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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
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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
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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
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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
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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