# Application of Intelligent Control in Chromatography Separation Process

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. SMB Mathematical Discrete Model

#### 2.1. TMB and SMB Equation Model

#### 2.2. SMB Digitization via Crank–Nicolson Method

#### 2.3. Stability Analysis

**Theorem**

**1.**

**Proof.**

**Theorem**

**2.**

**Proof.**

- (1)
- When $2\le l\le p-1$. According to ${A}^{-1}Bv=\lambda v\Rightarrow Bv=\lambda Av$, so we can obtain the equation in component $l$:

- (2)
- When $l=1$, it means that

- (3)
- When $l=p$, it means that

## 3. Simulation

#### 3.1. Experimental Environment and Data

#### 3.2. Sensitivity Analysis of Purity Flow Rates to Find Local Monotonic Intervals

_{II}= 6.96, Q

_{III}= 8.4 and Q

_{IV}= 2 remain unchanged and the switch time is 180 s. The purity of extract solution for material B decreases with the increase in the flow rate in Zone I. However, the concentration of raffinate for material A remains almost unchanged.

_{I}= 7.14, Q

_{III}= 8.4 and Q

_{IV}= 2, and the switch time is 180 s. The purity of the extract solution of material B remains almost unchanged as the flow rate of Zone II increases, but the purity of raffinate for material A decreases with an increase in the flow rate of ${Q}_{II}$.

_{I}= 6.96, Q

_{II}= 7.2 and Q

_{IV}= 2, and the switch time is 180 s. The purity of extract solution of material B decreases with an increase in the flow of Zone III, and the purity of raffinate of material A decreases with the increase in the flow of Zone III. But the decreasing tendency is very small, so it is better for fine tuning. However, whether it is material A or material B, the change amount is relatively small, so the flow rate in this area is suitable for fine-tuning control. The sensitivity analysis of flow velocity in Zone IV is similar to that in Zone III, so it is also suitable for fine tuning the control effect.

## 4. Smart Controller Design

#### 4.1. Fuzzy Rule Control and Hierarchical Design

_{1}(k) = B material desired output − C

_{E,B}

_{2}(k) = A material desired output − C

_{R,A}

_{1}, C

_{2}, C

_{3}, C

_{4}, C

_{5}) are set as { −0.15, −0.1, 0, 0.1, 0.15} for ΔQ

_{1}, {−0.006, −0.004, 0, 0.0.004, 0.006} for ΔQ

_{2}, and {−0.08, −0.05, 0, 0.05, 0.08} for ΔQ

_{3}. When conducting sensitivity analysis near the flow rate region, it is necessary to adjust the rule table to reflect the decrease in purity with the increasing flow rate. Thus, the rule table was developed as listed in Table 3.

#### 4.2. NN-like Fuzzy Controller Framework

## 5. SMB Control Experiments

#### 5.1. Purity Control Result

#### 5.2. Controller Comparison

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 10.**Purity control of the first experiment (switch time = 180 s) (actual B = 94%, desired B = 94%, actual A = 96%, desired A = 96%).

**Figure 11.**Purity control of the second experiment (switch time = 180 s) (actual B = 89.98%, desired B = 90%, actual A = 89.86%, desired A = 90%).

**Figure 12.**Purity control of the fourth experiment (switch time = 178 s) (actual B = 95%, desired B = 95%, actual A = 93.07%, desired A = 93%).

**Figure 15.**Comparison of two controllers under the disturbance of adsorbent parameters ${H}_{A}=0.01\to 0.03$.

**Figure 16.**Comparison of two controllers under the disturbance of feed port concentration ${C}_{{}_{f}}=4.5\to 5.2$.

**Figure 17.**Comparison of two controllers under the disturbance of switch time $\theta =178s\to 182s$.

Parameter | Nomenclature | Parameter | Nomenclature |
---|---|---|---|

$x(\mathrm{cm})$ | Axial distance | $Q({\mathrm{cm}}^{3}{\mathrm{min}}^{-1})$ | Volume flow rate |

$k({\mathrm{gL}}^{-1})$ | Comprehensive mass transfer constant | $t(\mathrm{second})$ | Time |

${v}^{\ast}(\mathrm{cm}{\mathrm{min}}^{-1})$ | Effect velocity of body | $D({\mathrm{cm}}^{2}{\mathrm{min}}^{-1})$ | Effective dispersion coefficient |

${u}_{s}(\mathrm{cm}{\mathrm{min}}^{-1})$ | Solid flow rate | $\epsilon $ | Bulk void fraction |

$C({\mathrm{gL}}^{-1})$ | Mobile phase concentration | $i$ | Material index: A or B |

$q({\mathrm{gL}}^{-1})$ | Solid phase concentration | $j$ | Column number: 1, 2, 3, 4, 5, 6, 7, 8 |

${q}^{\ast}({\mathrm{gL}}^{-1})$ | Solid phase concentration at equilibrium between solid phase and mobile phase |

Parameter | Value | Parameter | Value |
---|---|---|---|

$L(\mathrm{cm})$ | 25 | ${C}_{f,i}({\mathrm{gL}}^{-1})$ | 5 |

$d(\mathrm{cm})$ | 0.46 | $\theta (\mathrm{min})$ | 3 |

${H}_{A}$ | 0.001 | ${Q}_{I}({\mathrm{cm}}^{3}{\mathrm{min}}^{-1})$ | 6.75 |

${H}_{B}$ | 0.45 | ${Q}_{II}({\mathrm{cm}}^{3}{\mathrm{min}}^{-1})$ | 6.6 |

${D}_{A}({\mathrm{cm}}^{2}{\mathrm{min}}^{-1})$ | 0.2 | ${Q}_{III}({\mathrm{cm}}^{3}{\mathrm{min}}^{-1})$ | 7 |

${D}_{B}({\mathrm{cm}}^{2}{\mathrm{min}}^{-1})$ | 1.265 | ${Q}_{IV}({\mathrm{cm}}^{3}{\mathrm{min}}^{-1})$ | 2 |

$\epsilon $ | 0.8 | spatial number | 50 |

$\mathit{e}$ | NB | NS | ZE | PS | PB | |
---|---|---|---|---|---|---|

$\Delta \mathit{e}$ | ||||||

NB | PB | PB | PB | PS | NB | |

NS | PB | PS | PS | ZE | NB | |

ZE | PB | PS | ZE | NS | NB | |

PS | PB | ZE | NS | NS | NB | |

PB | PB | NS | NB | NB | NB |

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**MDPI and ACS Style**

Xie, C.-F.; Zhang, H.; Hwang, R.-C.
Application of Intelligent Control in Chromatography Separation Process. *Processes* **2023**, *11*, 3443.
https://doi.org/10.3390/pr11123443

**AMA Style**

Xie C-F, Zhang H, Hwang R-C.
Application of Intelligent Control in Chromatography Separation Process. *Processes*. 2023; 11(12):3443.
https://doi.org/10.3390/pr11123443

**Chicago/Turabian Style**

Xie, Chao-Fan, Hong Zhang, and Rey-Chue Hwang.
2023. "Application of Intelligent Control in Chromatography Separation Process" *Processes* 11, no. 12: 3443.
https://doi.org/10.3390/pr11123443