AREA DE RECAUDACION, EVALUACION DEL CONTROL INTERNO NORMA DE CONTROL INTERN 403-

The investigated MPC formulation assumes full-state feedback. There are three types of measurements required: pressures in all five volumes, temperatures in the volumes to allow for calculating the stored mass of gas and turbocharger speed.

In the simulation environment the sensors implemented in the 1D model were noise-free, of instantaneous response and set to indicate cycle-averaged values. In the real application the bandwidths of sensors and the characteristics of measured signals cannot be neglected.

Measuring turbocharger speed during transient conditions is the simplest in this set. A fast digital sensor is used to determine the speed of the compressor wheel, which due to a significant turbocharger shaft inertia does not show con-siderable variations during single engine cycle. Therefore, a raw signal from the sensor can be used for feedback.

1The code of the solver was supplied by Dr Edward Hartley.

Cycle-averaged pressure measurements

As it was shown in Figure 3.4, a high bandwidth of pressure transducers al-lows measurement of variations in pressure during a single engine cycle. In the discussion presented in the section 3.1.2 a non-causal cycle-averaging filter was used. For on-line execution two approaches were considered. The first option was to apply a discrete time filter (DTF). The filter parameters were determined discretising a 1^st order continuous time low-pass filter with the time constant τ given by:

τ = 2π Ne

= tct

2 (3.21)

The engine speedNe is expressed in radians per second andtct is the duration of a single engine cycle.

The second method involves integrating the measured pressure during one engine revolution and dividing the result by the time of integration. One en-gine revolution rather than the entire cycle is used in order to reduce the time delay introduced by this approach. Nevertheless, this method is referred to as cycle-average filters (CAF). This method, however, suffers from implementation difficulties. The pressure signal is sampled by the rapid prototyping system with the step of 1 ms. The shaft encoder attached to the crankshaft triggers the inte-grator reset every engine revolution. This period is speed dependent - 60 ms at 1000 RPM and 21.8 ms at 2750 RPM. As a result the resolution of capturing the pressure variations becomes worse at high engine speeds, which is then reflected in the resulting cycle-average value.

The results obtained applying the two methods to intake manifold pressure measurements are shown in Figure 3.16. Two sections of the tip-in manoeuvre are shown: a part of the manoeuvre with a steep increase in the intake manifold pressure (Figure 3.16a) and the steady-state operation at full load (Figure 3.16b).

It is observed that during steady-state operation results obtained with CAF are significantly better, i.e. the variation of calculated signal is smaller.

To improve our understanding of the effects these two methods may have on the MPC controller, the time instances of the controller execution are marked with crosses. It is observed that both approaches returned similar values during the

3.7 3.75 3.8 3.85 3.9 3.95 4 1.8

1.85 1.9 1.95 2 2.05 2.1

Time (s)

MAP (bar) Raw Measurement

Discrete Time Filter CAF

MPC sampling DTF MPC sampling CAF

(a) Boost pressure A

5.7 5.75 5.8 5.85 5.9 5.95 6

2.2 2.3 2.4 2.5 2.6 2.7

Time (s)

MAP (bar)

(b) Boost pressure B

0 2 4 6 8 10

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8 1

Time (s)

∆ MAP (bar/s)

MPC sampling DTF MPC sampling CAF

(c) State derivatives

Figure 3.16: Measuring pressure states and their derivatives.

test. However, the formulated controller also approximates state derivatives from last two measurements. The approximate state derivatives for the intake mani-fold pressure calculated during the entire manoeuvre are shown in Figure 3.16c.

The plot can be divided into two parts - a big transient in pressure happening before the time of 5 seconds, and from 6 seconds onwards, when the pressure was controlled to a constant value. The differences in state derivative estimates for the two methods, especially during the second part of the test, indicate that the CAF approach is more suitable.

Calculating temperatures for state-feedback

Measuring temperatures in the air-path volumes during transients is difficult due to the low bandwidth of the sensors (see discussion in 3.1.2 and Figure 3.4c).

In order to maintain the general controller structure, estimated temperatures

were calculated based on the steady-state characteristics of the elements prior to a considered volume. For example, the temperature of the gas in the post-compressor volume was estimated multiplying the pre-post-compressor temperature by the compressor temperature ratio. These characteristics are mainly based on the pressures across a considered element, turbocharger speed, engine speed and fuelling level. All these signals can be effectively measured during transient engine testing.

The results of such calculations (Static) were compared with the temperatures determined from solving the full MVEM (Dynamics) in Figure 3.17. This com-parison was performed for the simulation of a tip-in manoeuvre using the MVEM as an engine simulator.

−1 0 1 2 3 4 5 6

300 350 400 450 500

Time (s)

Post Comp Temperature (K) Dynamics

Static

(a) Post-compressor

−1 0 1 2 3 4 5 6

300 305 310 315 320 325 330

Time (s)

Int Man Temperature (K)

(b) Intake manifold

−1 0 1 2 3 4 5 6

400 500 600 700 800 900 1000 1100 1200

Time (s)

Exh Man Temperature (K)

(c) Exhaust manifold

Figure 3.17: Estimating the temperatures using steady-state characteristics.

It is observed that the effect on the pre compressor temperature is not

sig-nificant. The intake manifold temperature estimation is worse, but does not affect the overall operation significantly considering the scale of the temperature changes and the relative error. Omitting the temperature dynamics in the exhaust manifold has a considerable effect. However, comparing the error introduced by such calculation to temperature measurements shown in Figure 3.4c), leads to the conclusion that using the calculated values for feedback is superior to using the raw thermocouple readings.