# The Application of a New PID Autotuning Method for the Steam/Water Loop in Large Scale Ships

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## Abstract

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## 1. Introduction

- when the water turns between steam and liquid, the false water level phenomenon appears for reason of the shrink and swell in the water, which makes the drum water level control loop a non-minimum phase system [2].
- the water in the condenser goes to the deaerator, hence, strong interactions exist in the water control loops of the deaerator and the condenser.
- the steam required in the deaerator is from the exhaust manifold, which leads to strong coupling in the pressure control loops of the deaerator and exhaust manifold.
- the amount of required steam in the deaerator changes with the feedwater flow rate. Hence, the water level and the pressure are two strong coupling variables in the deaerator.

## 2. Introduction of the Steam/Water Loop

## 3. Detailed Theory of KC Autotuning Method

- (1)
- Obtain the critical frequency $\overline{\omega}$ of the system ($\overline{\omega}$ is usually critical frequency, but might be different);
- (2)
- Conduct sine tests around the operating points on the steam/water loop;
- (3)
- According to the loop margin requirements, calculate a ‘forbidden region’ on the Nyquist plane;
- (4)
- Calculate parameters for the PID controller for the points on the region edge (for $\alpha $ from ${0}^{\circ}$ to ${90}^{\circ}$);
- (5)
- Search for the point, where the slope of the loop $L\left(j\omega \right)$ is the same with the slope of the ‘forbidden region’;
- (6)
- The parameters for the PID controller are obtained from step 5).

#### 3.1. Slope of the ‘Forbidden Region’

#### 3.2. Slope of the Loop $L\left(J\omega \right)$

#### 3.2.1. Calculation for $C\left(J\omega \right)$ and Its Derivation

#### 3.2.2. Calculation for $P\left(J\omega \right)$ and Its Derivation

#### 3.3. Application to Mimo System

- (1)
- Apply sine test around the operating points on one of the sub-loops, while keeping other sub-loops to work at their own operating points. And the controller parameters can be calculated for the selected loop, with the magnitude and phase obtained from the sine test;
- (2)
- Keep the previous sub-loop working at its operating point with the obtained PID control, and conduct a new sine test on one the other sub-loops. The magnitude and phase can be obtained for the new sub-loop and the controller can be calculated;
- (3)
- Repeat step 2 for each sub-loop until the output magnitude and phase do not change significantly between consecutive tests.
- (4)
- The parameters for the PID controller can be obtained for all the sub-loops after step 3 is completed.

## 4. A Brief Introduction of Other PID Autotuners

## 5. Experiments and Results Analyses

#### 5.1. A Simple Single Input Single Output System Example

#### 5.2. Simulation on Steam/Water Loop in Large Scale Ships

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Scheme of steam/water loop [38] (reproduced with permission from Zhao, S.; Maxim, A.; Liu, S.; De Keyser, R.; and Ionescu, C, Processes; published by MDPI, 2018).

**Figure 2.**Graphic illustration of the KC autotuning principle [43] (reproduced with permission from Zhao, S.; Ionescu, C.M.; De Keyser, R.; and Liu, S. In 3rd IFAC Conference in Advances in Proportional-Integral-Derivative Control; published by Elsevier, 2018).

**Figure 3.**The scheme of sine test to obtain the knowledge of the process around the operating point [39] (reproduced with permission from De Keyser, R., Muresan, C. I. and Ionescu, C. M. A novel auto-tuning method for fractional order PI/PD controllers. ISA transactions, published by Elsevier, 2016).

**Figure 8.**Outputs of the steam/water loop with different PID autotuning methods (The outputs are listed on the left and the inputs are listed on the right).

**Figure 9.**Outputs of the steam/water loop with KC based PID controller and MPC (The outputs are listed on the left, and the inputs are listed on the right).

System Outputs | Operating Points | Range | Units |
---|---|---|---|

Drum water level | 1.79 | [1.39–2.19] | m |

Exhaust manifold pressure | 100.03 | [87.03–133.8] | MPa |

Deaerator pressure | 30 | [24.9–43.86] | KPa |

Deaerator water level | 0.7 | [0.49–0.89] | m |

Condenser water level | 0.5 | [0.32–0.63] | m |

PID | ${\mathit{k}}_{\mathit{p}}$ | ${\mathit{T}}_{\mathit{i}}$ | ${\mathit{T}}_{\mathit{d}}$ |
---|---|---|---|

AH | 85.42 | 6.81 | 1.70 |

PM | 100.66 | 10.46 | 2.62 |

KR | 52.86 | 12.67 | 3.17 |

KC | 257.76 | 8.49 | 2.12 |

Time (s) | 2–300 | 300–600 | 600–900 | 900–1200 | 1200–1500 |
---|---|---|---|---|---|

Drum Water Level (m) | 2 | 2 | 2 | 2 | 2 |

Exhaust Manifold Pressure (MPa) | 100.03 | 116 | 116 | 116 | 116 |

Deaerator Pressure (KPa) | 30 | 30 | 35 | 35 | 35 |

Deaerator Water Level (m) | 0.7 | 0.7 | 0.7 | 0.8 | 0.8 |

Condenser Water Level (m) | 0.5 | 0.5 | 0.5 | 0.5 | 0.6 |

Loop 1 | Loop 2 | Loop 3 | Loop 4 | Loop 5 | ||
---|---|---|---|---|---|---|

AH | ${k}_{p}$ | 0.83 | 0.28 | 0.27 | 2.77 | 2.87 |

${T}_{i}$ | 76.62 | 20.48 | 42.00 | 57.77 | 31.69 | |

${T}_{d}$ | 19.16 | 5.12 | 10.50 | 14.44 | 7.92 | |

PM | ${k}_{p}$ | 0.98 | 0.31 | 0.32 | 3.26 | 3.39 |

${T}_{i}$ | 117.76 | 24.14 | 49.56 | 88.79 | 48.70 | |

${T}_{d}$ | 29.44 | 6.03 | 12.39 | 22.20 | 12.17 | |

KR | ${k}_{p}$ | 0.98 | 0.29 | 0.29 | 3.28 | 3.50 |

${T}_{i}$ | 102.64 | 29.99 | 63.33 | 76.60 | 46.92 | |

${T}_{d}$ | 25.66 | 7.50 | 15.83 | 19.15 | 11.73 | |

KC | ${k}_{p}$ | 2.47 | 0.33 | 0.31 | 8.34 | 8.67 |

${T}_{i}$ | 96.24 | 31.48 | 64.56 | 72.02 | 39.50 | |

${T}_{d}$ | 24.06 | 7.87 | 16.14 | 18.01 | 9.88 |

Index | Autotuners | Loop 1 | Loop 2 | Loop 3 | Loop 4 | Loop 5 |
---|---|---|---|---|---|---|

$IARE$ | AH | 2.2063 | 1.5750 | 2.7951 | 3.6710 | 4.9961 |

PM | 2.9400 | 1.5464 | 2.6325 | 4.7586 | 6.3090 | |

KR | 2.5294 | 1.5087 | 3.1779 | 4.0973 | 5.9431 | |

KC | 1.2606 | 1.4744 | 3.2924 | 2.0025 | 2.8126 | |

$ISU$ | AH | 0.0288 | 1.0234 | 0.1766 | 0.2405 | 2.9971 |

PM | 0.0425 | 0.9210 | 0.1799 | 0.2934 | 2.9572 | |

KR | 0.0345 | 0.8095 | 0.2205 | 0.2586 | 2.9566 | |

KC | 0.0204 | 0.7241 | 0.2043 | 0.1284 | 2.6393 |

Index | loops | AH vs. PM | AH vs. KR | AH vs. KC | PM vs. KR | PM vs. KC | KR vs. KC |
---|---|---|---|---|---|---|---|

$RIARE$ | loop 1 | 0.7504 | 0.8723 | 1.7502 | 1.1623 | 2.3322 | 2.0064 |

loop 2 | 1.0185 | 1.0440 | 1.0683 | 1.0250 | 1.0488 | 1.0233 | |

loop 3 | 1.0618 | 0.8795 | 0.8490 | 0.8284 | 0.7996 | 0.9652 | |

loop 4 | 0.7715 | 0.8960 | 1.8332 | 1.1614 | 2.3763 | 2.0461 | |

loop 5 | 0.7919 | 0.8406 | 1.7763 | 1.0616 | 2.2431 | 2.1130 | |

$RISU$ | loop 1 | 0.6768 | 0.8342 | 1.4100 | 1.2325 | 2.0834 | 2.0834 |

loop 2 | 1.1112 | 1.2643 | 1.4134 | 1.1377 | 1.2720 | 1.2720 | |

loop 3 | 0.9813 | 0.8007 | 0.8645 | 0.8159 | 0.8810 | 0.8810 | |

loop 4 | 0.8199 | 0.9301 | 1.8739 | 1.1344 | 2.2855 | 2.2855 | |

loop 5 | 1.0135 | 1.0137 | 1.1356 | 1.0002 | 1.1205 | 1.1205 | |

J | 0.8997 | 0.9375 | 1.3974 | 1.0559 | 1.6442 | 1.5796 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhao, S.; Liu, S.; De Keyser, R.; Ionescu, C.-M.
The Application of a New PID Autotuning Method for the Steam/Water Loop in Large Scale Ships. *Processes* **2020**, *8*, 196.
https://doi.org/10.3390/pr8020196

**AMA Style**

Zhao S, Liu S, De Keyser R, Ionescu C-M.
The Application of a New PID Autotuning Method for the Steam/Water Loop in Large Scale Ships. *Processes*. 2020; 8(2):196.
https://doi.org/10.3390/pr8020196

**Chicago/Turabian Style**

Zhao, Shiquan, Sheng Liu, Robain De Keyser, and Clara-Mihaela Ionescu.
2020. "The Application of a New PID Autotuning Method for the Steam/Water Loop in Large Scale Ships" *Processes* 8, no. 2: 196.
https://doi.org/10.3390/pr8020196