A Study on Optimal Speed Trajectory during Engine Start for Minimum Torsional Vibration*

Abstract

This paper studies optimal speed trajectory during engine start in order to achieve minimum vibration. First of all, the target diesel powertrain is introduced and its dynamic model is established. The vibration index which represents the severity of vibration is brought out. Secondly, the optimal control problem is formulated in Pontryagin’s minimum principle form, and numerical solution is obtained. In the third part, different cost function of the optimal problem is discussed, results in different optimal speed trajectory. Finally, this paper presents an optimal speed trajectory, and corresponding input cranking torque, which could be used as feed forward in real-time engine start control.