## 4 Design of Dynamic Torque-Coordinated Control That Considers Engine Starting Conditions
### Engine Segment Active Control
#### 4.1.2 Controls of Engine Fuel Injection and Ignition Timing  
According to the bench test results, the equivalent jerk based on an engine working cycle number is obtained as shown in Figure 12. Note that the vehicle jerk is the second derivative of the vehicle speed [38] and the engine crankshaft angle every 720 deg of rotation is an engine working cycle. It can be seen from this figure that the transmission system has obvious jerks during engine starting. For the jerks after ignition, it is found that the equivalent jerk of the first three working cycles (3 rd, 4 th and 5 th) after ignition is greater than that of subsequent engine working cycles. Therefore, this part is mainly focused on reducing the shocks and vibrations of the first three working cycles after ignition. Moreover, as shown in Figure 12, we can see that the second derivative of engine speed, \(\vec{\theta}_{\text{Eng\_out}}\) has a similar fluctuation pattern with an equivalent jerk, which shows that the \(\vec{\theta}_{\text{Eng\_out}}\) can indirectly reflect the fluctuation phenomenon of a vehicle jerk. This provides a basis for choosing an objective function \(F_{GA1}\) optimized by a genetic algorithm. Since the running time of the first three working cycles after ignition is about 300 ms, it is necessary to realize the transient torque change by means of fast engine response control. Although the engine output torque can be greatly adjusted by the throttle control method, its control response time is longer. Compared to engine throttle control, fuel injection and ignition controls have a faster control effect on engine transient torque [39]. Therefore, controls of fuel injection and ignition timing based on an engine working cycle will be used to rapidly change engine output torque to reduce jerks of the powertrain system during initial engine combustion, especially the first three working cycles after engine ignition in stage 4. As shown in Figure 13, in this paper, according to the engine working cycle and cooling water temperature of engine, the engine fuel injection \(F_{  
Figure 11: Effect of ICA on engine output torque with \(\theta_{irct}=150\) deg. Figure 12: Jerk analysis based on engine working cycle number. \(\theta_{it\_cycyj}\) of the first three working cycles after engine ignition are optimized by using a genetic algorithm [40]. Since the main purpose of this paper is to reduce shocks in mode switching, which that includes engine starting, the effect of emissions will not be considered as a subject of interest. The injection volume \(F_{it\_cycyj}\) of the first three working cycles after ignition is expressed as follows:  
\[F_{it\_cycyj}=C_{frc\_cyj}*F_{bf\_cyj} \tag{16}\]  
where \(C_{frc\_cyj}\) and \(F_{bf\_cyj}\) are the fuel-ratio coefficient and basic fuel injection at the \(j\)th working cycle (\(j=3\), \(4\), \(5\)), respectively. In the initial combustion of an engine startup, a too large or too small ignition angle will lead to a fuel injection combustion misfire [41]. Therefore, in practice, the engine ignition angle and fuel injection need to be limited to a certain range to ensure a smooth start. The combustion misfire constraints of the engine from engine experimental data are as follows. \[\left\{ \begin{array}{l}C_{frc\_cyc3}\in[0.9\ 1.6]\\ C_{frc\_cy4}\in[0.4\ 1.6]\\ C_{frc\_cy5}\in[0.2\ 1.2]\\ \theta_{it\_cy3}\in[-20\ 5]\\ \theta_{it\_cy4}\in[-25\ 10]\\ \theta_{it\_cy5}\in[-30\ 15]\\ \end{array} \right. \tag{17}\]  
where the ignition timing at the top dead point is defined as zero. The negative \(\theta_{it\_cycyj}\) is the ignition advance angle, and the positive \(\theta_{it\_cycyj}\) is the ignition delay angle.