Procesos Habilitantes operativos y de apoyo.

the OCP result. The steady-state level of boost was tracked without any error.

4 4.5 5 5.5 6

1400 1600 1800 2000 2200

Time (s)

Engine Speed (RPM)

4 4.5 5 5.5 6

0 0.2 0.4 0.6 0.8 1

Time (s)

VGT (−)

4 4.5 5 5.5 6

1.6 1.8 2 2.2 2.4 2.6

Time (s)

MAP (bar)

4 4.5 5 5.5 6

120 140 160 180

Time (s)

TurboSpeed (kRPM)

OCP Setup III MPC

Figure 3.11: The comparison of the results of OCP maximising the integral of the intake manifold pressure and MPC control.

The above analysis gives some insight into the characteristics of the controller;

because of the simplified system model used for prediction, the actuation of VGT is less smooth around the knee region. A more detailed analysis of MPC calcula-tions and the influence of simplificacalcula-tions used in this particular formulation can be found in the Appendix C.

to the longer time constant of standard thermocouples.

The focus of the remaining results is on the air-path control system perfor-mance. To allow for a better comparison with the previous results the engine models are now operated using the engine speed and fuelling taken from the OCP results. If the models were operated with the driveline included, the ab-solute response times would be affected by differences in the treatment of the combustion process.

Figure 3.12 shows the results for both the new setup and the case when the MPC controls the MVEM. The boost pressure from the MPC controlled WAVE model shows a satisfactory tracking performance with a less sharp knee region.

No overshoot, undershoot or steady-state error in reference tracking are observed.

The latter feature is ensured by using the estimate of the state derivatives from measurements (see eq. 3.15). The simplifications present in the MVEM can be seen in the differences in the final turbocharger speed but overall, the results confirm that the 1D engine model can be effectively controlled by MPC based on a related MVEM.

Controlling the engine within constraints

In the previous section it was shown that the controller ensures close-to-optimal operation of 1D engine simulation model. In this part, the controller’s capability of ensuring the engine’s operation within physical limits is considered.

Control system requirements for tip-in manoeuvres and some related physical limits were discussed in 3.2.2. Here, three constraints of a different nature are considered:

maximum exhaust manifold pressure - The dynamics of pressure in the ex-haust manifold is one of the fastest in the MVEM, because of a small vol-ume of this part of the air-path. Additionally, this was the state, for which MVEM validation was the poorest (see Figure 2.22).

maximum turbocharger speed - Turbocharger speed dynamics is the slowest mode of the air-path

4 4.5 5 5.5 6 1400

1600 1800 2000 2200

Time (s)

Engine Speed (RPM)

4 4.5 5 5.5 6

0 0.5 1

Time (s)

VGT (−)

4 4.5 5 5.5 6

1.5 2 2.5

Time (s)

MAP (bar)

4 4.5 5 5.5 6

120 140 160 180

Time (s)

Turbo Speed (kRPM)

MVEM 1D Model

Figure 3.12: The comparison of the closed-loop performances of the MVEM and WAVE models controlled with the same MPC controller. Close to optimal per-formance of 1D model is achieved using the MPC controller based on a related MVEM.

compressor surge limit - This is a state-dependent constraint sensitive to ac-tuator operation

Operation at high altitudes

Matching a turbocharger to an engine is a compromise. On the one hand, the selected combination is required to achieve excellent performance in nominal am-bient conditions. On the other hand, the system has to be capable of operating at high altitudes and a significant range of temperatures. This requires ensuring certain margins in the design. Therefore, in the case of the tip-in manoeuvre at nominal ambient conditions (pressure ∼1 bar and temperature ∼20 deg C), the system usually operates with a safe margin from the limits of operation.

Simulations of 1D model with ambient pressure of 0.8 bar are now investigated.

This pressure corresponds to the altitude of about 2000 metres above the sea level. To satisfy the same boost pressure demand as at the sea level, the required

turbocharger speed is significantly higher. The compressor and the turbine needs to operate at much higher pressure ratios.

Two constraints are now investigated: the maximum exhaust manifold pres-sure of 4 bar and the maximum turbocharger speed of 210000 RPM.

Both variables are states of the MVEM and the required limits can be readily added to the MPC controller. Soft constraints were used in this setup. This allowed, but heavily penalised, the exhaust pressure and the turbocharger speed exceeding their limits, but ensured the feasibility of optimisations. Exceeding the limits is often unavoidable, because of the mismatch between the prediction model and the actual plant.

The results of such simulations are shown in Figure 3.13. It is observed that the demanded pressure of 2.4 bar was achieved significantly later than it was in the case when nominal conditions were investigated. Meeting the boost demand required accelerating the turbocharger to higher speeds. Before this was achieved, the pressure in the exhaust manifold had become very high and the MPC con-troller had generated a demand for opening the VGT. Maintaining a constant boost pressure required progressive opening of the VGT which resulted in a drop in the exhaust pressure. Soon after that, the turbocharger speed achieved its maximum permitted value. The MPC controller sacrificed the reference tracking to keep the turbocharger speed at the specified limit.