Integrated Moving Horizon-Based Dynamic Real-Time Optimization and Hybrid MPC-PID Control of a Direct Compaction Continuous Tablet Manufacturing Process

Abstract

In this manuscript, a moving horizon-based real-time optimization (MH-RTO) has been integrated with a hybrid model predictive control (MPC) system for a continuous tablet manufacturing process for quality by design (QbD)-based efficient continuous manufacturing. In the proposed approach, the integrated MH-RTO provides the optimal operational set points for the tablet production rate in real time. The MH-RTO takes into consideration the capital and operating cost, the market fluctuations, the product inventory, the product quality assurance strategy, the regulatory constraints, and the product rejections. An advanced hybrid model predictive control system then ensures that the required production rate with desired quality is met with minimum resources and time. A robust optimization strategy and an efficient control system have been integrated to achieve the maximum profit. The MH-RTO integrated with a hybrid control strategy ensures the maximum possible profit irrespective of the market demand fluctuations. The basic advantage of the MH-RTO framework is that it takes into consideration the future demand and thus can lead to increased profit compared to a standard real-time optimization approach.

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Acknowledgments

This work is supported by the National Science Foundation Engineering Research Center on Structured Organic Particulate Systems, through Grant NSF-ECC 0540855.

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Correspondence to Rohit Ramachandran.

Appendix A

Appendix A

Pilot Plant

The snapshot of the pilot plant is shown in Fig. 21 (whole plant is not shown).

Fig. 21
figure21

Continuous direct compaction tablet manufacturing pilot plant. (1) Feeders, (2) Co-mill and blender, (3) Tablet press

DEM Simulation

The transfer function model relating blender holdup with weir height has been developed using a DEM simulation. The effect of the weir length on the holdup has been determined by running DEM simulations of the mixing operation. The simulations have been run using EDEM™ (DEM Solutions). The weir length has been varied as 10, 30, and 50 mm. Each simulation trial has been run for 50 s. A commercial blender (Gericke GCM250™) with impeller blades in alternating forward and backward orientation has been simulated. The impeller speed of the mixer has been maintained at 250 rpm. Normal particle size distribution with a mean radius of 1 mm with 5 % standard deviation has been used. A feed rate of 0.018 kg/s has been maintained throughout. A detailed description of the DEM simulation has been provided previously by the authors [50]. The DEM simulations have been post-processed to obtain the mean residence time of the particles within the mixer. The holdup has been calculated from the input flow rate and the mean residence time. A transfer function has been fitted to relate the holdup with the weir length. Figure 22 presents an illustration of the mixer geometry (as seen in EDEM™). A weir placed at the blender outlet can be seen in the figure.

Fig. 22
figure22

Blender as simulated in EDEM to generate the step response data for blender holdup and weir length

Illustration of the Development of Transfer Function Model from Step Response Experiment

The development of the transfer function model from the step response experiment is illustrated in Fig. 23 using drug concentration as a demonstrative example. The step change has been made in the input variable, and the output variable (drug concentration at blender outlet) has been measured using NIR sensor. From the step response plot, the dead time (152 s), process gain (0.5000375), and the first-order time constant (70.7099) have been calculated as shown in the figure. Based on this information, the transfer function model is then developed as follows:

$$ G(S)=\frac{y(s)}{u(S)}=\frac{K}{\tau \kern0.5em S+1}{e}^{-{\tau}_{\mathrm{d}}S}=\frac{0.500374}{70.7099\kern0.5em \mathrm{S}+1}{e}^{-152\kern0.5em S} $$
Fig. 23
figure23

Development of transfer function model from step response experiment

From the above equation the step response model can be develop as follows:

$$ y(t)=0.500374.M\left(1-{e}^{\left(\frac{t-152}{70.7000}\right)}\right);\kern1em t>152 $$

Where M is the magnitude of the step change. The step response generated using the model is shown in Fig. 24. Figure 24 shows a similar response as shown in Fig. 23 which was obtained experimentally. Similarly, the step response models for other variables have been developed.

Fig. 24
figure24

Step response of transfer function model

Process Model Summary

Detailed process model of each unit operation involved in direct compaction tablet manufacturing process and corresponding references are given in Table 7.

Table 7 Direct compaction tablet manufacturing process model and references

The inputs and outputs involved in transfer function model are listed in Table 8.

Table 8 Summary of transfer function model inputs and outputs

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Singh, R., Sen, M., Ierapetritou, M. et al. Integrated Moving Horizon-Based Dynamic Real-Time Optimization and Hybrid MPC-PID Control of a Direct Compaction Continuous Tablet Manufacturing Process. J Pharm Innov 10, 233–253 (2015). https://doi.org/10.1007/s12247-015-9221-x

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Keywords

  • Continuous tablet manufacturing
  • Real-time optimization
  • MPC
  • Process economics