This content is not included in your SAE MOBILUS subscription, or you are not logged in.
Optimal Speed Profile for Minimum Vibration during Engine Start Using Pontryagin’s Minimum Principle Approach
ISSN: 0148-7191, e-ISSN: 2688-3627
Published November 04, 2019 by SAE International in United States
Annotation ability available
An imperceptible engine start is critical to the acceptance of hybrid vehicles. This paper focusses on an optimal control problem that tries to reduce vibration during engine start. Efforts are made to obtain the optimal speed trajectory that could cause minimum vibration during engine start. In the first section, the target diesel powertrain is introduced. A four cylinder diesel engine is coaxially paralleled with an ISG motor. The ISG motor serves as the engine starter and engine flywheel. Its dynamic model is established using crank-link dynamics. Secondly, an index is brought out to evaluate the severity of vibration. The cylinder pressure variation is the main cause of engine torque ripple, which in turn results in engine speed fluctuation. The square of the angular acceleration is chosen as the index of vibration. The index shows a positive relation of cylinder pressure in terms of amplitude. Then, the author models this problem as a continuous-time optimal control problem with a fixed terminal time and a partially free terminal state, then solve it by the Pontryagin’s minimum principle. Finally, this paper presents an optimal engine start speed trajectory which is linearly increasing with time, and the corresponding control input should vary with engine torque ripple. The optimal control input of ISG torque consists of two parts. One is the constant value to counter the rotating inertial, and the other varies with engine torque to compensate for the torque ripple.
CitationDu, L., Xu, L., Hu, Y., Ouyang, M. et al., "Optimal Speed Profile for Minimum Vibration during Engine Start Using Pontryagin’s Minimum Principle Approach," SAE Technical Paper 2019-01-5026, 2019, https://doi.org/10.4271/2019-01-5026.
- Canova , M. , Guezennec , Y. , and Yurkovich , S. On the Control of Engine Start/Stop Dynamics in a Hybrid Electric Vehicle Journal of Dynamic Systems, Measurement, and Control 131 6 061005 2009 10.1115/1.4000066
- Kum , D. , Peng , H. , and Bucknor , N.K. Control of Engine-Starts for Optimal Drivability of Parallel Hybrid Electric Vehicles Journal of Dynamic Systems, Measurement, and Control 135 2 2013 10.1115/1.4023067
- Kuang , M.L. An Investigation of Engine Start-Stop NVH in a Power Split Powertrain Hybrid Electric Vehicle SAE Technical Paper 2006-01-1500 2006 10.4271/2006-01-1500
- Beer , J. and Teulings , W. Optimized Start Strategy for Stop/Start Operation of a μ-Hybrid Vehicle SAE Technical Paper 2007-01-0298 2007 10.4271/2007-01-0298
- Opila , D.F. , et al. Incorporating Drivability Metrics into Optimal Energy Management Strategies for Hybrid Vehicles Decision and Control, 2008. CDC 2008. 47th IEEE Conference on IEEE 2008 10.1109/CDC.2008.4738731
- Geering , H.P. Optimal Control with Engineering Applications Springer 2007
- Wu , G. , Zhang , X. , and Dong , Z. Optimal Control for Ensured Drivability of Paralell HEVs/PHEVs during Mode Transition SAE Technical Paper 2014-01-1895 2014 10.4271/2014-01-1895
- Hwang , H.-Y. Minimizing Seat Track Vibration that is Caused by the Automatic Start/Stop of an Engine in a Power-Split Hybrid Electric Vehicle Journal of Vibration and Acoustics 135 6 061007 2013 10.1115/1.4023954