Online Optimization

One of the most challenging parts of HCCI implementation is the control of combustion phasing. In the FPE with the piston trajectory-based HCCI combustion control, the ultimate freedom of piston motion can be used as an additional control means to regulate combustion phasing. In this subsection, a searching process of the optimal piston trajectory enabling the best combustion phasing is presented. Additionally, due to the lack of crankshaft mechanism, the widely-used parameter CA50, which represents the HCCI combustion phase in the conventional ICE, is replaced by T50, representing the time instant when 50% fuel chemical energy has been released in this study.

As shown in Figure 7.6, a single-input-single-output feedback loop is utilized to achieve the optimal Ω of the piston trajectory. The objective is to force the T50 locating

at the TDC point in order to realize the ideal Otto cycle and reduce the ringing intensity. To achieve this objective, a heat release analyzer is developed in order to calculate the simulated T50. Afterward, the error between the calculated T50 and the targeted value is sent to a PI controller and the adjustment of Ω is calculated. In this way, the new piston trajectory is generated and the corresponding error in the following cycle will be reduced.

Figure 7.6 Block diagram of the feedback loop searching the optimal piston trajectory with desired combustion phasing

The heat release analyzer calculates the chemical heat release by integrating the instantaneous heat release rate, which is obtained from the piston trajectory and the in- cylinder gas temperature and pressure [29]:

Q P V V P Q_HR            1 1 1    (7.8)

where γ is the heat capacity ratio of the in-cylinder gas, which is set as 1.31 [66] and Q is the heat transfer rate. The combustion is assumed to occur if the heat release reaches a preset threshold and the T50 value can then be calculated.

As shown in Figure 7.7, when CR = 31, AFR = 2.0, the first piston trajectory, whose Ω = 3.0, triggers combustion early than the TDC point which increases the ringing intensity significantly. Using the feedback loop described above, the Ω of the piston

trajectories in following cycles are reduced from 3.0 to 0.9 and the T50 values are moving closer to the TDC point, as shown in Figure 7.8 (the negative value of the calculated T50 indicates the corresponding instant is before the TDC time). Hence, the fine tuning of the combustion phase is realized by adjusting the piston trajectory and the optimal piston trajectory, which locates T50 at the TDC point, is determined eventually. The optimal piston trajectory is then sent to the detailed model and the comparison between the proposed model and the detailed model presents good agreement again, as shown in Figure 7.9.

Figure 7.8 Calculated T50 for each engine cycle

Figure 7.9 Temperature traces of combustion along the optimal piston trajectory using the detailed model and the proposed model respectively

The performance of the feedback loop searching method is also investigated during the variation among multiple working conditions. As shown in Figure 7.10, the left side of the green dashed line represents different working conditions with various AFRs under CR = 31 and the right side represents different working conditions with same AFRs

under CR = 34. As can be seen, no matter how the CR or the AFR is changed, the feedback loop searching method with the proposed model can always achieve an optimal Ω, realizing the desired combustion phasing, after 3 or 4 cycle’s simulation, which only lasts 0.3 to 0.4s. In other words, a real time optimal control of the HCCI combustion phasing is achieved through the feedback loop searching method with the assistance of the proposed control-oriented model. As a comparison, the detailed model is also implemented into the feedback loop searching method to determine the optimal Ω for the combustion phasing control. However, the turnaround time of this process is about 20s, which is far beyond the requirement for the real time application.

7.3 Conclusion

In this chapter, the approach to optimizing piston trajectory for the trajectory-based HCCI combustion control is presented. As claimed by the concept of trajectory-based combustion control, the derived optimal piston trajectory is considered as the optimal control signal to the FPE, which provides ultimate engine performance, in terms of maximal engine thermal efficiency and minimal emissions production. Both offline and online optimization are presented.

Refer to the offline optimization, two approaches are proposed and implemented into the model: The first approach represents the piston trajectory as a function of parameter Ω and converts the original problem to a parameters optimization problem. Both optimal symmetric trajectories (represented as a function of single Ω) and asymmetric trajectories (represented as a function of two Ωs) are derived at given CR. The advantages of this optimization approach lie on its much lighter computational burden and easily implemented result; the second method transforms the trajectory optimization problem into a static constrained nonlinear programming and then solves it via the SQP algorithm. By removing the constraints placed by parameter functions, this approach enlarges the candidate pool of various piston trajectories. Hence, the derived optimal trajectory further increases the engine output work and sustains the NOx emissions at the same level.

For the online optimization, a searching process is developed with the assistance of the proposed control-oriented model. The main idea of this searching process is to utilize the result of the control-oriented model to adjust the implemented piston motion pattern in order to achieve the designed the combustion phasing control. The simulation results

clearly show that no matter what kinds of variation on the working conditions are employed, the designed piston motion pattern can always be derived within 0.4s, which proves the effectiveness of this approach as an online optimization control on the HCCI combustion phasing.