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


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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20


  1. 1.

    PhRMA. Profile: Biopharmaceutical research industry. Pharmaceutical Research and Manufacturers of America, Washington DC. 2013. Accessed 23 March 2015.

  2. 2.

    U. S. Food and Drug Administration. Guidance for industry: PAT-A framework for innovative pharmaceutical development, manufacturing and quality assurance. U. S. Food and Drug Administration, Rockville, MD. September 2004. Accessed 4 May 2015.

  3. 3.

    DiMasi JA, Grabowski H. Economics of new oncology drug development. J Clin Oncol. 2007;25(2):209–16.

    PubMed  Article  Google Scholar 

  4. 4.

    Williams M, Malick JB. Drug discovery and development. New York: Humana Press; 1987.

    Book  Google Scholar 

  5. 5.

    Behr A, Brehme V, Ewers C, Gron H, Kimmel T, Kuppers S, et al. New developments in chemical engineering for the production of drug substances. Eng Life Sci. 2004;4:15–24.

    CAS  Article  Google Scholar 

  6. 6.

    Khanna I. Drug discovery in pharmaceutical industry: productivity challenges and trends. Drug Discov Today. 2012;17(19/20):1088–102.

    PubMed  Article  Google Scholar 

  7. 7.

    Camejo RR, McGrath C, Herings R. A dynamic perspective on pharmaceutical competition, drug development and cost effectiveness. Health Policy. 2011;100:18–24.

    Article  Google Scholar 

  8. 8.

    Muzzio F, Singh R, Chaudhury A, Rogers A, Ramachandran R, Ierapetritou MG. Pharm Tech Mag Eur. 2013;37(6):40–1.

    CAS  Google Scholar 

  9. 9.

    Kumar A, Gernaey KV, De Beer T, Nopens I. Model-based analysis of high shear wet granulation from batch to continuous processes in pharmaceutical production—a critical review. Eur J Pharm Biopharm. 2013;85:814–32.

    CAS  PubMed  Article  Google Scholar 

  10. 10.

    Cutler CR, Perry RT. Real time optimization with multivariable control is required to maximize profits. Comp Chem Eng. 1983;7(5):663–7.

    Article  Google Scholar 

  11. 11.

    Nath R, Alzein Z. On-line dynamic optimization of olefins plants. Comp Chem Eng. 2000;24(2–7):533–8.

    CAS  Article  Google Scholar 

  12. 12.

    Kadam JV, Schlegel M, Srinivasan B, Bonvin D, Marquardt W. Dynamic optimization in the presence of uncertainty: from off-line nominal solution to measurement-based implementation. J Proc Contr. 2007;17(5):389–98.

    CAS  Article  Google Scholar 

  13. 13.

    Aske EMB. Status on real-time optimization as seen both from an industrial and academic point of view. Norwegian University of Science and Technology (NTNU). 2009.…/TrialLecture.pdf. Accessed 8 Aug 2014.

  14. 14.

    Würth L, Hannemann R, Marquardt W. Neighboring-extremal updates for nonlinear model-predictive control and dynamic real-time optimization. J Proc Contr. 2009;19:1277–88.

    Article  Google Scholar 

  15. 15.

    Souza GD, Odloak D, Zanin AC. Real time optimization (RTO) with model predictive control (MPC). Comp Chem Eng. 2010;34:1999–2006.

    Article  Google Scholar 

  16. 16.

    Darby ML, Nikolaou M, Jones J, Nicholson D. RTO: an overview and assessment of current practice. J Proc Contr. 2011;21:874–84.

    CAS  Article  Google Scholar 

  17. 17.

    Gopalakrishnan A, Biegler LT. Economic nonlinear model predictive control for periodic optimal operation of gas pipeline networks. Comp Chem Eng. 2013;52:90–9.

    CAS  Article  Google Scholar 

  18. 18.

    Alamo T, Ferramosca A, González AH, Limon D, Odloak D. A gradient-based strategy for the one-layer RTO + MPC controller. J Proc Contr. 2014;24:435–47.

    CAS  Article  Google Scholar 

  19. 19.

    Boukouvala F, Niotis V, Ramachandran R, Muzzio FJ, Ierapetritou MG. An integrated approach for dynamic flowsheet modeling and sensitivity analysis of a continuous tablet manufacturing process. Comp Chem Eng. 2012;42:30–47.

    CAS  Article  Google Scholar 

  20. 20.

    Singh R, Ierapetritou M, Ramachandran R. An engineering study on the enhanced control and operation of continuous manufacturing of pharmaceutical tablets via roller compaction. Int J Pharm. 2012;438:307–26.

    CAS  PubMed  Article  Google Scholar 

  21. 21.

    Sen M, Rogers A, Singh R, Chaudhury A, John J, Ierapetritou MG, et al. Flowsheet optimization of an integrated continuous purification-processing pharmaceutical manufacturing operation. Chem Eng Sci. 2013;102:56–66.

    CAS  Article  Google Scholar 

  22. 22.

    Singh R, Sahay A, Karry KM, Muzzio F, Ierapetritou M, Ramachandran R. Implementation of a hybrid MPC-PID control strategy using PAT tools into a direct compaction continuous pharmaceutical tablet manufacturing pilot-plant. Int J Pharm. 2014;473:38–54.

    CAS  PubMed  Article  Google Scholar 

  23. 23.

    Singh R, Ierapetritou M, Ramachandran R. System-wide hybrid model predictive control of a continuous pharmaceutical tablet manufacturing process via direct compaction. Eur J Pharm Biopharm. 2013;85(3):1164–82.

    CAS  PubMed  Article  Google Scholar 

  24. 24.

    Schaber SD, Gerogiorgis D, Ramachandran R, Evans JMB, Barton PI, Trout BL. Economic analysis of integrated continuous and batch pharmaceutical manufacturing: a case study. Ind Eng Chem Res. 2008;50:10083–92.

    Article  Google Scholar 

  25. 25.

    DiMasi JA, Hansen RW, Grabowski HG. The price of innovation: new estimates of drug development costs. J Health Econ. 2003;22(2):151–85.

  26. 26.

    DiMasi JA. New drug innovation and pharmaceutical industry structure: trends in the output of pharmaceutical firms. Drug Informat J. 2000;34:1169–194.

  27. 27.

    Hansen RW. The pharmaceutical development process: estimates of current development costs and times and the effects of regulatory changes. In: Chien RI, editor. Issues in pharmaceutical economics. Lexington: Lexington Books; 1979. p. 151–87.

    Google Scholar 

  28. 28.

    Giaccotto C, Golec J, Vernon J. New estimates of the cost of capital for pharmaceutical firms. J Corp Fin. 2011;17:526–40.

    Article  Google Scholar 

  29. 29.

    Basu P, Joglekar G, Rai S. Analysis of manufacturing costs in pharmaceutical companies. J Pharm Innov. 2008;3:30–40.

    Article  Google Scholar 

  30. 30.

    Gao Y, Muzzio F, Ierapetritou MG. Optimizing continuous powder mixing processes using periodic section modeling. Chem Eng Sci. 2012;80:70–80.

    CAS  Article  Google Scholar 

  31. 31.

    Singh R, Barrasso D, Chaudhury A, Sen M, Ierapetritou M, Ramachandran R. Closed-loop feedback control of a continuous pharmaceutical tablet manufacturing process via wet granulation. J Pharm Innov. 2014. doi:10.1007/s12247-014-9170-9.

    Google Scholar 

  32. 32.

    Benyahia B, Lakerveld R, Braatz RD, Barton PI. Model-based design of a plant-wide control strategy for a continuous pharmaceutical plant. AIChE J. 2013;59:3671–85.

    Article  Google Scholar 

  33. 33.

    Singh R, Sahay A, Muzzio F, Ierapetritou M, Ramachandran R. Systematic framework for onsite design and implementation of the control system in continuous tablet manufacturing process. Comp Chem Eng. 2014;66:186–200.

    CAS  Article  Google Scholar 

  34. 34.

    Francois G, Bonvin D. Measurement-based real-time optimization of chemical processes. Advan Chem Eng. 2013;43:1–50.

    CAS  Article  Google Scholar 

  35. 35.

    Boss EA, de Vasco Toledo EC, Filho RM. Real time optimization for freeze drying process. Comp Aid Chem Eng. 2004;18:595–600.

    CAS  Article  Google Scholar 

  36. 36.

    Giridhar A, Hamdan I, Joglekar G, Venkatasubramanian V, Reklaitis GV. Real-time process management in particulate and pharmaceutical systems. Comp Aid Chem Eng. 2011;29:1035–9.

    Article  Google Scholar 

  37. 37.

    Yang G, Li X, Qian Y. A real-time updated model predictive control strategy for batch processes based on state estimation. Chin J Chem Eng. 2014;22:318–29.

    CAS  Article  Google Scholar 

  38. 38.

    Nelder JA, Mead R. A simplex method for function minimization. Comput J. 1965;7(4):308–13.

    Article  Google Scholar 

  39. 39.

    Singh R, Boukouvala F, Jayjock E, Ramachandran R, Ierapetritou M, Muzzio F. Flexible multipurpose continuous processing. PharmPro Mag Pharm Proc. 2012;27(6):22–5.

    Google Scholar 

  40. 40.

    Vanarase A, Gao Y, Muzzio FJ, Ierapetritou MG. Characterizing continuous powder mixing using residence time distribution. Chem Eng Sci. 2011;66(3):417–25.

    Article  Google Scholar 

  41. 41.

    Portillo PM, Vanarase A, Ingram A, Seville JK, Ierapetritou MG, Muzzio FJ. Investigation of the effect of impeller rotation rate, powder flow rate, and cohesion on powder flow behavior in a continuous blender using PEPT. Chem Eng Sci. 2010;65:5658–68.

    CAS  Article  Google Scholar 

  42. 42.

    Sen M, Singh R, Vanarase A, John J, Ramachandran R. Multi-dimensional population balance modeling and experimental validation of continuous powder mixing processes. Chem Eng Sci. 2012;80:349–60.

    CAS  Article  Google Scholar 

  43. 43.

    Singh R, Gernaey KV, Gani R. ICAS-PAT: a software for design, analysis & validation of PAT systems. Comput Chem Eng. 2010;34(7):1108–36.

    CAS  Article  Google Scholar 

  44. 44.

    Kawakita K, Ludde KH. Some considerations on powder compression equations. Powder Technol. 1971;4:61–8.

    Article  Google Scholar 

  45. 45.

    Kuentz M, Leuenberger H. A new model for the hardness of a compacted particle system, applied to tablets of pharmaceutical polymers. Powder Technol. 2000;111:143–5.

    Article  Google Scholar 

  46. 46.

    Kimber JA, Kazarian SG, Stepánek F. Microstructure-based mathematical modelling and spectroscopic imaging of tablet dissolution. Comp Chem Eng. 2011;35:1328–39.

    CAS  Article  Google Scholar 

  47. 47.

    Fette. OCIF-OPC, OPC Server for Fette Tablet Presses User manual. FETTE GmbH, Reg. No. 36.50.3; V1.5; 2009.

  48. 48.

    Check master. Operating instructions manual, Check master CM 4.2. FETTE GmbH, Ident.-Nr.: 9140874, version: 51.55.56; 2009. Accessed 13 April 2015.

  49. 49.

    Mulligan T, Media, D. How to reduce material handling costs. Hearst Newspapers, LLC. 2014. Accessed 7 Aug 2014.

  50. 50.

    Sen M, Dubey A, Singh R, Ramachandran R. Mathematical development and comparison of a hybrid PBM-DEM description of a continuous powder mixing process. J Powder Technol. 2013. doi:10.1155/2013/843784.

Download references


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

Author information



Corresponding author

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

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

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

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

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

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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).

Download citation


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