# Dynamic Matrix Control for the Thermal Power of MHTGR-Based Nuclear Steam Supply System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. MHTGR-Based NSSS

#### 2.1. System Description

#### 2.2. Inner Loop Control Scheme

**Remark**

**1.**

#### 2.3. Problem Formulation

## 3. Dynamic Matrix Control for Thermal Power

#### 3.1. Cascade Control Scheme

**Remark**

**2.**

#### 3.2. Step Response Model

#### 3.2.1. Step Signal Test

**Remark**

**3.**

#### 3.2.2. State Space Model

#### 3.3. Optimization

**Remark**

**4.**

#### 3.4. Estimator

**Remark**

**5.**

**Remark**

**6.**

**Remark**

**7.**

#### 3.5. Tuning of the DMC

- large value $R$ adds the cost of using large values of the derivative revision signal, to the cost of missing a small amount of the thermal power tracking. Since the step response coefficient matrix is sampled around a specified operating point, the inevitable model error makes it meaningless to tune the parameter $R$ aggressively by solving the QP.
- By solving Equation (9), small value of $R$ may result in a large $\Delta u$. From Equation (13), a large $\Delta u$ causes large variation in estimator error, and hence should be avoided.

## 4. Application to NSSS Thermal Power Control

#### 4.1. Implementation of DMC

#### 4.2. Simulation Setting and Results

#### 4.3. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Lanning, D.D. Modularized high-temperature gas-cooled reactor systems. Nucl. Technol.
**1989**, 88, 139–156. [Google Scholar] [CrossRef] - Wu, Z.; Lin, D.; Zhong, D. The design features of the HTR-10. Nucl. Eng. Des.
**2002**, 218, 25–32. [Google Scholar] [CrossRef] - Dong, Z.; Zhang, Z.; Dong, Y.; Huang, X. Multi-layer perception based model predictive control for the thermal power of nuclear superheated-steam supply systems. Energy
**2018**, 151, 116–125. [Google Scholar] [CrossRef] - Shtessel, Y.B. Enhanced Sliding mode control of the space nuclear reactor system. IEEE Trans. Aero. Electron. Syst.
**1998**, 34, 579–589. [Google Scholar] [CrossRef] - Huang, Z.; Edwards, R.M.; Lee, K.Y. Fuzzy-adapted recursive sliding-mode controller design for a nuclear power plant control. IEEE Trans. Nucl. Sci.
**2004**, 51, 256–266. [Google Scholar] [CrossRef] - Qaiser, S.H.; Bhatti, A.I.; Iqbal, M.; Samar, R.; Qadir, J. Model validation and higher order sliding mode controller design for a research reactor. Ann. Nucl. Energy
**2009**, 36, 37–45. [Google Scholar] [CrossRef] - Ansarifar, G.R.; Rafiei, M. Higher order sliding mode controller design for a research nuclear reactor considering the effect of xenon concentration during load following operation. Ann. Nucl. Energy
**2015**, 75, 728–735. [Google Scholar] [CrossRef] - Dong, Z. Physically-based power-level control for modular high temperature gas-cooled reactors. IEEE Trans. Nucl. Sci.
**2012**, 59, 2531–2549. [Google Scholar] [CrossRef] - Dong, Z.; Pan, Y.; Zhang, Z.; Dong, Y.; Huang, X. Model-free adaptive control for nuclear superheated-steam supply systems. Energy
**2017**, 135, 53–67. [Google Scholar] [CrossRef] - Eom, M.; Chwa, D.; Baang, D. Robust disturbance observer-based feedback linearization control for a research reactor considering a power change rate constraint. IEEE Trans. Nucl. Sci.
**2015**, 62, 1301–1312. [Google Scholar] [CrossRef] - Han, S.; Sun, L.; Shen, J.; Pan, L.; Lee, K.Y. Optimal Load-Tracking Operation of Grid-Connected Solid Oxide Fuel Cells through Set Point Scheduling and Combined L1-MPC Control. Energies
**2018**, 11, 801. [Google Scholar] [CrossRef] - Kong, X.B.; Liu, X.J.; Lee, Y.K. Nonlinear multivariable hierarchical model predictive control for boiler-turbine system. Energy
**2015**, 93, 309–322. [Google Scholar] [CrossRef] - Na, M.G.; Shin, S.H.; Kim, W.C. A model predictive controller for nuclear reactor power. Nucl. Eng. Technol.
**2003**, 35, 399–411. [Google Scholar] [CrossRef] - Na, M.G.; Upadhyaya, B.R. Application of model predictive control strategy based on fuzzy identification to an SP-100 space reactor. Ann. Nucl. Energy
**2006**, 33, 1467–1478. [Google Scholar] [CrossRef] - Na, M.G.; Hwang, I.J.; Lee, Y.J. Design of a fuzzy model predictive power controller for pressurized water reactors. IEEE Trans. Nucl. Sci.
**2006**, 53, 1504–1514. [Google Scholar] [CrossRef] - Etchepareborda, A.; Lolich, J. Research reactor power controller design using an output feedback nonlinear receding horizon control method. Nucl. Eng. Des.
**2007**, 237, 268–276. [Google Scholar] [CrossRef] - Eliasi, H.; Menhaj, M.B.; Davilu, H. Robust nonlinear model predictive control for a PWR nuclear power plant. Prog. Nucl. Energy
**2012**, 54, 177–185. [Google Scholar] [CrossRef] - Mayne, D.Q.; Rawlings, J.B.; Rao, C.V.; Scokaert, P.O.M. Constrained model predictive control: Stability and optimality. Automatica
**2000**, 36, 789–814. [Google Scholar] [CrossRef] - Vajpayee, V.; Mukhopadhyay, S.; Tiwari, A.P. Data-Driven Subspace Predictive Control of a Nuclear Reactor. IEEE Trans. Nucl. Sci.
**2018**, 65, 666–679. [Google Scholar] [CrossRef] - Moon, U.C.; Lee, K. Step-response model development for dynamic matrix control of a drum-type boiler-turbine system. IEEE Trans. Energy Convers.
**2009**, 24, 423–430. [Google Scholar] [CrossRef] - Moon, U.C.; Lee, Y.; Lee, K.Y. Practical dynamic matrix control for thermal power plant coordinated control. Control Eng. Pract.
**2018**, 71, 154–163. [Google Scholar] [CrossRef] - Qin, S.; Badgwell, T. A survey of industrial model predictive control technology. Control Eng. Pract.
**2003**, 11, 733–764. [Google Scholar] [CrossRef] [Green Version] - Zhang, Z.; Wu, Z.; Wang, D.; Xu, Y.; Sun, Y.; Li, F.; Dong, Y. Current status and technical description of Chinese 2 × 250 MWth HTR-PM demonstration plant. Nucl. Eng. Des.
**2009**, 239, 2265–2274. [Google Scholar] [CrossRef] - Mercorelli, P. Trajectory tracking using MPC and a velocity observer for flat actuator systems in automotive applications. In Proceedings of the 2008 IEEE International Symposium on Industrial Electronics, Cambridge, UK, 30 June–2 July 2008; pp. 1138–1143. [Google Scholar]
- Morari, M.; Ricker, N.L. Model Predictive Control Toolbox—For Use with MATLAB, 2nd ed.; The MathWorks, Inc.: Natick, MA, USA, 1995. [Google Scholar]
- Dong, Z.; Pan, Y.; Zhang, Z.; Dong, Y.; Huang, X. Dynamical modeling and simulation of the six-modular high temperature gas-cooled reactor plant HTR-PM600. Energy
**2016**, 155, 971–991. [Google Scholar] [CrossRef]

**Figure 2.**Schematic diagram of NSSS cascade control system (Inner loop: NC-based controller; Outer loop: MPC-based optimizer).

**Figure 4.**Open loop control of NSSS thermal power by the coordinated control law in [9].

Parameters | Unit | Value |
---|---|---|

Thermal power of reactor module | MW_{th} | 250 |

Core power density | MW/m^{3} | 3.22 |

Electricity efficiency | % | 42 |

Core diameter/height | m | 3/11 |

Helium pressure | MPa | 7 |

Helium temperature at reactor inlet/outlet | °C | 250/750 |

Helium flowrate | kg/s | 96 |

Steam pressure | MPa | 13.24 |

Steam temperature | °C | 576 |

Steam flowrate | kg/s | 96 |

Module | Input | Output |
---|---|---|

MHTGR | Rod speed | Neutron flux |

OTSG | Helium flowrate | Helium temperature |

Feedwater flow | Live steam temperature |

© 2018 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**

Jiang, D.; Dong, Z.; Liu, M.; Huang, X.
Dynamic Matrix Control for the Thermal Power of MHTGR-Based Nuclear Steam Supply System. *Energies* **2018**, *11*, 2651.
https://doi.org/10.3390/en11102651

**AMA Style**

Jiang D, Dong Z, Liu M, Huang X.
Dynamic Matrix Control for the Thermal Power of MHTGR-Based Nuclear Steam Supply System. *Energies*. 2018; 11(10):2651.
https://doi.org/10.3390/en11102651

**Chicago/Turabian Style**

Jiang, Di, Zhe Dong, Miao Liu, and Xiaojin Huang.
2018. "Dynamic Matrix Control for the Thermal Power of MHTGR-Based Nuclear Steam Supply System" *Energies* 11, no. 10: 2651.
https://doi.org/10.3390/en11102651