# A Soft Sensor for Estimation of In-Flow Rate in a Flow Process Using Pole Placement and Kalman Filter Methods

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## Abstract

**:**

## 1. Introduction

## 2. Problem Description

#### 2.1. Flow Process Experimental Setup

#### 2.2. Identification of the Control Valve Model

#### Pseudo Random Signal Response

## 3. Design of Observers

#### 3.1. Pole Placement Technique

#### 3.2. Kalman Filter Technique

## 4. Results

^{3}/h, measurements of proposed technique are also converted from lph to m3/h. After conversion, three performance parameters: mean absolute error (MAE), mean square error (MSE) and root-mean-square error (RMSE) were calculated and have been compared with the results of reference [4]. From Table 4, the proposed technique shows better performance compared with the results of reference [4].

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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References | Technique/Method | Findings |
---|---|---|

[4] | Artificial neural network | It is reported that the models developed using artificial neural networks are for forecasting of flow rate. Lesser computational effort |

[5] | Doppler shift | Accuracy of 0.1 L/min for a 0–6 L/min range. Limited to laminar flow measurement. |

[6] | Particle Counting method Mass estimation method | Suitable for measurement in common and large seed flow rate with accuracy greater than 95%. |

[7] | Thermal anemometry grid sensor | Flow rate deviation of less than 2% for 83% of tested data. |

[8] | Positron emission particle tracking algorithm | Majorly used for turbulent flow rates. |

[11] | Integrated piezoelectric sensor | Integrated piezoelectric sensor placed in straight and bent pipes, with high sensitivity towards 900 bends. |

[12] | Image flow measurement | The flow rate was measured through real-time video acquisition. This is a non-contact technique. |

[13] | Hall probe sensor | The flow rate was measured through a hall probe sensor connected to the rotameter with a magnetic float. Limited range due to magnetic float size. |

Kalman Filter Observer | Pole Placement | |
---|---|---|

IAE | 0.4896 | 0.165 |

ISE | 0.038 | 0.053 |

ITAE | 6.732 | 11.745 |

Actual Flow Rate (lph) | Estimated Flow Rate (lph) | Percentage Error |
---|---|---|

440 | 442 | −0.45 |

460 | 459 | 0.22 |

490 | 489 | 0.20 |

510 | 513 | −0.59 |

540 | 548 | −1.48 |

550 | 552 | −0.36 |

580 | 588 | −1.38 |

610 | 613 | −0.49 |

630 | 642 | −1.90 |

660 | 657 | 0.45 |

680 | 684 | −0.59 |

720 | 728 | −1.11 |

750 | 744 | 0.80 |

780 | 772 | 1.03 |

830 | 827 | 0.36 |

870 | 877 | −0.80 |

920 | 926 | −0.65 |

980 | 984 | −0.41 |

1030 | 1041 | −1.07 |

1080 | 1087 | −0.65 |

1120 | 1134 | −1.25 |

1170 | 1163 | 0.60 |

1210 | 1204 | 0.50 |

1260 | 1265 | −0.40 |

1300 | 1309 | −0.69 |

1350 | 1342 | 0.59 |

1410 | 1400 | 0.71 |

1460 | 1452 | 0.55 |

1500 | 1517 | −1.13 |

1540 | 1543 | −0.19 |

1580 | 1572 | 0.51 |

1630 | 1616 | 0.86 |

1680 | 1673 | 0.42 |

1720 | 1711 | 0.52 |

1780 | 1776 | 0.22 |

Parameters | Proposed Method Using Kalman Filter | Nonlinear Autoregressive Exogenous Model Reported in Reference [4] |
---|---|---|

MAE | 8.6 × 10^{−4} | 0.2041 |

MSE | 5.96 × 10^{−5} | 0.1111 |

RMSE | 0.0077 | 0.3332 |

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**MDPI and ACS Style**

Navada, B.R.; Venkata, S.K.; Rao, S. A Soft Sensor for Estimation of In-Flow Rate in a Flow Process Using Pole Placement and Kalman Filter Methods. *Machines* **2019**, *7*, 63.
https://doi.org/10.3390/machines7040063

**AMA Style**

Navada BR, Venkata SK, Rao S. A Soft Sensor for Estimation of In-Flow Rate in a Flow Process Using Pole Placement and Kalman Filter Methods. *Machines*. 2019; 7(4):63.
https://doi.org/10.3390/machines7040063

**Chicago/Turabian Style**

Navada, Bhagya R., Santhosh K. Venkata, and Swetha Rao. 2019. "A Soft Sensor for Estimation of In-Flow Rate in a Flow Process Using Pole Placement and Kalman Filter Methods" *Machines* 7, no. 4: 63.
https://doi.org/10.3390/machines7040063