# Double-Loop Control Structure for Rotary Drum Granulation Loop

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^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Granulation Loop Model

#### 2.1. Rotary Drum

#### 2.2. Screens

#### 2.3. Crusher

## 3. System Dynamics

#### 3.1. Simulation Setup

#### 3.2. Effect of Crusher Gap Parameters on Process Dynamics

#### 3.3. Recycle of Product-Sized Particles

## 4. Control Strategies

#### 4.1. Background

#### 4.2. Control Strategy 1

#### 4.3. Control Strategy 2

## 5. Double-Loop Control Structure for CC Controllers

#### 5.1. Inner Controller

#### 5.2. Outer Controller

## 6. Simulation Results and Discussion

#### 6.1. Control Strategy 1

#### 6.2. Control Strategy 2

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of a rotary drum granulation loop [7].

**Figure 3.**${d}_{50}$ of the influent/effluent as a response to the step-by-step change of the crusher gap ${d}_{\mathrm{crush}}=3.0\to 2.7\to 2.4\to 2.1\to 2.0$ mm.

**Figure 4.**${d}_{50}$ of the influent/effluent as a response to the step-by-step change of the crusher gap ${d}_{\mathrm{crush}}=2.0\to 1.7\to 1.5\to 1.3$ mm.

**Figure 5.**Total mass flow rates of the influent/effluent as a response to the step-by-step change of the crusher gap ${d}_{\mathrm{crush}}=2.0\to 1.7\to 1.5\to 1.3$ mm.

**Figure 6.**Mass flow rates of over-sized, product-sized and under-sized particles as a response to the step-by-step change of the crusher gap ${d}_{\mathrm{crush}}=2.0\to 1.7\to 1.5\to 1.3$ mm.

**Figure 7.**${d}_{50}$ of the influent/effluent as a response to the step change of the product-sized particle flow: between $92<t<165$, 20% of the particle-sized flow rate was recycled.

**Figure 8.**Schematic diagram of CS1. CT—composition (${d}_{50}$) transmitter; CC—composition (${d}_{50}$) controller.

**Figure 9.**Schematic diagram of CS2. CT—composition (${d}_{50}$) transmitter; CC—composition (${d}_{50}$) controller; $\alpha $—valve opening.

**Figure 10.**The proposed double-loop control algorithm. u—control signal, y—controlled variable, r—reference point [18].

**Figure 11.**Simulation of CS1: manipulatable variable—crusher gap, controlled variable—${d}_{50}$ of the effluent. Controller is turned on at the maximum point of the cycle at $t=13$ h and turned off at $t=46$ h.

**Figure 12.**Simulation of CS1: manipulatable variable—crusher gap, controlled variable—${d}_{50}$ of the effluent. Controller is turned on at the minimum point of the cycle at $t=11$ h and turned off at $t=47$ h.

**Figure 13.**Simulation of CS1: stabilization of granulation loop process. Controller is turned on at the maximum point of the cycle at $t=13$ h and turned off at $t=46$ h.

**Figure 14.**Simulation of CS2: manipulatable variable—valve opening, controlled variable—${d}_{50}$ of the effluent. Controller is turned on at $t=20$ h and turned off at $t=60$ h.

**Figure 15.**Simulation of CS2: mass flow rates. Controller is turned on at the minimum point of the cycle at $t=20$ h and turned off at $t=60$ h.

**Figure 16.**Simulation of CS2: Controller is turned on at the maximum point of the cycle at $t=10$ h and turned off at $t=44$ h.

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

Range of d [mm] | 0–8 |

Number of particle classes | 80 |

Grid type | linear |

Length of granulator [m] | 10 |

Number of compartments | 3 |

$\rho $ [kg·m${}^{-3}$] | 1300 |

${\beta}_{0}$ [s${}^{-1}$] | $1.0\times {10}^{-13}$ |

${\dot{m}}_{\mathrm{sl},\mathrm{i}}$ [kg·h${}^{-1}$] | 1000 |

${d}_{\mathrm{screen},\phantom{\rule{4.pt}{0ex}}\mathrm{upp}}$ [mm] | 3.3 |

${d}_{\mathrm{screen},\phantom{\rule{4.pt}{0ex}}\mathrm{low}}$ [mm] | 1.9 |

${K}_{\mathrm{eff},\phantom{\rule{4.pt}{0ex}}\mathrm{upp}}$ | 45 |

${K}_{\mathrm{eff},\phantom{\rule{4.pt}{0ex}}\mathrm{low}}$ | 45 |

${d}_{\mathrm{crush}}$ [mm] | 2.0–1.3 |

${\sigma}_{\mathrm{crush}}$ | 0.25 |

${T}_{\mathrm{R}}$ [s] | 600 |

Transport delay [s] | 600 |

Time step for RK4 [s] | 20 |

Parameter | Expression |
---|---|

${\tau}_{\mathrm{eff}}$ | $\tau +0.5{T}_{2}$ |

${T}_{\mathrm{eff}}$ | ${T}_{1}+0.5{T}_{2}$ |

${T}_{1}$ | $\frac{{\zeta}_{\mathrm{i}}+\sqrt{{\zeta}_{\mathrm{i}}^{2}-1}}{{\omega}_{\mathrm{i}}}$ |

${T}_{2}$ | $\frac{{\zeta}_{\mathrm{i}}-\sqrt{{\zeta}_{\mathrm{i}}^{2}-1}}{{\omega}_{\mathrm{i}}}$ |

${K}_{\mathrm{c}}$ | $\frac{{T}_{\mathrm{eff}}}{{K}_{\mathrm{p}}^{\mathrm{i}}({T}_{\mathrm{c}}+{\tau}_{\mathrm{eff}})}$ |

${T}_{\mathrm{i}}$ | $\mathrm{min}({T}_{\mathrm{eff}},4({T}_{\mathrm{c}}+{\tau}_{\mathrm{eff}}))$ |

${K}_{\mathrm{p}}^{\mathrm{i}}$ | $\frac{{K}_{\mathrm{p}}}{1+{K}_{\mathrm{c}}^{\mathrm{i}}{K}_{\mathrm{p}}}$ |

${T}_{\mathrm{c}}$ | $-{\tau}_{\mathrm{eff}}<{T}_{\mathrm{c}}<\infty $ |

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**MDPI and ACS Style**

Vesjolaja, L.; Glemmestad, B.; Lie, B. Double-Loop Control Structure for Rotary Drum Granulation Loop. *Processes* **2020**, *8*, 1423.
https://doi.org/10.3390/pr8111423

**AMA Style**

Vesjolaja L, Glemmestad B, Lie B. Double-Loop Control Structure for Rotary Drum Granulation Loop. *Processes*. 2020; 8(11):1423.
https://doi.org/10.3390/pr8111423

**Chicago/Turabian Style**

Vesjolaja, Ludmila, Bjørn Glemmestad, and Bernt Lie. 2020. "Double-Loop Control Structure for Rotary Drum Granulation Loop" *Processes* 8, no. 11: 1423.
https://doi.org/10.3390/pr8111423