# Advanced Control Strategies to Improve Nonlinear Automotive Dynamical Systems Consumption

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Control Algorithms

## 3. Vehicle′s Architecture and Mathematical Model

_{2}) emissions. To respect these limits, the MHEVs needs to increase the efficiency and improve the accuracy of the measurements every year. Configurations of an MHEV that are presented by the industrial market are five: P0, P1, P2, P3, P4. Nowadays, the market prefer the configurations P0, P2, and P4. Another arrangement, mostly used in literature, classify the vehicle as series-series or series-parallel. Figure 2 shows the difference between these classifications. When considering the standard classification of powertrain electrification technology, for the MHEVs, the P2 configuration offers an attractive solution to achieve the reduction of emissions as compared with costs. The optimization present in the vehicle includes E-charging that significantly improves the overall behavior and reduce consumption. In the vehicle study, a full dynamic is implemented that includes a longitudinal dynamic added to a vertical dynamic. The architecture schema is composed of an inverter, an engine, an electric motor, battery, and axle as shown in Figure 2a,b. Different types of battery and electronic units have been analyzed to study the performance. The investigation of real-world measurements of a 48 V mild-hybrid electric motor with the target powertrain configuration offers impressive results, reducing costs. The real data are used to test electric motor behavior during the driving cycle. Simplifications for several model parameters are considered to reduce complexity, starting from the vehicle model containing the nonlinear system dynamics.

^{3}; ${\mathrm{c}}_{\mathrm{w}}$ dependent on the shape of the vehicle drag coefficient; A is the projected face in (m

^{2}); ${v}_{rel}$ is the relative speed of vehicle (m/s); ${F}_{Roll}$ is the rolling resistance in (N); ${m}_{{F}_{vehicle}}$ is the mass of the vehicle in (kg); ${m}_{load}$ is the mass of the load of the vehicle in (kg); g = 9.81 m/s

^{2}the gravitational acceleration; ${f}_{Roll}$ is the rolling resistance coefficient; α is the angle in rad; ${F}_{grad}$ is the slope resistance (N); ${e}_{i}$ is the mass factor (>1), which takes into account the moments of inertia of the accelerated, rotating masses in the drive train; $a$ is the acceleration of the vehicle (m/s

^{2}); ${F}_{dri{v}_{res}}$ is the total driving resistance; and, ${P}_{drive}$ is the drive power. The vehicles are different from a set of parameters that is ${\mathrm{c}}_{\mathrm{w}}$, $\mathrm{A}$, ${m}_{{F}_{vehicle}},\text{}\mathrm{and}\text{}{m}_{load}$. In this case study, the c

_{w}is 0.28, A is 2.20, ${m}_{{F}_{vehicle}}$ is 1.385, and ${m}_{load}$ is zero. A different set that corresponds to different vehicles and the difference from a hatchback and SUV or luxury cars depends on this set.

## 4. Simulation Results and Discussion

_{2}emissions, fuel, energy consumption, and electric range for vehicles based on real-driving data (RDE) and in laboratory test. The RDE test measures the NO

_{x}and pollutants that were emitted by cars while being driven on the road. Three different cycles are developed based on the power of the vehicle:

- Class 1 – low power vehicles with PWr <= 22;
- Class 2 – vehicles with 22 < PWr <= 34; and,
- Class 3 – high-power vehicles with PWr > 34.

_{2}/km. This emission level corresponds to fuel consumption of around 4.1 l/100 km of petrol or 3.6 l/100 km of diesel.

_{2}. The circuit presented differs for consumption. This paper aims to compare the New European Driving Cycle (NEDC) with WLTP emissions and extend the analysis to the most used driving cycle in the world (Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13). The NEDC is composed of two parts. The former is ECE-15 (Urban Driving Cycle), (Figure 4) repeated four times, and the latter is EUDC (Figure 5) once repeated. The cycle has been designed to represent typical driving conditions of busy European cities. Figure 6 shows the complete cycle. The ECE-15 cycle is used for EU type-approval testing of emissions and fuel consumption from light-duty vehicles. The EUDC (Extra Urban Driving Cycle) segment has been added for more aggressive, high speed driving modes. The characteristic of overall driving cycle is shown in Table 1, Table 2 and Table 3. When the speed is equal to zero, the emissions are considered to be zero if the engine is turned off. During the driving cycle, the emissions are equal to 2.380 g/L, the standard value measured when the speed is zero.

_{2}based on the chemical structure of CO

_{2}. Table 4 shows the driving cycles consumptions.

## 5. Conclusions

_{2}emissions. The estimated measurements show the excellent performance of the MPC scheme to control the vehicle, including on-vehicle disturbances. The experimental results strongly indicate the potential of MPC, and it is interesting to change the configuration to extend the controller to other series-parallel configuration and define the fuel consumption, which will be the focus of future work. Moreover, the proposed control design might be expanded to other vehicle applications that have similar operating conditions, such as long trucks and delivery vehicles.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Fanesi, M.; Scaradozzi, D. Optimize the Mild Hybrid Electric Vehicles control system to reduce the Emission. In Proceedings of the 2019 IEEE 23rd International Symposium on Consumer Technologies (ISCT), Ancona, Italy, 19–21 June 2019. [Google Scholar]
- Wdaah, L.; Muller, S. Catering truck of the future—Efficiency increase by full electrification. In Proceedings of the 2017 2nd IEEE International Conference on Intelligent Transportation Engineering, ICITE 2017, Singapore, 1–3 September 2017. [Google Scholar]
- Lequesne, B. Automotive Electrification: The Nonhybrid Story. IEEE Trans. Transp. Electrif.
**2015**, 1, 40–53. [Google Scholar] [CrossRef] - Thibault, L.; Sciarretta, A.; Degeilh, P. Reduction of pollutant emissions of diesel mild hybrid vehicles with an innovative energy management strategy. In Proceedings of the IEEE Intelligent Vehicles Symposium, Los Angeles, CA, USA, 11–14 June 2017. [Google Scholar]
- Xiang, Z.; Zhu, X.; Quan, L.; Du, Y.; Zhang, C.; Fan, D. Multilevel Design Optimization and Operation of a Brushless Double Mechanical Port Flux-Switching Permanent-Magnet Motor. IEEE Trans. Ind. Electron.
**2016**, 63, 6042–6054. [Google Scholar] [CrossRef] - Tsunata, R.; Takemoto, M.; Ogasawara, S.; Watanabe, A.; Ueno, T.; Yamada, K. Development and Evaluation of an Axial Gap Motor Using Neodymium Bonded Magnet. IEEE Trans. Ind. Appl.
**2018**, 54, 254–262. [Google Scholar] [CrossRef] - Chau, K.T.; Chan, C.C.; Liu, C. Overview of Permanent-Magnet Brushless Drives for Electric and Hybrid Electric Vehicles. IEEE Trans. Ind. Electron.
**2008**, 55, 2246–2257. [Google Scholar] [CrossRef] [Green Version] - Chan, C. The state of the art of electric and hybrid vehicles [Prolog]. Proc. IEEE
**2002**, 90, 245–246. [Google Scholar] [CrossRef] - Zeraoulia, M.; El, M.; Benbouzid, H.; Diallo, D. Electric Motor Drive Selection Issues for HEV Propulsion Systems: A Comparative Study. IEEE Trans. Veh. Technol.
**2006**, 55, 1756–1764. [Google Scholar] [CrossRef] [Green Version] - Zeng, X.; Wang, J. A Parallel Hybrid Electric Vehicle Energy Management Strategy Using Stochastic Model Predictive Control with Road Grade Preview. IEEE Trans. Control Syst. Technol.
**2015**, 23, 2416–2423. [Google Scholar] [CrossRef] - Golchoubian, P.; Azad, N.L. Real-Time Nonlinear Model Predictive Control of a Battery–Supercapacitor Hybrid Energy Storage System in Electric Vehicles. IEEE Trans. Veh. Technol.
**2017**, 66, 9678–9688. [Google Scholar] [CrossRef] - Yu, J.; Zhang, T.; Qian, J. Electrical Motor Products: International Energy-Efficiency Standards and Testing Methods; Elsevier: Amsterdam, The Netherlands, 2011. [Google Scholar]
- Manias, S. Power Electronics and Motor Drive Systems; Academic Press: Cambridge, MA, USA, 2016. [Google Scholar]
- Kumar, B.P.; Krishnan, C.M.C. Comparative study of different control algorithms on Brushless DC motors. In Proceedings of the 2016 Biennial International Conference on Power and Energy Systems: Towards Sustainable Energy (PESTSE), Bangalore, India, 21–23 January 2016. [Google Scholar]
- Wang, S.; Li, C.; Che, C.; Xu, D. Direct Torque Control for 2L-VSI PMSM Using Switching Instant Table. IEEE Trans. Ind. Electron.
**2018**, 65, 9410–9420. [Google Scholar] [CrossRef] - Ren, Y.; Zhu, Z.Q. Reduction of Both Harmonic Current and Torque Ripple for Dual Three-Phase Permanent-Magnet Synchronous Machine Using Modified Switching-Table-Based Direct Torque Control. IEEE Trans. Ind. Electron.
**2015**, 62, 6671–6683. [Google Scholar] [CrossRef] - Xia, C.; Chen, H.; Li, X.; Shi, T. Direct self-control strategy for brushless DC motor with reduced torque ripple. IET Electr. Power Appl.
**2018**, 12, 398–404. [Google Scholar] [CrossRef] - Masmoudi, M.; Badsi, B.E.; Masmoudi, A. Direct Torque Control of Brushless DC Motor Drives With Improved Reliability. IEEE Trans. Ind. Appl.
**2014**, 50, 3744–3753. [Google Scholar] [CrossRef] - Sun, G.; Ma, Z.; Yu, J. Discrete-Time Fractional Order Terminal Sliding Mode Tracking Control for Linear Motor. IEEE Trans. Ind. Electron.
**2018**, 65, 3386–3394. [Google Scholar] [CrossRef] - Quang, N.K.; Hieu, N.T.; Ha, Q.P. FPGA-Based Sensorless PMSM Speed Control Using Reduced-Order Extended Kalman Filters. IEEE Trans. Ind. Electron.
**2014**, 61, 6574–6582. [Google Scholar] [CrossRef] - Guney, E.; Demir, M. A comparative velocity control study of permanent magnet tubular linear DC motor by using PID and fuzzy-PID controllers. In Proceedings of the 2017 International Conference on Control, Automation and Diagnosis, ICCAD 2017, Hammamet, Tunisia, 19–21 January 2017. [Google Scholar]
- Lievre, A.; Pelissier, S.; Sari, A.; Venet, P.; Hijazi, A. Luenberger observer for SoC determination of lithium-ion cells in mild hybrid vehicles, compared to a Kalman filter. In Proceedings of the 2015 10th International Conference on Ecological Vehicles and Renewable Energies, EVER, Monte Carlo, Monaco, 31 March–2 April 2015. [Google Scholar]
- Abdelhamid, B.; Radhouane, L.; Bilel, A. Real time implementation of perturb and observe algorithm and PI controller for DC/DC converter. In Proceedings of the 2017 18th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA), Monastir, Tunisia, 21–23 December 2017. [Google Scholar]
- Seibel, A.; Stübig, C.; Wecker, M.; Steffen, J.; Kandasamy, K.; Mertens, A.; Nielebock, S. Distributed Control of a Multi-Pole Permanent Magnet Synchronous Generator for Wind Turbine Application. In Proceedings of the 2016 18th European Conference on Power Electronics and Applications (EPE’16 ECCE Europe), Karlsruhe, Germany, 5–9 September 2016. [Google Scholar]
- Salazar-Caceres, F.; Student, O.D.M.; Bueno-López, M.; Garcés, A. LQR Control for Superconducting Magnetic Energy Storage on Distribution Networks Using Feedback Linearization. In Proceedings of the 2017 IEEE 3rd Colombian Conference on Automatic Control (CCAC), Cartagena, Colombia, 18–20 October 2017. [Google Scholar]
- Seiffert, U.W.; Braess, H.H. (Eds.) Handbook of Automotive Engineering; Springer: Berlin/Heidelberg, Germany, 2013; ISBN 978-3-658-01691-3. [Google Scholar]

Characteristics | Unit | ECE 15 | EUDC | NEDC | ADR 81/02 | SFTP US06 | SFTP SC03 |
---|---|---|---|---|---|---|---|

Distance | km | 0.9941 | 6.9549 | 10.9313 | 19.44 | 12.8 | 5.8 |

Total time | s | 195 | 400 | 1180 | 1797 | 596 | 596 |

Average speed | km/h | 18.35 | 62.59 | 33.35 | 38.95 | 77.89225 | 34.76183 |

Maximum speed | km/h | 50 | 120 | 120 | 120 | 129.2303 | 88.19205 |

Maximum acceleration | m/s^{2} | 1.042 | 0.833 | 1.042 | 3.61 | 3.7833333 | 2.279904 |

Characteristic Artemis | Urban | Art Road | Motorway 130 | Motorway 150 |
---|---|---|---|---|

Duration (s) | 993 | 1082 | 1068 | 1068 |

Distance (km) | 4.874 | 17.275 | 28.737 | 29.547 |

Average speed (trip), km/h | 17.7 | 57.5 | 96.9 | 99.6 |

Maximum speed, km/h | 57.3 | 111.1 | 131.4 | 150.4 |

Characteristics WLTP | Unit | Class 1 | Class 2 | Class 3 |
---|---|---|---|---|

Distance | km | 8.091 | 14.664 | 23.262 |

Total time | s | 1022 | 1477 | 1800 |

Average speed | km/h | 28.5 | 35.7 | 46.5 |

Driving Cycle | Consumption (gr of CO_{2}/km) |
---|---|

ECE 15 | 84.2122 |

EUDC | 35.4201 |

NEDC | 47.4958 |

WLTP | 38.7439 |

US FTP-72 (UDDS) | 53.4914 |

Artemis road | 32.5134 |

Artemis Urban | 102.8975 |

Artemis rw130 | 17.7410 |

Artemis rw150 | 16.0875 |

FTP | 51.5420 |

© 2019 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**

Scaradozzi, D.; Fanesi, M.
Advanced Control Strategies to Improve Nonlinear Automotive Dynamical Systems Consumption. *Axioms* **2019**, *8*, 123.
https://doi.org/10.3390/axioms8040123

**AMA Style**

Scaradozzi D, Fanesi M.
Advanced Control Strategies to Improve Nonlinear Automotive Dynamical Systems Consumption. *Axioms*. 2019; 8(4):123.
https://doi.org/10.3390/axioms8040123

**Chicago/Turabian Style**

Scaradozzi, David, and Marika Fanesi.
2019. "Advanced Control Strategies to Improve Nonlinear Automotive Dynamical Systems Consumption" *Axioms* 8, no. 4: 123.
https://doi.org/10.3390/axioms8040123