# Predictive Control Strategy for Continuous Production Systems: A Comparative Study with Classical Control Approaches Using Simulation-Based Analysis

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## Abstract

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## 1. Introduction

- A new predictive control strategy, adapted for a continuous pharmaceutical tablet manufacturing plant using dry granulation, was developed.
- The control performance of the algorithm was tested and analyzed by simulations performed on a benchmark simulator designed based on the models that are available in the literature.
- A comparison between the results provided by the proposed predictive control strategy and those obtained using PID and LQR algorithms was performed.

## 2. Direct Compression vs. Dry/Wet Granulation

## 3. Process Description

#### 3.1. Process Structure

#### 3.2. Process Modelling

## 4. Closed-Loop Control System Framework

#### 4.1. Control System Architecture

#### 4.2. Model Predictive Control Strategy

## 5. Simulation Results

#### 5.1. Simulation Setup

#### 5.2. Comparison Control Strategies

#### 5.2.1. Proportional-Integral-Derivative Controller

#### 5.2.2. Linear Quadratic Regulator

#### 5.3. Illustrative Results

#### 5.4. Numerical Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

API | Active Pharmaceutical Ingredient |

CM | Continuous Manufacturing |

CPS | Cyber-Physical System |

DC | Direct Compression |

DG | Dry Granulation |

FRtool | Frequency Response tool |

GMP | Good Manufacturing Practice |

ISE | Integral-Square-Error |

IT | Information Technology |

ITAE | Integral of Time Absolute Error |

LB | Lower Bounds |

LQG | Linear Quadratic Gaussian |

LQI | Linear Quadratic Integral |

LQR | Linear Quadratic Regulator |

MIMO | Multiple-Input Multiple-Output |

MPC | Model Predictive Control |

NISE | Normalized Integral-Square-Error |

PID | Proportional-Integral-Derivative |

RC | Roller Compactor |

SISO | Single-Input Single-Output |

TP | Tablet Press |

UB | Upper Bounds |

WG | Wet Granulation |

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**Figure 1.**Continuous pharmaceutical tablet manufacturing processes via wet granulation (red) and via direct compaction (green).

**Figure 8.**Out1—Closed-loop performance, setpoint tracking, and disturbance rejection, in case of blender mass flowrate [kg/h].

**Figure 11.**Out2—Closed-loop performance, setpoint tracking, and disturbance rejection, in case of API concentration.

**Figure 14.**Out7—Closed-loop performance, setpoint tracking, and disturbance rejection, in case of tablet hardness [MPa].

**Figure 16.**Out8—Closed-loop performance, setpoint tracking, and disturbance rejection, in case of tablet mass [g].

Property | Wet Granulation | Dry Granulation | Direct Compression |
---|---|---|---|

Compactability | Harder tablets in case of hard compactable substances. | Influenced by powder particle size and shape. | Potential problem for high loading of poorly compactable API substances. |

Flow | The granules formed are slightly more spherical than powders and have better flowability. | There may be some issues with powder flow. | Raw materials must have proper flowability and mixed with APIs, sometimes they may need lubricants before compression. |

Particle size | Greater with a longer range. | Narrower with a narrower range. | |

Content uniformity | It ensures better uniformity of content. | The resulting granulation increased confidence in uniformity. | It is at risk because it is difficult to accurately mix a small amount of API into a large volume of excipients. |

Mixing | Prevents segregation of components. | Segregation of components may occur after mixing. | A high shear can reduce particle size. |

Lubrication | Not so sensitive. | The compression step becomes easier and not sticky. | Reduces mixing time. |

Disintegration | Increased intragranular levels are required because of the negative impact of wet granulation on disintegrants. | They have an improved disintegration time because the dry binder used has a lower adhesive effect and therefore a quicker disintegration. | It allows them to disintegrate into API particles rather than granules. |

Dissolution | Providing hydrophilic properties to the surface of the granules can improve the dissolution rate. | The slowness of dissolution from granules during storage, particularly if an intragranular disintegrant is not used. | Difference in dissolution speeds up the process and allows better absorption for API tablets that are poorly soluble. |

Cost | Higher investments costs because of the time, labour, energy, and equipment. | Lower equipment costs than wet granulation. | DC has an economic advantage over granulation as it requires fewer resources. |

Sensitivity to raw material variability | Raw material wetting is influenced more by changes in raw material properties. | The properties of the raw material matter, the characteristics of API powders, and excipients are important. | Precise selection of excipients is needed as raw materials must have adequate flowability and compressibility for a successful operation. |

Stability | Not suitable for use on heat or moisture-sensitive materials. | Suitable for using on heat or moisture-sensitive materials. | |

Tableting speed | Higher | Decreased speed if the flow is low. |

Input | Value | LB | UB | Unit |
---|---|---|---|---|

Screw speed excipient feeder $\left({\omega}_{Exc}\right)$ | 207.6 | 0 | 240 | rpm |

Screw speed API feeder $\left({\omega}_{API}\right)$ | 37.4 | 0 | 240 | rpm |

Hydraulic pressure RC $\left({P}_{h}ydraulic\right)$ | 1 | 1 | 10 | MPa |

Feed speed $\left({u}_{d}\right)$ | 2.017 | 1 | 5 | cm/s |

Angular velocity rolls RC $\left({\omega}_{RC,rolls}\right)$ | 5 | 1 | 10 | rpm |

Turret speed TP $\left({\omega}_{TP,turret}\right)$ | 45 | 40 | 50 | rpm |

Height tablet $\left({L}_{tablet}\right)$ | 0.004 | 0.0038 | 0.005 | m |

Feed volume $\left({V}_{feed}\right)$ | 9.6 × 10${}^{-7}$ | 9 × 10${}^{-7}$ | 11 × 10${}^{-7}$ | m${}^{3}$ |

Output | Value | LB | UB | Unit |
---|---|---|---|---|

Mass flow rate outlet blender $\left({\dot{m}}_{blender}\right)$ | 20 | 17 | 23 | kg/h |

Concentration API $\left({C}_{API}\right)$ | 0.15 | 0.10 | 0.20 | - |

Density outlet RC $\left({\rho}_{RC}\right)$ | 1.057 | 0.8 | 1.2 | g/cm${}^{3}$ |

Roller gap RC $\left({h}_{0,RC}\right)$ | 1.6 | 1 | 5 | mm |

Mass flow rate outlet RC $\left({\dot{m}}_{out,RC}\right)$ | 20 | 17 | 23 | kg/h |

Mass flow rate outlet TP $\left({\dot{m}}_{TP}\right)$ | 20 | 17 | 23 | kg/h |

Hardness tablet $\left({H}_{tablet}\right)$ | 5.433 | 4 | 6 | MPa |

Mass tablet $\left({M}_{tablet}\right)$ | 0.4566 | 0.44 | 0.47 | g |

Out1 (${10}^{-3}$) | Out2 (${10}^{-7}$) | Out7 (${10}^{-3}$) | Out8 (${10}^{-6}$) | |
---|---|---|---|---|

MPC | 3.519 | 6.263 | 2.655 | 2.361 |

LQR | 4.279 | 7.223 | 2.717 | 3.158 |

PID | 168 | 14,612 | 1021 | 175 |

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## Share and Cite

**MDPI and ACS Style**

Chindrus, A.; Copot, D.; Caruntu, C.-F.
Predictive Control Strategy for Continuous Production Systems: A Comparative Study with Classical Control Approaches Using Simulation-Based Analysis. *Processes* **2023**, *11*, 1258.
https://doi.org/10.3390/pr11041258

**AMA Style**

Chindrus A, Copot D, Caruntu C-F.
Predictive Control Strategy for Continuous Production Systems: A Comparative Study with Classical Control Approaches Using Simulation-Based Analysis. *Processes*. 2023; 11(4):1258.
https://doi.org/10.3390/pr11041258

**Chicago/Turabian Style**

Chindrus, Amelia, Dana Copot, and Constantin-Florin Caruntu.
2023. "Predictive Control Strategy for Continuous Production Systems: A Comparative Study with Classical Control Approaches Using Simulation-Based Analysis" *Processes* 11, no. 4: 1258.
https://doi.org/10.3390/pr11041258