Configuraciones de orden polinomial y taps óptimos

In Fig. 3.13 three typical transients are presented. These are a ramp up and down in engine speed neng, a step up and down in injection quantity uinj and a step up and down in injection quantity

followed by a ramp up respectively down in engine speed. The latter can be regarded as accelera- tion respectively deceleration event. The air path states and the crank angle of main injection are adjusted by feedforward controls of their actuators. The desired values for m_airand p_2i, marked as dashed lines in the plot, are taken from a series calibration for stationary conditions. For the engine speed, a ramp is applied rather than a step, since it can not be changed instantaneously. On the other hand, the injection quantity can be adjusted cyclewise, why a step is applied.

The presented results are derived from a simulation of the overall engine model, as introduced in Fig. 3.1. Therefore, the dynamic air path model, as presented in App. A, is applied together with the combustion model, presented in the previous sections. For the injection system no model is applied, since it is assumed that the injection characteristics follow their desired values without any dynamics.

At t D 5 s a ramp in engine speed is shown. The desired values for m_airand p_2iare changed together with the change in engine operation point, see dashed lines in the plots. The air path states follow with significant dynamics, since they are adjusted by open loop controls of their actuators. The NOx and soot emissions are marginally affected by the ramp up in engine speed at t D 5 s, but the

NOx emissions increase for the ramp down at t D 10 s. The ramp down in engine speed increases

the air mass per cycle, which again leads to the formation of NOx, which is negative.

For the step in injection quantity at t D 15 s, the soot emissions are strongly affected. The stationary emissions are increased for both, the NOxand the soot emissions, as is apparent by the dashed lines.

The soot emissions overshoot their stationary value, whereas the NOx emissions approach their

stationary value from the lower side. Hence, the NOx soot trade-off is also apparent for transient

operations. For the step down, the NOx emissions are higher than their stationary value, since the

change in engine operation point also causes a change in desired values for mairand p2i.

The acceleration and deceleration events, t D 25 s and t D 30 s, show a similar behaviour as the separate investigated steps in injection quantity and ramps in engine speed, but the reactions of the emissions are more pronounced. This is due to a more significant change in desired values for mair

and p2i. The acceleration event shows an overshoot in soot emissions, whereas the deceleration

event shows an overshoot in NOx emissions, which is due to the increased air mass per cycle.

Summarising, a step up in injection quantity poorly affects the soot emissions and a ramp down in engine speed poorly affects the NOx emissions. The increased soot emissions are due to the

Figure 3.13:Dynamic simulation of the overall engine model, applying models for the dynamic

air path and the stationary combustion process. Engine operation point trajectory is shown in the topmost plot. The first two transients illustrate separately the dynamics in engine speed and injection quantity, whereas the latter can be regarded as typical acceleration respectively deceleration event. The model actuators are adjusted by open loop controls, which is why there are relatively long settling times for mairand p2i (second and third plot). Engine outputs are

instantaneous increase of fuel mass and the consequential deficiency of air. The soot emissions are even more significant, if the step is followed by a ramp in engine speed, as is the case for the acceleration event. To lower the emissions for such transients, closed loop controls of the air path states are applied. Thus, the stationary states are reached faster and the overshoots are lowered. In Chap. 5 a non-linear offline optimisation of an acceleration event is regarded and closed loop controls are discussed. To further avoid high soot emissions during accelerations, a smoke limitation is presented in Sect. 5.4. On the other hand, the ramp down in engine speed poorly affects the NOx

emissions, because of the variations in air mass per cycle. The variations in air mass per cycle result from a change in the desired value for mair, but also from the increased number of cycles per

minute, determined by the engine speed.

To analyse the increased NO_x emissions for a ramp down in engine speed, the air mass per cycle mairand the air mass flow rate Pmairare regarded in Fig. 3.14. For the ramp down in engine speed at

t D 10s and t D 30 s, the air mass per cycle increases for the first second instead of decreasing, as is intended by its desired value. This is due to the influence of the engine speed on the air mass per cycle. Regarding the air mass flow rate, Pmair in the bottom plot in Fig. 3.14, it decreases from

the beginning of the ramp, but the simultaneous decrease in engine speed (topmost plot) causes a higher air mass per cycle (middle plot) for the duration of the engine ramp, t D 10 11s and t D 30 31s. Since the combustion depends on the air mass per cycle rather than the air mass flow rate, this favours the formation of NOx, as is observable in Fig. 3.13. In Sect.5.3 a coupled actuator

control structure is introduced to reduce the dynamic deviations for these ramps down in engine speed..

The properties observed in this overall simulation are also observable for measurements from the engine test bed, as is shown in App. B.4. These measurements further validate the overall engine simulation with the connected models, as introduced in Fig. 3.1. A detailed investigation of the measurement dynamics is made in the following section applying dynamic measurements.