# Recurrent Neural Network-Based Model Predictive Control for Continuous Pharmaceutical Manufacturing

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Plant Model and Control Scenarios

#### 2.1. Plant Model

#### 2.2. Closed-Loop Control Scenarios

## 3. Methodology

#### 3.1. Non-Linear Time-Series System Identification via Recurrent Neural Networks

`scipy.integrate.solve_ivp`function.

#### 3.2. Control Problem Formulation

`scipy.optimize.minimize`function, and the sequential least squares quadratic programming (SLSQP) algorithm was selected as the option for this solver.

## 4. Results and Discussion

#### 4.1. System Identification

#### 4.2. RNN-MPC Closed-Loop Control Performance

## 5. Conclusions and Future Research

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Adam | Adaptive Moment Estimation |

ANN | Artificial Neural Network |

API | Active Pharmaceutical Ingredient |

BPTT | Back-Propagation Through Time |

CPP | Critical Process Parameter |

CQA | Critical Quality Attribute |

CSTR | Continuous-Stirred Tank Reactor |

FBU | Feeding Blending Unit |

LSTM | Long Short-Term Memory |

MPC | Model Predictive Control |

MV | Manipulated Vector |

NLP | Non-Linear Programming |

NMPC | Non-Linear MPC |

PID | Proportional-Integral-Derivative (Control) |

QbD | Quality by Design |

QDMC | Quadratic Dynamic Matrix Control |

RMSE | Root-Mean-Square Error |

RNN | Recurrent Neural Network |

RNN-MPC | RNN-based MPC |

SLSQP | Sequential Least Squares Quadratic Programming |

## Appendix A. Kinetic Parameters for Plant Model

## Appendix B. Long Short-Term Memory Cells

## References

- Lakerveld, R.; Benyahia, B.; Heider, P.L.; Zhang, H.; Wolfe, A.; Testa, C.J.; Ogden, S.; Hersey, D.R.; Mascia, S.; Evans, J.M.; et al. The application of an automated control strategy for an integrated continuous pharmaceutical pilot plant. Org. Process Res. Dev.
**2015**, 19, 1088–1100. [Google Scholar] [CrossRef] [Green Version] - Schaber, S.D.; Gerogiorgis, D.I.; Ramachandran, R.; Evans, J.M.B.; Barton, P.I.; Trout, B.L. Economic analysis of integrated continuous and batch pharmaceutical manufacturing: A case study. Ind. Eng. Chem. Res.
**2011**, 50, 10083–10092. [Google Scholar] [CrossRef] - Glasnov, T. Continuous-Flow Chemistry in the Research Laboratory: Modern Organic Chemistry in Dedicated Reactors at the Dawn of the 21st Century; Springer International Publishing: Basel, Switzerland, 2016; p. 119. [Google Scholar]
- Gutmann, B.; Cantillo, D.; Kappe, C.O. Continuous-flow technology—A tool for the safe manufacturing of active pharmaceutical ingredients. Angew. Chem. Int. Ed.
**2015**, 54, 6688–6728. [Google Scholar] [CrossRef] [PubMed] - Poechlauer, P.; Colberg, J.; Fisher, E.; Jansen, M.; Johnson, M.D.; Koenig, S.G.; Lawler, M.; Laporte, T.; Manley, J.; Martin, B.; et al. Pharmaceutical roundtable study demonstrates the value of continuous manufacturing in the design of greener processes. Org. Process Res. Dev.
**2013**, 17, 1472–1478. [Google Scholar] [CrossRef] - Benyahia, B.; Lakerveld, R.; Barton, P.I. A plant-wide dynamic model of a continuous pharmaceutical process. Ind. Eng. Chem. Res.
**2012**, 51, 15393–15412. [Google Scholar] [CrossRef] - Susanne, F.; Martin, B.; Aubry, M.; Sedelmeier, J.; Lima, F.; Sevinc, S.; Piccioni, L.; Haber, J.; Schenkel, B.; Venturoni, F. Match-making reactors to chemistry: A continuous manufacturing-enabled sequence to a key benzoxazole pharmaceutical intermediate. Org. Process Res. Dev.
**2017**, 21, 1779–1793. [Google Scholar] [CrossRef] - Mascia, S.; Heider, P.L.; Zhang, H.; Lakerveld, R.; Benyahia, B.; Barton, P.I.; Braatz, R.D.; Cooney, C.L.; Evans, J.M.B.; Jamison, T.F.; et al. End-to-end continuous manufacturing of pharmaceuticals: Integrated synthesis, purification, and final dosage formation. Angew. Chem. Int. Ed.
**2013**, 52, 12359–12363. [Google Scholar] [CrossRef] [PubMed] - Brueggemeier, S.B.; Reiff, E.A.; Lyngberg, O.K.; Hobson, L.A.; Tabora, J.E. Modeling-based approach towards quality by design for the ibipinabant API step modeling-based approach towards quality by design for the ibipinabant API step. Org. Process Res. Dev.
**2012**, 16, 567–576. [Google Scholar] [CrossRef] - Mesbah, A.; Paulson, J.A.; Lakerveld, R.; Braatz, R.D. Model predictive control of an integrated continuous pharmaceutical manufacturing pilot plant. Org. Process Res. Dev.
**2017**, 21, 844–854. [Google Scholar] [CrossRef] - Rasoulian, S.; Ricardez-Sandoval, L.A. Stochastic nonlinear model predictive control applied to a thin film deposition process under uncertainty. Chem. Eng. Sci.
**2016**, 140, 90–103. [Google Scholar] [CrossRef] - Rasoulian, S.; Ricardez-Sandoval, L.A. A robust nonlinear model predictive controller for a multiscale thin film deposition process. Chem. Eng. Sci.
**2015**, 136, 38–49. [Google Scholar] [CrossRef] - Hussain, M.A. Review of the applications of neural networks in chemical process control simulation and online implementation. Artif. Intell. Eng.
**1999**, 13, 55–68. [Google Scholar] [CrossRef] - Cheng, L.; Liu, W.; Hou, Z.G.; Yu, J.; Tan, M. Neural-network-based nonlinear model predictive control for piezoelectric actuators. IEEE Trans. Ind. Electron.
**2015**, 62, 7717–7727. [Google Scholar] [CrossRef] - Xiong, Z.; Zhang, J. A batch-to-batch iterative optimal control strategy based on recurrent neural network models. J. Process Control
**2005**, 15, 11–21. [Google Scholar] [CrossRef] - Tian, Y.; Zhang, J.; Morris, J. Modeling and optimal control of a batch polymerization reactor using a hybrid stacked recurrent neural network model. Ind. Eng. Chem. Res.
**2001**, 40, 4525–4535. [Google Scholar] [CrossRef] - Mujtaba, I.; Hussain, M. Applications of Neural Networks and Other Learning Technologies in Process Engineering; Imperial College Press: London, UK, 2001. [Google Scholar]
- Nagy, Z.K. Model based control of a yeast fermentation bioreactor using optimally designed artificial neural networks. Chem. Eng. J.
**2007**, 127, 95–109. [Google Scholar] [CrossRef] - Alanqar, A.; Durand, H.; Christofides, P.D. On identification of well-conditioned nonlinear systems: Application to economic model predictive control of nonlinear processes. AIChE J.
**2015**, 61, 3353–3373. [Google Scholar] [CrossRef] - Wang, X.; El-Farra, N.H.; Palazoglu, A. Proactive Reconfiguration of Heat-Exchanger Supernetworks. Ind. Eng. Chem. Res.
**2015**, 54, 9178–9190. [Google Scholar] [CrossRef] - Byeon, W.; Breuel, T.M.; Raue, F.; Liwicki, M. Scene labeling with LSTM recurrent neural networks. In Proceedings of the 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Boston, MA, USA, 7–12 June 2015; pp. 3547–3555. [Google Scholar]
- Cho, K.; van Merrienboer, B.; Gülçehre, Ç.; Bougares, F.; Schwenk, H.; Bengio, Y. Learning phrase representations using RNN encoder-decoder for statistical machine translation. arXiv, 2014; arXiv:1406.1078. [Google Scholar]
- Lee, J.H.; Shin, J.; Realff, M.J. Machine learning: Overview of the recent progresses and implications for the process systems engineering field. Comput. Chem. Eng.
**2018**, 114, 111–121. [Google Scholar] [CrossRef] - Rehrl, J.; Kruisz, J.; Sacher, S.; Khinast, J.; Horn, M. Optimized continuous pharmaceutical manufacturing via model-predictive control. Int. J. Pharm.
**2016**, 510, 100–115. [Google Scholar] [CrossRef] [PubMed] - Rawlings, J.B.; Mayne, D.Q. Model Predictive Control: Theory and Design; Nob Hill: Madison, WI, USA, 2009. [Google Scholar]
- Tatjewski, P. Advanced Control of Industrial Processes, Structures and Algorithms; Springer: London, UK, 2007. [Google Scholar]
- Garcia, C.E.; Morshedi, A. Quadratic programming solution of dynamic matrix control (QDMC). Chem. Eng. Commun.
**1986**, 46, 73–87. [Google Scholar] [CrossRef] - Pan, Y.; Wang, J. Model predictive control of unknown nonlinear dynamical systems based on recurrent neural networks. IEEE Trans. Ind. Electron.
**2012**, 59, 3089–3101. [Google Scholar] [CrossRef] - Seyab, R.A. Differential recurrent neural network based predictive control. Comput. Chem. Eng.
**2008**, 32, 1533–1545. [Google Scholar] [CrossRef] [Green Version] - Koppel, L.B. Input multiplicities in nonlinear, multivariable control systems. AIChE J.
**1982**, 28, 935–945. [Google Scholar] [CrossRef] - Seki, H.; Ooyama, S.; Ogawa, M. Nonlinear model predictive control using successive linearization—Application to chemical reactors. Trans. Soc. Instrum. Control Eng.
**2004**, E-3, 66–72. [Google Scholar] - Bequette, B.W. Non-linear model predictive control : A personal retrospective. Can. J. Chem. Eng.
**2007**, 85, 408–415. [Google Scholar] [CrossRef] - Kingma, D.P.; Ba, J. Adam: A Method for stochastic optimization. arXiv, 2014; arXiv:1412.6980. [Google Scholar]
- Pascanu, R.; Gulcehre, C.; Cho, K.; Bengio, Y. How to construct deep recurrent neural networks. arXiv, 2013; arXiv:1312.6026. [Google Scholar]

**Figure 2.**Initial conditions for cases I (start-up) and II (upset-recovery) relative to the set-point.

**Figure 3.**Illustration of a recurrent neural network (RNN) layer in compact form (

**left**) and unfolded form (

**right**).

**Figure 5.**Example of an experimental sequence and the dynamic response with $\Delta t=0.1$ time units.

**Figure 6.**System identification performance of the optimised RNN. (

**a**) Training performance of the optimised RNN. (

**b**) Validation performance of the optimised RNN on test data.

**Figure 7.**Control performance of RNN-MPC with 250 hidden nodes and two RNN layers. (

**a**) Control performance for case I (start-up). (

**b**) Control performance for case II (upset-recovery).

**Figure 8.**Control performance of RNN-MPC with 500 hidden nodes and two RNN layers. (

**a**) Control performance for case I (start-up). (

**b**) Control performance for case II (upset-recovery).

**Figure 9.**Control performance of RNN-MPC with 1000 hidden nodes and two RNN layers. (

**a**) Control performance for case I (start-up). (

**b**) Control performance for case II (upset-recovery).

**Figure 10.**Control performance of RNN-MPC with 2000 hidden nodes and two RNN layers. (

**a**) Control performance for case I (start-up). (

**b**) Control performance for case II (upset-recovery).

Control Scenario | ${\mathit{C}}_{\mathit{A}}$ | ${\mathit{C}}_{\mathit{R}}$ | q | T |
---|---|---|---|---|

I: Start-up | 0.692 | 0.287 | 0.800 | 0.800 |

II: Upset-recovery | 0.822 | 0.152 | 0.800 | 1.100 |

Set-point (maximum ${C}_{R}/{C}_{A}$) | 0.324 | 0.406 | 0.800 | 1.043 |

No. Layers / No. Nodes | 250 | 500 | 1000 |
---|---|---|---|

1 | 0.0299 | 0.0268 | 0.0206 |

2 | 0.0238 | 0.0118 | 0.0083 |

3 | 0.0262 | 0.0119 | 0.0125 |

**Table 3.**RMSE over test data of RNNs with hidden layers and either 1000 or 2000 nodes trained over 1000 epochs.

No. Layers | No. Nodes | RMSE |
---|---|---|

2 | 1000 | 0.0083 |

2 | 2000 | 0.0177 |

No. Nodes | Average Performance Index,${\mathcal{I}}_{\mathrm{avg}}$ | Comments |

250 | 93.7 | Steady-state Offset |

500 | 95.8 | Steady-state Offset |

1000 | 100.0 | Desired Performance |

2000 | 98.6 | Steady-state Offset |

NMPC | RNN-MPC | |
---|---|---|

Time required | 1.55 ms | 1.17 ms |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wong, W.C.; Chee, E.; Li, J.; Wang, X.
Recurrent Neural Network-Based Model Predictive Control for Continuous Pharmaceutical Manufacturing. *Mathematics* **2018**, *6*, 242.
https://doi.org/10.3390/math6110242

**AMA Style**

Wong WC, Chee E, Li J, Wang X.
Recurrent Neural Network-Based Model Predictive Control for Continuous Pharmaceutical Manufacturing. *Mathematics*. 2018; 6(11):242.
https://doi.org/10.3390/math6110242

**Chicago/Turabian Style**

Wong, Wee Chin, Ewan Chee, Jiali Li, and Xiaonan Wang.
2018. "Recurrent Neural Network-Based Model Predictive Control for Continuous Pharmaceutical Manufacturing" *Mathematics* 6, no. 11: 242.
https://doi.org/10.3390/math6110242