# Design of a Dead-Time Compensator Robust H∞ State Feedback Temperature Controller for a Precalciner of a Cement Rotary Kiln

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Identification of the Temperature Dynamic Behaviour in a Precalciner

#### 2.2. Model Validation

#### 2.3. Design of a DTC-H∞-SFC Controller

- (i)
- $(A,{B}_{1})$ is stabilizable and $({C}_{1},A)$ is detectable;
- (ii)
- $(A,{B}_{2})$ is stabilizable and $({C}_{2},A)$ is detectable.

## 3. Results and Discussion

^{3}/h. As a result, the hot gases that reach the precalciner (from the rotary kiln) decrease in temperature and cause a variation in the precalciner temperature. The DTC-H∞-SFC controller completely rejects this negative effect in a time period of approximately 800 s, while the PI refuses it in a time period of approximately 2300 s, that is in a time interval 2.87 larger.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Diagram of the designed precalciner temperature control system with the designed DTC-H∞-SFC controller.

**Figure 6.**Time response of the control system with the DTC-H∞-SFC controller designed, as well as the control effort against a change in the command signal from 920 to 950 °C.

**Figure 7.**Performance comparative results of the control system with DTC-H∞-SFC vs. DTC+PI controllers against variations in the command signal, and external disturbance.

Model Structure | Model Order | Performance Index(FIT) | |||||
---|---|---|---|---|---|---|---|

na | nb | nc | nd | nf | nk | ||

ARMAX | 4 | 4 | 4 | - | - | 10 | 90.04% |

BJ | - | 4 | 4 | 4 | 4 | 9 | 86.72% |

ARX | 4 | 4 | - | - | - | 10 | 84.25% |

OE | - | 2 | - | - | 2 | 11 | 85.45% |

**Table 2.**Comparative results of integral squared error (ISE) performance index of the control system with the DTC-H∞-SFC and DTC+PI designed controllers and external disturbance.

ISE | ISE | |
---|---|---|

(NOMINAL) | (DISTURBANCE) | |

DTC+PI | 14,149 | 140 |

DTC-H∞-SFC | 13,230 | 45 |

**Table 3.**Comparative results of integral absolute error (IAE) performance index of the control system with the DTC-H∞-SFC and DTC+PI designed controllers and external disturbance.

IAE | IAE | |
---|---|---|

(NOMINAL) | (DISTURBANCE) | |

DTC+PI | 302 | 42 |

DTC-H∞-SFC | 277 | 17 |

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**MDPI and ACS Style**

Salcedo-Hernández, J.; Rivas-Perez, R.; Sotomayor-Moriano, J.
Design of a Dead-Time Compensator Robust H∞ State Feedback Temperature Controller for a Precalciner of a Cement Rotary Kiln. *Appl. Sci.* **2022**, *12*, 2594.
https://doi.org/10.3390/app12052594

**AMA Style**

Salcedo-Hernández J, Rivas-Perez R, Sotomayor-Moriano J.
Design of a Dead-Time Compensator Robust H∞ State Feedback Temperature Controller for a Precalciner of a Cement Rotary Kiln. *Applied Sciences*. 2022; 12(5):2594.
https://doi.org/10.3390/app12052594

**Chicago/Turabian Style**

Salcedo-Hernández, José, Raul Rivas-Perez, and Javier Sotomayor-Moriano.
2022. "Design of a Dead-Time Compensator Robust H∞ State Feedback Temperature Controller for a Precalciner of a Cement Rotary Kiln" *Applied Sciences* 12, no. 5: 2594.
https://doi.org/10.3390/app12052594