Optimal Speed Profile for Minimum Vibration during Engine Start Using Pontryagin’s Minimum Principle Approach
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.