# Model-Based Flow Rate Control with Online Model Parameters Identification in Automatic Pouring Machine

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## Abstract

**:**

## 1. Introduction

## 2. Automatic Pouring Machine

## 3. Mathematical Model of Pouring Process

#### 3.1. Motor Model

#### 3.2. Pouring Process Model

#### 3.3. Load Cell Model

## 4. Pouring Flow Rate Control System

#### 4.1. Feedforward Control Using Inverse Dynamics of Pouring Process and Motor

#### 4.2. Derivation System of Model Parameters from Ladle Shape

#### 4.3. Online Model Parameters Identification

#### 4.4. Updating Controller’s Parameters

#### 4.5. Reference Function of Model Parameters Using a Look-Up Table for Fast Model Parameters Identification

## 5. Experimental Verification

## 6. Conclusions

- 1.
- In the pouring process model, the liquid volume over the pouring mouth was represented precisely for realizing the high-precision pouring in the ladle’s large tilting angle.
- 2.
- The model parameters for the ladle shape were derived systematically from the 3D-computer aided design (CAD) data through the subroutine.
- 3.
- The golden section method identified the ladle’s tilting angle at the start of the outflow liquid for quickly completing the model parameters identification. Similarly, the Gauss–Newton method identified the liquid density and the flow rate coefficient. Moreover, the look-up table was used in the reference function of the model parameters.
- 4.
- In the experiments using the tilting-ladle-type automatic pouring machine, the ladle’s water was poured precisely by updating the controller’s parameters after the proposed online model parameters identification.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Abbreviations

CAE | Computer-Aided Engineering |

DC | Direct Current |

3D-CAD | Three-Dimensional Computer-Aided Design system |

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**Figure 12.**Model parameters obtained from ladle shape shown in Figure 3.

Number of Pouring | Target Weight [kg] | Mean Absolute Error, ${\mathit{M}\mathit{A}\mathit{E}}_{\mathit{e}\mathit{x}\mathit{p}-\mathit{r}\mathit{e}\mathit{f}}$ [kg] | Mean Absolute Error, ${\mathit{M}\mathit{A}\mathit{E}}_{\mathit{e}\mathit{x}\mathit{p}-\mathit{i}\mathit{d}\mathit{e}\mathit{n}}$ [kg] |
---|---|---|---|

1-1 | 0.80 | 0.1347 | 0.0527 |

1-2 | 1.00 | 0.1553 | 0.0397 |

1-3 | 1.20 | 0.0523 | 0.0420 |

2-4 | 1.40 | 0.0640 | 0.0386 |

2-5 | 1.60 | 0.0498 | 0.0490 |

Number of Pouring | Parameter Used in Experiment | Identified Parameters | Processing Time in Proposed Approach [s] | Processing Time in Conventional Approach (Downhill Simplex Method) [s] | ||||
---|---|---|---|---|---|---|---|---|

${\mathit{\theta}}_{\mathit{s}}$ | $\mathit{\rho}$ | c | ${\mathit{\theta}}_{\mathit{s}}$ | $\mathit{\rho}$ | c | |||

1-1 | 10.0 | 1000 | 0.80 | 13.3 | 999.8 | 0.76 | 2.69 | 55.38 |

1-2 | 17.3 | 999.8 | 0.76 | 21.0 | 996.9 | 0.77 | 2.59 | 50.18 |

1-3 | 31.5 | 996.9 | 0.77 | 31.0 | 995.1 | 0.76 | 2.38 | 60.54 |

2-4 | 19.7 | 995.1 | 0.76 | 20.7 | 993.8 | 0.74 | 3.01 | 79.57 |

2-5 | 34.9 | 993.8 | 0.74 | 35.2 | 991.1 | 0.72 | 3.65 | 78.08 |

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**MDPI and ACS Style**

Kabasawa, N.; Noda, Y.
Model-Based Flow Rate Control with Online Model Parameters Identification in Automatic Pouring Machine. *Robotics* **2021**, *10*, 39.
https://doi.org/10.3390/robotics10010039

**AMA Style**

Kabasawa N, Noda Y.
Model-Based Flow Rate Control with Online Model Parameters Identification in Automatic Pouring Machine. *Robotics*. 2021; 10(1):39.
https://doi.org/10.3390/robotics10010039

**Chicago/Turabian Style**

Kabasawa, Nobutoshi, and Yoshiyuki Noda.
2021. "Model-Based Flow Rate Control with Online Model Parameters Identification in Automatic Pouring Machine" *Robotics* 10, no. 1: 39.
https://doi.org/10.3390/robotics10010039