# Dependable Sensor Fault Reconstruction in Air-Path System of Heavy-Duty Diesel Engines

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- A diesel engine air-path system is studied completely, and by considering the sensor faults and disturbances which can affect the system, a complete model of the air-path system is presented.
- The nonlinear discontinuous term causes chattering of fault reconstruction, while proper higher-order sliding mode observer can weaken this problem. A higher-order sliding mode observer can also eliminate the deviation from true states and fault reconstruction in the presence of disturbances. Therefore, in the next step, a second-order sliding mode observer is designed.
- Although this paper’s approach is developed for a diesel engine air-path system, it can be broadened to other industrial processes and applications for reconstructing various possible faults in the presence of disturbances.

## 2. Diesel Engine Air-Path Modeling

#### 2.1. Diesel Engine Overview

#### 2.2. Manifold Modeling

#### 2.3. Turbocharger Speed Modeling

#### 2.4. EGR Mass Flow Modeling

#### 2.5. Cylinder Flow Modeling

#### 2.6. Unified Model of a Diesel Engine Air-Path

#### 2.7. Disturbance and Sensor Fault Modeling

## 3. Sensor Fault Reconstruction Using Second-Order Sliding Mode Observer

## 4. Simulation Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Nguyen, N.P.; Mung, N.X.; Thanh Ha, L.N.N.; Huynh, T.T.; Hong, S.K. Finite-Time Attitude Fault Tolerant Control of Quadcopter System via Neural Networks. Mathematics
**2020**, 8, 1541. [Google Scholar] [CrossRef] - Ghanbarpour, K.; Bayat, F.; Jalilvand, A. Wind turbines sustainable power generation subject to sensor faults: Observer-based MPC approach. Int. Trans. Electr. Energy Syst.
**2020**, 30, e12174. [Google Scholar] [CrossRef] - Gonzalez-Prieto, I.; Duran, M.J.; Rios-Garcia, N.; Barrero, F.; Martin, C. Open-switch fault detection in five-phase induction motor drives using model predictive control. IEEE Trans. Ind. Electron.
**2017**, 65, 3045–3055. [Google Scholar] [CrossRef] - Bahrami, M.; Naraghi, M.; Zareinejad, M. Adaptive super-twisting observer for fault reconstruction in electro-hydraulic systems. ISA Trans.
**2018**, 76, 235–245. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Khan, A.; Hwang, H.; Kim, H.S. Synthetic Data Augmentation and Deep Learning for the Fault Diagnosis of Rotating Machines. Mathematics
**2021**, 9, 2336. [Google Scholar] [CrossRef] - Ghanbarpour, K.; Bayat, F.; Jalilvand, A. Dependable power extraction in wind turbines using model predictive fault tolerant control. Int. J. Electr. Power Energy Syst.
**2020**, 118, 105802. [Google Scholar] [CrossRef] - Luenberger, D. An introduction to observers. IEEE Trans. Autom. Control
**1971**, 16, 596–602. [Google Scholar] [CrossRef] - Alwi, H.; Edwards, C.; Tan, C.P. Fault Detection and Fault-Tolerant Control Using Sliding Modes; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2011. [Google Scholar]
- Thanh, H.L.N.N.; Mung, N.X.; Nguyen, N.P.; Phuong, N.T. Perturbation observer-based robust control using a multiple sliding surfaces for nonlinear systems with influences of matched and unmatched uncertainties. Mathematics
**2020**, 8, 1371. [Google Scholar] [CrossRef] - Edwards, C.; Spurgeon, S.K.; Patton, R.J. Sliding mode observers for fault detection and isolation. Automatica
**2000**, 36, 541–553. [Google Scholar] [CrossRef] - Taherkhani, A.; Bayat, F. Wind turbines robust fault reconstruction using adaptive sliding mode observer. IET Gener. Transm. Distrib.
**2019**, 13, 3096–3104. [Google Scholar] [CrossRef] - Zhang, L.; Obeid, H.; Laghrouche, S.; Cirrincione, M. Second order sliding mode observer of linear induction motor. IET Electr. Power Appl.
**2019**, 13, 38–47. [Google Scholar] [CrossRef] - Lin, C.; Sun, S.; Walker, P.; Zhang, N. Accelerated adaptive second order super-twisting sliding mode observer. IEEE Access
**2018**, 7, 25232–25238. [Google Scholar] [CrossRef] - Levant, A. Robust exact differentiation via sliding mode technique. Automatica
**1998**, 34, 379–384. [Google Scholar] [CrossRef] - Boiko, I.; Fridman, L.; Pisano, A.; Usai, E. Analysis of chattering in systems with second-order sliding modes. IEEE Trans. Autom. Control
**2007**, 52, 2085–2102. [Google Scholar] [CrossRef] - Mohamed, G.; Sofiane, A.A.; Nicolas, L. Adaptive super twisting extended state observer based sliding mode control for diesel engine air path subject to matched and unmatched disturbance. Math. Comput. Simul.
**2018**, 151, 111–130. [Google Scholar] [CrossRef] - Sankar, G.S.; Shekhar, R.C.; Manzie, C.; Sano, T.; Nakada, H. Model predictive controller with average emissions constraints for diesel airpath. Control Eng. Pract.
**2019**, 90, 182–189. [Google Scholar] [CrossRef] [Green Version] - Kekik, B.; Akar, M. Model predictive control of diesel engine air path with actuator delays. IFAC-PapersOnLine
**2019**, 52, 150–155. [Google Scholar] [CrossRef] - Yin, L.; Turesson, G.; Tunestål, P.; Johansson, R. Sliding mode control on receding horizon: Practical control design and application. Control Eng. Pract.
**2021**, 109, 104724. [Google Scholar] [CrossRef] - Chua, W.S.; Chan, J.C.L.; Tan, C.P.; Chong, E.K.P.; Saha, S. Robust fault reconstruction for a class of nonlinear systems. Automatica
**2020**, 113, 108718. [Google Scholar] [CrossRef] - Chu, Z.; Meng, F.; Zhu, D.; Luo, C. Fault reconstruction using a terminal sliding mode observer for a class of second-order MIMO uncertain nonlinear systems. ISA Trans.
**2020**, 97, 67–75. [Google Scholar] [CrossRef] - Chen, L.; Shi, P.; Liu, M. Fault reconstruction for Markovian jump systems with iterative adaptive observer. Automatica
**2019**, 105, 254–263. [Google Scholar] [CrossRef] - Zhirabok, A.; Shumsky, A.; Zuev, A. Fault diagnosis in linear systems via sliding mode observers. Int. J. Control
**2019**, 94, 327–335. [Google Scholar] [CrossRef] - Tan, C.P.; Edwards, C. Robust fault reconstruction in uncertain linear systems using multiple sliding mode observers in cascade. IEEE Trans. Autom. Control
**2010**, 55, 855–867. [Google Scholar] - Li, R.; Yang, Y. Sliding-mode observer-based fault reconstruction for TS fuzzy descriptor systems. IEEE Trans. Syst. Man Cybern. Syst.
**2019**, 51, 5046–5055. [Google Scholar] [CrossRef] - Dai, C.; Liu, Y.; Sun, H. Fault Reconstruction for Lipschitz Nonlinear Systems Using Higher Terminal Sliding Mode Observer. J. Shanghai Jiaotong Univ. Sci.
**2020**, 25, 630–638. [Google Scholar] [CrossRef] - Mollenhauer, K.; Tschöke, H.; Johnson, K.G. Handbook of Diesel Engines; Springer: Berlin, Germany, 2010; Volume 1. [Google Scholar]
- Guzzella, L.; Onder, C. Introduction to Modeling and Control of Internal Combustion Engine Systems; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2009. [Google Scholar]
- Eriksson, L.; Nielsen, L. Modeling and Control of Engines and Drivelines; John Wiley & Sons: Hoboken, NJ, USA, 2014. [Google Scholar]
- Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V. Linear Matrix Inequalities in System and Control Theory; SIAM: Philadelphia, PA, USA, 1994. [Google Scholar]
- Tan, C.P.; Edwards, C. Sliding mode observers for robust detection and reconstruction of actuator and sensor faults. Int. J. Robust Nonlinear Control IFAC-Affil. J.
**2003**, 13, 443–463. [Google Scholar] [CrossRef]

**Figure 3.**The manifold gas pressure sensor fault and its reconstruction using the proposed SOSMO method.

**Figure 4.**The EGR mass flow rate sensor fault and its reconstruction using the proposed SOSMO method.

**Figure 5.**The EGR mass flow rate sensor fault and its reconstruction using SMO method [31].

Symbol | Description | Value | Unit |
---|---|---|---|

${\eta}_{vol}$ | Volumetric efficiency | 0.043 | - |

${V}_{d}$ | Displaced volume | 12.4 | m${}^{3}$ |

${\omega}_{e}$ | Engine speed | 1500 | $\frac{\mathrm{rad}}{min}$ |

${V}_{im}$ | Intake manifold volume | 0.00192 | m${}^{3}$ |

${T}_{im}$ | Intake gas temperature | 315.2 | K |

${P}_{amb}$ | The downstream pressure ratio of EGR | $1.55\times {10}^{5}$ | Pa |

${R}_{c}$ | The radius of the compressor blade | $45\times {10}^{-3}$ | m |

${\phi}_{c}$ | Volumetric flow efficiency | 0.6 | - |

${T}_{amb}$ | Ambient temperature of the intake gas | 750 | K |

${C}_{{P}_{a}}$ | Heat capacity of intake gas | 1.1 | - |

${R}_{a}$ | Ideal gas constant for the air | 287 | $\frac{\mathrm{J}}{\mathrm{kg}\xb7\mathrm{K}}$ |

${\eta}_{c}$ | Compressor efficiency | 0.73 | - |

${\omega}_{t}$ | Turbocharger speed | $6.7\times {10}^{4}$ | $\frac{\mathrm{rad}}{min}$ |

${J}_{t}$ | Rotating inertia of the turbocharger | $75\times {10}^{-4}$ | kg·m${}^{2}$ |

${P}_{im}$ | Intake gas pressure | $1.9\times {10}^{5}$ | Pa |

${\gamma}_{a}$ | Heat capacity ratio of intake gas | 2.2 | - |

${A}_{vg{t}_{max}}$ | The maximum nominal flow area of VGR | 8.5 | m${}^{2}$ |

${P}_{em}$ | Exhaust pressure before the turbine | $2.25\times {10}^{5}$ | Pa |

${f}_{\mathrm{\Pi}}$ | Mass flow depends on the pressure ratio | 0.4 | - |

${\eta}_{tm}$ | Turbine efficiency | 0.526 | - |

${C}_{pe}$ | Heat capacity of exhaust gas | 1.31 | - |

${T}_{em}$ | Gas exhaust temperature before the turbine | 693 | K |

${R}_{e}$ | Ideal gas constant for exhaust gas | 22.55 | $\frac{\mathrm{J}}{\mathrm{kg}\xb7\mathrm{K}}$ |

${\gamma}_{e}$ | Heat capacity ratio of exhaust gas | 1.7 | - |

${A}_{eg{r}_{max}}$ | Maximum nominal flow area of EGR | 8.4 | m${}^{2}$ |

${\psi}_{egr}$ | The function of the pressure ratio | 1.7 | - |

Sensor Fault | ${\mathit{J}}_{\mathit{observer}}$ | ${\mathit{J}}_{\mathit{sensor}}$ |
---|---|---|

Manifold gas pressure | 0.122 | 0.2572 |

EGR mass flow rate (SOSMO) | 0.112 | 0.0332 |

EGR mass flow rate (SMO) | 0.125 | 0.751 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Taherkhani, A.; Bayat, F.; Mobayen, S.; Bartoszewicz, A.
Dependable Sensor Fault Reconstruction in Air-Path System of Heavy-Duty Diesel Engines. *Sensors* **2021**, *21*, 7788.
https://doi.org/10.3390/s21237788

**AMA Style**

Taherkhani A, Bayat F, Mobayen S, Bartoszewicz A.
Dependable Sensor Fault Reconstruction in Air-Path System of Heavy-Duty Diesel Engines. *Sensors*. 2021; 21(23):7788.
https://doi.org/10.3390/s21237788

**Chicago/Turabian Style**

Taherkhani, Ashkan, Farhad Bayat, Saleh Mobayen, and Andrzej Bartoszewicz.
2021. "Dependable Sensor Fault Reconstruction in Air-Path System of Heavy-Duty Diesel Engines" *Sensors* 21, no. 23: 7788.
https://doi.org/10.3390/s21237788