Model III: Redox Reactions on the Electrolyte
TWC 1 TWC 2
6.3 Control of the Relative Oxygen Storage Levels
6.3.3 Sensor Diagnosis
be performed in a sufficiently reproducible manner. Notice that only a close- coupled TWC was in use.
The results of the considerably aged TWC meet the expectations fairly well.
With an increasing conversion rate ratioqO2/qCO, the NO emissions increase, whereas the HC and CO emissions decrease. With the TWC controller in use, the performance is slightly better than with aλcontroller only. With a more aggressive TWC controller, the NO conversion is significantly improved at the cost of the CO conversion, which is slightly deteriorated. Hence, when choos- ing a parametrisation, the performance of the second TWC should be taken into account. If this converter is able to oxidise the CO efficiently, a more aggressive controller can be used for the close-coupled TWC.
Considering the results of the moderately aged and the fresh TWCs, the pic- ture is not as clear as for the considerably aged one. The main reason is cer- tainly the very low concentrations, which cannot be covered with sufficient accuracy by the measurement equipment in use. Another reason might be that the reproducibility of the measurements is too low to resolve the small dif- ferences between the different controller configurations. This is actually the good news: Less aged TWCs seem to be less sensitive to the controller con- figuration, at least, when the conversion efficiencies are concerned. However, it can be clearly seen that the use of the TWC controller is very important for the balance of the TWC. Especially the conversion rate of NO is significantly improved when the TWC controller is used. The reason is the generally bet- ter adjusted oxygen storage levels, which has already been shown in Figures 6.7and6.8. Fresher TWCs only recover very slowly or not at all from a fuel cut-off, if no TWC control strategy is used.
To summarise, it can be stated that TWC controller tuning should mainly fo- cus on more aged converters. Depending on the underfloor TWC (and of course on the emission limits enforced by legislation), a more aggressive strategy can be implemented, which improves the NO conversion at the cost of the CO. As for less aged TWCs, a robust balance is required in order to avoid high oxygen storage levels, which deteriorate the NO conversion. With this prerequisite met, fresher TWCs always perform better with respect to the three critical species addressed by legislation.
0.98 1 1.02
λ exh [−]
0.6 0.7 0.8
U λ st [V]
0 0.5 1
θ O,1 [−]
0 0.5 1
θ O,2 [−]
0.6 0.7 0.8
θ O,3 [−]
0 0.1 0.2
θ CO,3 [−]
0 100 200 300 400 500 600
−2
−1 0 1 2x 10−3
time [s]
∆λ calc [−]
measured estimated (EKF)
θO,1 setpoint
θO,2 setpoint θO,3 setpoint
unfiltered filtered
Figure 6.12: Test of the upstream wide-rangeλsensor diagnosis without correction of the error occurring from drifting CO occupancies. An offset of +0.1% is added toλexh
at20 s. The TWC control outputλcalchas been normalised to zero at the beginning of the experiment.
value, whereas the controller forces the oxygen occupancies to the setpoints.
This is achieved by the integrating part of the TWC controller. Hence, when the new steady-state level is reached, the integrator compensates for the offset of the wide-rangeλsensor at the inlet of the TWC. The output of TWC con- troller can thus be interpreted as the sensor offset, because it is actually the setpoint for theλcontroller due to the cascade structure. This procedure was tested on the test bench. The engine was run in steady-state conditions with the TWC controller used. The sensor signal was then distorted by 0.1%. The result is shown in Figure6.12. The disturbance was imposed at approximately 20 s. Since theλcontroller immediately reacts, no excursion can be seen in theλexh-signal. However, from the switch-typeλsensor signal and from the occupancies, it can be seen that the system was disturbed. The control signal
∆λ, which has been normalised to 0 at the beginning of the experiment, fol- lows the error within approximately100 s. The signal has been additionally filtered for illustration. Unfortunately, the initially correctly indicated error drifts away after about200 s. Notice that this goes hand in hand with the drift of the deactivation of cell 3. The problem is that the setpoints of the oxygen occupancies are not adjusted to the catalyst deactivation, i. e., to the CO occu- pancies. If these occupancies are increasing as in the example presented here, the controller has to shift theλto the lean side to maintain the desired oxy- gen occupancy. Hence,∆λdrifts to the lean side. Theoretically, this should be accounted for, if the conversion rate ratios are to be maintained exactly, as can be seen from (6.9). As far as the overall conversion efficiency of the TWC is concerned, this adjustment is not crucial, as has been demonstrated above.
However, for the detection of smallλsensor offsets, this cannot be neglected.
Therefore, the difference between the actual CO occupancy and its calculated steady-state value has been taken into account using (6.9) and the controller gainK3of cell 3 for the correction of the calculated sensor error.
∆λcorr= ∆λ+ µ
−qO2
qCO
k1
2 +k6
2 +k5
¶
∆θCO,3
qO2
qCO
k1
2 +k2−k5
K3 (6.23)
The result of this correction is presented in Figure6.13. Now, the indicated offset remains at the correct value, the sensor offset can be accurately deter- mined with this method. Thus, this method is suitable for the diagnosis of the wide-rangeλsensor.
The example presented here is of course somewhat academic, since every- thing runs under nice steady-state conditions. During transient operation, such a robust and accurate result could hardly be obtained. However, in reality, the
0.98 1 1.02
λ exh [−]
0.6 0.7 0.8
U λ st [V]
0 0.1 0.2
θ CO,3 [−]
0 100 200 300 400 500 600
−2
−1 0 1 2x 10−3
time [s]
∆λ corr [−]
measured estimated (EKF)
θCO,3 setpoint
unfiltered filtered
Figure 6.13: Test of the upstream wide-rangeλsensor diagnosis with correction of the error occurring from drifting CO occupancies. An offset of +0.1% is added toλexh
at20 s. The corrected TWC control outputλcorr has been normalised to zero at the beginning of the experiment.
goal of the diagnosis is not to detect such small offsets quantitatively as in the example, but rather significant faults occurring from sensor malfunctions.
An open question is of course the reliability of the switch-type sensor, on which the concept is based. This problem has not been investigated here. How- ever, a hint can be given about how it can be approached. The main challenge is to differ between errors of the upstream and the downstream sensors. If there is a satisfactory solution at all, this can only be obtained by investigating the dy- namics of the observer, especially the interaction of the sensor signals and the oxygen occupancies. It is likely that this behaviour is differently influenced by distortions of the two sensor signals. If the types of behaviours can be reliably separated, the diagnosis of the downstream sensor can be realised.