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346 M. A. Boojari et al.
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Fig. 5 Overview of the complete control system design of the downstream process
to the higher intrinsic complexity of downstream process units, a comprehensive
analysis of the system degrees of freedom and control loop interactions has not been
carried out. On the other hand, a trial and error strategy has been adopted, whose
methodology is to select manipulated and controlled variables based on process
control experience and literature examples and then simulate the effect of external
disturbances in the designed computational model to prove their effectiveness and
stability.
The upper limit for residual biomass concentration in the centrifuge outlet
stream has been observed introducing a PI controller that enhances the centrifuge’s
separation efficiency by increasing its rotational speed. The first buffer tank has
been provided with a sluggish PI level controller that smooths the inlet flow
rate oscillations to the outlet stream, which is then pumped by a variable speed
pump to pass through the nanofiltration membrane. To achieve a stable lovastatin
concentration in the retentate stream, a PI controller regulates the pump’s rotational
speed needed to provide the correct pressure gradient to the nanofiltration process.
For the second buffer tank, a different type of level control has been designed,
which is not operating continuously and has a discrete-time nature. This discretetime P controller follows the discontinuous nature of chromatography columns,
actuating its corrective action every time right before each injection run of the
chromatography columns. The control purpose is to increase or reduce the sample
volumes injected in the chromatography columns in order to keep a fixed amount of
liquid volume of the tank. The complete control structure of the downstream process
is reported in Fig. 5.
As for the upstream process, the implemented controllers’ settings have been
tuned by applying analytical tuning rules or using an integrated Simulink tuning
tool with the designed controller parameters specified as shown in Table 9.

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Table 9 Downstream controllers and tuned parameter values
Controller parameters
Controlled
variable
Residual biomass
concentration,
C
X,7
Buffer tank “A”
level, V
Buffer tank “B”
level, V
Produced
lovastatin
concentration,
C
LOV,10
Manipulated
variable
Centrifuge
rotational
speed
Buffer tank
“A” outlet flow
rate, Q
9
Buffer tank
“A” outlet flow
rate, Q
11
Rotational
speed of the
pump
Tuning method K
PID tuner −4.8 × 10
SIMC −71 × 10
PID tuner 0.17 – –
PID tuner 0.23 1 –
c
−4
−4
τI[h] τD[h]
0.1 –
560 –
9 Unification of the Computational Models and Final
Simulation
In this section, the upstream and downstream computational models are finalized
and ready to be unified in a single comprehensive Simulink model, which will be
further tested for several disturbances. The comprehensive Simulink computational
model is represented in Fig. 6.
In this context, the medium stream nitrogen concentration C
case for testing the designed control system is subjected to a permanent −15% step
change at time t = 200 h, as reported in Fig. 7.
The whole control system performs a coordinated response, in which each
controller adjusts the manipulated variables to take action against the disturbance,
thus moving the controlled variables back to their set points. The plots of the
upstream and downstream manipulated and controlled variables are summarized in
Figs. 8 and 9, respectively.
The lack of the nitrogen substrate has an inhibitory effect on lovastatin production, as can be appreciated from the drop of CSTR lovastatin concentration in the
bottom center graph of Fig. 8. The concentration controller closes the purge stream
valve to enhance biomass recirculation, increasing recirculation flow rate Q
then recirculation factor RF. This generates an increment in the CSTR volume, not
appreciable from the bottom left graph of Fig. 8 because of the tight level controller
that closes the CSTR outlet stream valve, reducing the flow rate Q
a longer residence time of biomass cells in the reactor, which have more time to
produce lovastatin. To reestablish the RF to its set point, the third controller closes
the medium stream valve to reduce the mixer’s feed flow rate Q
top-right graph of Fig. 8. Eventually, after a prolonged time due to the slow kinetics
as a simulation
N,1
R
. This implies
4
, as shown in the
1
and

348 M. A. Boojari et al.
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Fig. 6 Unified Simulink model of upstream and downstream processes
Fig. 7 Step change disturbance in medium nitrogen concentration C
of the biological production of lovastatin, a new steady-state operating point is
reached in which all the controlled variables are settled back to their set point values.
Due to the simulated disturbance, the stream entering the centrifuges contains a
reduced amount of biomass, and its flow rate Q
from the bottom left biomass concentration graph of Fig. 9. The residual biomass
concentration set point is already at an acceptable value; instead of keeping the
rotational speed of the centrifuge (and thus the separation factor X
value than required, a reduction of the rotational speed contributes to saving electric
power. The reduced flow rate from the upstream makes the buffer tank volume V
decrease, as shown in the bottom center graph of Fig. 9. The level controller closes
the tank outlet stream valve to achieve a reduction in the outlet flow rate Q
smoothly settles to a new steady-state value.The reduction of Q
of permeate Q
and retentate Q10flow rates; at the same time, the retentate stream
PE
is more concentrated, meaning that its lovastatin concentration rises. As reported
in the top-right graph of Fig. 9, the pump head pressure P initially rises slightly
N,1
is lower. The first effect is visible
5
) at a higher
2
, which
9
implies a reduction
9
A

Dynamic Modeling and Control of a Continuous Biopharmaceutical... 349
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Fig. 8 Upstream process manipulated variables (above) and respective controlled variables
(below) following the introduction of a step change in the medium nitrogen concentration
Fig. 9 Downstream process manipulated variables (above) and respective controlled variables
(below)
because of the reduced Q9but afterward drops because of the motor pump rotational
speed N reduction (also in this case, with the purpose of saving electric power)
induced by the lovastatin concentration controller. As stated in Sect. 8.2,thelevel
controller of buffer tank “A” is sluggish and is not affecting the correct functionality
of the lovastatin concentration controller, which is tuned with settings that are more
aggressive.

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10 Conclusion
A dynamic modeling was developed for a continuous biopharmaceutical manufacturing plant. The modeling of the unit operations was implemented in a
MATLAB/Simulink framework. The benchmark simulator includes an upstream
section, in which a CSTR bioreactor is implemented with a biomass recycle system,
and a downstream section, which is composed of a sequence of centrifugation,
nanofiltration, and chromatography operations for the isolation of the target API.
Various regulatory and supervisory control strategies can be used for the control
of the developed dynamic model. As a case study, we simulated a semicontinuous
benchmark plant for the production of lovastatin by using a multiple PI control
system. The introduced model can be used for dynamic simulation of CBM
processes and as a testbed for confirming the effectiveness of optimization and
control.
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Overview of Scheduling Methods for
https://t.me/medicina_free
Pharmaceutical Production
Shamik Misra and Christos T. Maravelias
1 Introduction
Increasing competition and strong government regulations compel the pharmaceutical industry to adopt improved decision-making practices to develop efficient
manufacturing processes. Pharmaceutical products are generally produced on a
small scale and required to meet high purity standards [1]. Though continuous
pharmaceutical manufacturing processes are investigated [2], the majority of the
facilities in a pharmaceutical plant still operate in batch mode due to product
variability and strict quality requirement [3]. As manufacturing is riddled with
complexities involving shared resources, cleaning requirements, and unit setups,
production scheduling plays an important role in maintaining efficient time-tomarket performance.
Scheduling is a decision-making process which concerned with the allocation of
limited shared resources to different competing activities over time while aiming to
optimize single or multiple objectives. Despite several exact and approximate solution methods proposed over the last three decades, production scheduling remains
one of the most active topics of research in the process systems engineering (PSE)
community [4–9]. Exact scheduling methods based on mixed-integer programming
models can be classified into two categories: (1) precedence-based models [10–16]
and (2) time grid-based models. The latter can further be categorized based on the
S. Misra
Department of Chemical and Biological Engineering, University of Wisconsin, Madison, WI,
USA
e-mail: misra7@wisc.edu
C. T. Maravelias (
Andlinger Center for Energy and the Environment and Department of Chemical and Biological
Engineering, Princeton University, Princeton, NJ, USA
e-mail: maravelias@princeton.edu
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
A. Fytopoulos et al. (eds.), Optimization of Pharmaceutical Processes, Springer
Optimization and Its Applications 189, https://doi.org/10.1007/978-3-030-90924-6_13
)
355

356 S. Misra and C. T. Maravelias
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time representation techniques used, viz., discrete time [17–22], continuous time
[23–29], and mixed time [30–32] representation.
In the following, we restrict our review to some specific scheduling frameworks
proposed in the literature that have direct application toward the pharmaceutical industry. Castro et al. studied a pharmaceutical batch plant and proposed
a decomposition-based solution strategy to tackle the complexity of the large
production facilities [33]. The same problem was further investigated by Kopanos
et al., who proposed two precedence-based MILP models to address complexities
related to changeover costs and due times [34]. Stefansson et al. investigated a
multistage, multiproduct pharmaceutical production problem and proposed both
discrete and continuous time grid-based scheduling frameworks [35]. Kabra et al.
proposed a continuous time grid-based model to solve the problem introduced by
Lakhdar et al. [36] and include specific features related to the handling of shelf
life, waste disposal, and changeovers in a biopharmaceutical plant [37]. Liu et al.
proposed a discrete time-based MIP model to simultaneously optimize production and maintenance decisions of a biopharmaceutical plant under performance
decay [38]. Motivated by the real-world scheduling problem in the chemicalpharmaceutical industry, Moniz et al. proposed a discrete time-based scheduling
model that solves multiple instances of the problem and produces optimal schedules
and also helps to evaluate the process alternatives and their associated costs [39].
Eberle et al. proposed an immediate precedence-based scheduling model for a
single-unit, single-stage, multiple product sterile drug manufacturing facility while
incorporating complexities regarding sterile holding times [40].
One of the major advantages of models based on discrete-time grid(s) is
that the common time grid provides a reference grid of time to all the shred
resources such as materials and utilities. Discrete-time grid is also advantageous
in monitoring and modeling consumption/inventory profiles of utilities/inventories
without introducing nonlinear constraints [41, 42]. Furthermore, the discrete-time
models are easily scalable and can be extended to incorporate multiple units/stages,
with minimal structural changes. In the following, we present an overview of
discrete time grid-based production scheduling models starting from single-unit
single-stage problems to multiunit multistage problems. We also present concepts
and modeling techniques to incorporate complexities related to changeover times
and costs, batching decisions, shared resources, and storage.
2 Single-Unit Scheduling
Though scarce in chemical engineering applications, a single-unit scheduling
environment can be considered a building block toward formulating models for
more complex scheduling environments. In the single-unit environment, multiple
batches need to be scheduled on a single unit. As all the production is met by
one unit, the number of batches required to complete the production need can be
precalculated, so the batching decisions can be made independently. We assume that
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