Model with PID Controllers

The load step transient study was repeated five times for 1600 and 1100 engine speeds by limiting the amount of power (from 1 to 5 kW) provided as electrical assistance to the compressor, as shown in Figure 22.

**Figure 22.** Limits and level of power provided to the compressor during tip-in transient: (**a**) 1600 rpm; (**b**) 1100 rpm.

It is clear that the maximum power limit set for the 1100 rpm case exceeds the model requirement, based on the current PID tuning, for achieving the fastest possible response.

The results in Figure 23 reveal that an electrical assistance of 1 kW can reduce the transient response time of the engine by 70% while higher levels of power can lead to a reduction of more than 85%. As shown in Figure 23a, power levels of more than 3 kW have almost a negligible effect on the response time of the engine. It is obvious by looking at Figure 23b that the improvement in response time is due to the rapid increase of the turbocharger's shaft speed. The fact that the initial shaft speed is higher, as a result of the smaller turbine, also contributes to a fast transient change. Moreover, Figure 23c shows that the electrical assistance provided to the turbocharger pushes the operation of the compressor towards the right side of the mass flow/pressure ratio map, which leads to a more efficient operation of the compressor.

**Figure 23.** *Cont.*

**Figure 23.** Load tip-in results at 1600 rpm engine speed: (**a**) BMEP response time; (**b**) turbocharger speed response time; (**c**) compressor performance.

On the other hand, the transient improvement at very low engine speeds is of higher magnitude, as shown in Figure 24a,b. This happens due to the very low pre-turbine pressures occurring at 1100 rpm. Moreover, as illustrated in Figure 24c, the electrical assistance provided to the turbocharger pushes the operation of the compressor towards the surge line of the map.

**Figure 24.** Load tip-in results at 1100 rpm engine speed; the two peaks highlighted in the red circle are a result of the mass flow rate fluctuation when the throttle valve opens: (**a**) BMEP response time; (**b**) turbocharger speed response time; (**c**) compressor performance.
