε

u2,d

(8)

upert,2=

u1,d

u2,d+ε

(9)

This means that by running three experiments, one with the nominal parameters udand one for each set of perturbed parameters upert ,1 and upert ,2, it is possible to obtain a model of the system around the nominal point In essence, Jestis a linearized model

of F around the point (ud ,yd) and G=Jest can be substituted into

Eq.(4)

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

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uk+1[16]

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 de-

notes a model that translates the process input to its output [16]

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 inverse-

model learning ﬁlter may be overly sensitive to small errors if ap-

plied to a real system, leading to overcorrection by means of a dis-

proportionately 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]

min

u k+1

J k+1=

ek+12

Q+ uk+12

R

(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 ag-

gressive 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− ukis 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=

GTQG+R −1

Given a process input-output model G as well as the weight-

ing matrices Q and R, the controller learning ﬁlter can be com-

puted 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 ad-

justed 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 = 0 causes Eq.(15)to collapse into K=G−1, i.e., a direct

inversion controller .

When designing a multivariable controller, it is important to

take cross-coupling between input and output signals into account

As mentioned in Section2.1, linear gradient elution with initial and

ﬁnal elution buffer proportions as control signals results in cou-

pling between the retention volumes, i.e., the measurement sig-

nals It is easier to control a multivariable process when its system

matrix G is triangular or diagonal, as this makes it possible to de-

sign 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

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=

G11 G12

G21 G22

D11 D12

D21 D22

=

T11 0

0 T22

(16)

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

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

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

D=

1 −G12

G11

−G21

G22 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]

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−1yd+mk

(20)

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

A chromatographic separation process was set up on an ÄKTA TM Pure chromatography system from Cytiva (Uppsala, Sweden) A

1 ml HiTrap TM 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

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Fig 2 Diagram of the chromatography process, set up on an ÄKTA TM Pure sys-

tem 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 phos-

phate buffer, pH 6.8), both acquired from Sigma-Aldrich (St Louis,

MO, USA)

The ÄKTA TM 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 detec-

tors: 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

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 non- adsorbing 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 flush- ing it with equilibration buffer for 10 CV All phases were run at a flowrate of 1 ml/min

Control of the chromatography process was implemented using the Orbit software developed at the department of Chemical En- gineering of Lund University [20] This software connects to the UNICORN TM software used to control the ÄKTA TM system and al- lows for pre-scripting and implementation of advanced control via Python programming [21] A Python function that executed se- quential 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

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

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Fig. 3 The control conﬁguration used in all experiments At cycle k , the proportions of elution buffer, or the inputs u k , are sent to the chromatography process, here denoted as G , and results in the retention volumes of the two peaks, the outputs y k The process error e k is calculated as the difference between the process set point,

yd,k and y k , and the input for the following cycle, u k+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, u k , using the difference between the set points of the current and previous cycles, yd = y d,k − y d,k−1

detectors The numeric ﬁrst order derivative was computed as the

discrete difference of the UV values divided by the discrete differ-

ence of the time values, converted to CVs, while the second or-

der derivative was computed by dividing the discrete difference of

the ﬁrst order derivative by the discrete difference of the CV val-

ues A minimum UV level was deﬁned, identifying the required ab-

sorbance 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 consid-

ered 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 con-

sidered a peak if, and only if, all of the above criteria were met, in

which case the corresponding CV value was recorded as the reten-

tion 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 over-

lap, 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 follow-

ing criteria were satisﬁed, was used: (i) the second order deriva-

tive 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

4 Results and discussion

The ﬁnal control system conﬁguration, illustrated in Fig 3, in-

cluded two types of control: ILC of deviations in the measurement

signals yk from the set points yd ,k at cycle k, and feed-forward

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 d u, d G and d y, respectively The disturbances to the control signals, d u, 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, d G, 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 act- ing 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 Section4.6 Finally, disturbances to the measurement signal, d y, stem from inaccuracies in the peak detection due to ir- regularities 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

The model matrix G was estimated using a ﬁnite-difference linear Jacobian around the point u b =[ 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 were scaled by a factor 1

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

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Fig. 4 Chromatograms from the model parameter estimation experiments The nominal case was run ﬁrst, followed by a run with perturbed x B,i and, ﬁnally, a run with perturbed x B, 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 vol-

umes of both peaks The suspicion was further conﬁrmed by com-

puting 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 de-

coupled process model, T, was computed A comparison between

the original and decoupled process model matrices is shown in 22

G=

−0.022 −0.010

−0.021 −0.017

, T=

−9.2· 10−3 0

−5.2· 10−19 −7.4· 10−3

(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

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 con-

trol signals on cycle 4, which resulted in almost restored reten-

tion volumes The corresponding effect can be seen in the mea-

surement 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, indi-

cating that the controller had already compensated for something

despite no disturbance having been applied Second, after the con-

troller had compensated for the disturbance buffer on cycles 4 and

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 x B , 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 = 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 dis- tance 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 over- compensates 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 =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

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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 x B, f Of particular interest is that no corresponding oscillations in x B,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 inter-

est 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

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

x B,i increased and x B, f decreased The higher initial salt concen-

tration worked to accelerate the elution of the ﬁrst peak, while

the decreased gradient slope delayed the elution of both peaks

Fig.7makes 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 cor-

rection 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

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 Section4.6

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 sur- rounding 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

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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 in-

puts, 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 elu-

tion 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 keep-

ing 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

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, mean-

ing 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 reten-

tion volumes to their set points This is indicative of a system- atic 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 Conse- quently, 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

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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 be-

ing 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 differ-

ences in derivatives can be detected between them, the peak de-

tection method would result in a single peak detected Such dis-

turbances would have a greater effect if the ratio of concentra-

tion 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 anti-

body 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 un-

detectable 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 concentra-

tions 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 re-

sulted in straightforward control of the individual retention vol-

umes 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 af- fects the resolution of product and impurity If a method to es- timate 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 How- ever, 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

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Tiêu đề	Binary separation control in preparative gradient chromatography using iterative learning control
Tác giả	Daniel Espinoza, Niklas Andersson, Bernt Nilsson
Trường học	Lund University
Chuyên ngành	Chemical Engineering
Thể loại	Journal Article
Năm xuất bản	2022
Thành phố	Lund

Định dạng
Số trang	12
Dung lượng	1,61 MB