*5.2. Power Split Supercharger Operation during a Transient Drive Cycle*

This section presents the details of the hardware and energy management system operation during the HIL experiments. Figure 13 shows the intake manifold pressure, *p*im. Figure 13a shows *p*im over the entire cycle along with the PSS brake position. The intake manifold pressure increased to more than the ambient pressure (around 100 kpa) only during few instances, which correspond to vehicle accelerations where the PSS switches to boosting mode (*u*br = 0). Figure 13b shows *pim* variation during a portion of the cycle in more detail (marked with blue square in Figures 11b and 13a) on top of the desired signal value, *p*des im , and the supercharger bypass valve position. As mentioned before, when *p*des im is less than the ambient pressure, the supercharger is bypassed and the throttle controls *p*im. When *p*des im increases to more than the ambient pressure, the throttle opens wide, the bypass valve closes, and the supercharger controls *p*im. With the current controller gains, the 0→90% response time to achieve full boost is around 1 s, but it can be reduced to around 0.7 s with more rigorous calibration and gain scheduling.

Figure 14 shows the engine speed, the motor speed, and the supercharger brake position for the same portion of drive cycle. The motor speed is multiplied by *<sup>R</sup> <sup>n</sup>*im*n*ri(*gR*+*gS*), which corresponds to the gear ratio between the motor and crankshaft when the supercharger is locked. During the boosting mode the supercharger speed, *ω*sc, is related to the motor and crankshaft speed by

$$
\omega\_{\rm f} = \frac{\mathcal{g}\mathcal{s}}{(\mathcal{g}\_{\rm S} + \mathcal{g}\_{\rm R})} \omega\_{\rm s\mathcal{E}} + \frac{R}{n\_{\rm im} n\_{\rm ri} (\mathcal{g}\_{\rm R} + \mathcal{g}\_{\rm S})} \omega\_{\rm m} \tag{28}
$$

when the PSS switches to boosting mode the brake opens and the motor has to decrease its own speed by applying some negative torque to increase the supercharger speed. The motor torque and power during the selected interval are shown in Figure 15. The motor torque is the reported value by the motor control unit, and the motor power, *Pm*, is measured by the AVL battery simulator. The time gap corresponds to a vehicle acceleration; hence, the motor is assisting the crankshaft when PSS is in torque assist mode (positive motor torque). When switching to boosting mode the motor initially applies some negative torque to speed up the supercharger, and then the motor torque is controlled to track the desired intake manifold pressure. Finally, when boosting is not required, the motor speed increases by applying a positive torque, and when the motor speed is high enough (supercharger speed close to zero) the supercharger is locked again. The brake position is also shown on these plots to distinguish between boosting and torque assist modes. Note that the motor power sign depends on both its torque and speed signs because the PSS motor can rotate in both directions.

**Figure 13.** Intake manifold pressure during FTP75 cycle, (**a**) intake manifold pressure and PSS mode

over the entire cycle, (**b**) intake manifold pressure, desired intake manifold pressure, and supercharger bypass during *t* = 130 s to *t* = 190 s.

The final piece of the HIL experiments is controlling the desired engine speed. Figure 16 shows the commanded engine speed and its actual value controlled by the dynamometer. As seen, the dynamometer can perfectly track the desired engine speed.

**Figure 14.** Engine and motor speed for the hardware-in-the-loop experiments during *t* = 130 s to *t* = 190 s.

**Figure 15.** Motor operation for the hardware-in-the-loop experiments during *t* = 130 s to *t* = 190 s (**a**) motor torque, (**b**) motor power.

**Figure 16.** Engine speed and its desired value for the hardware-in-the-loop experiments during *t* = 130 s to *t* = 190 s.

#### **6. Conclusions**

This work presented optimal energy management and hardware-in-the loop experiments for a novel low-voltage hybrid system that can be used either as a flexible supercharger or as a parallel hybrid system, enabling start-stop, regenerative braking, and torque assist. An adaptive equivalent consumption minimization strategy from the literature was modified and customized to the PSS system for selecting both the device mode and the power split ratio in hybrid mode. It was shown that when the relative cost of the electric power is higher, the algorithm chooses to use the supercharger across a wider range of operating points, while when the electric power is relatively cheaper the energy management system supplies the motor torque directly to the engine crankshaft. The implementation of drive cycle hardware-in-the loop experiments on an engine dynamometer testbed was discussed in detail, and some of practical aspects were explained. It was shown that the new device with the developed energy management system decreased Ford Escape fuel consumption by 18.4% compared to a baseline turbocharged engine over the FTP75 standard cycle, which is only 4.4% less than the global optimal solution from dynamic programming. Finally, the details of the PSS operation and mode transitions during experiments were shown and discussed in detail. Possible future research directions would be further analysis of the A-ECMS adaptation law and testing the PSS and the developed A-ECMS algorithm in a vehicle.

**Author Contributions:** Conceptualization, S.N., J.S., R.M. and A.S.; methodology, S.N.; software, S.N. and R.M.; validation, S.N., J.S. and R.M.; formal analysis, S.N.; writing—original draft preparation, S.N.; writing—review and editing, R.M. and A.S.; supervision, A.S.; project administration, A.S.; funding acquisition, A.S. and J.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** The information, data, or work presented herein was funded in part by the Advanced Research Projects Agency-Energy (ARPA-E), U.S. Department of Energy, under Award Number DE-AR0000659. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

**Acknowledgments:** The authors would like to thank the EATON corporation and Southwest Research Institute for providing technical support instrumental to the success of this work.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **Abbreviations**

The following abbreviations are used in this manuscript:

HIL hardware-in-the-loop ICE internal combustion engine MPC model predictive control NA naturally aspirated PI proportional+integral PSS power split supercharger RPECS rapid prototyping electronic control system SC supercharger SI spark ignition SoC state of charge TC torque converter
