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NH3 Filling Level Control for SCR Catalysts on the Basis of Real-timecapable Physical Models Based on a physical model of SCR, IAV has developed a software to compute the quantity of AdBlue dosed in SCR systems.
© IAV
The low-dimensional SCR model is computed on the control unit and can be continuously checked against the information measured by the downstream NOx sensor using an extended Kalman filter. This results in a closed-loop control of the NH3 filling level in the SCR catalyst with a high degree of robustness to faults in the hardware of the dosing system.
AUTHORS
Dr. Gregor Gelbert is Development Engineer, Algorithm Development – Exhaust Gas Aftertreatment Diesel, at IAV GmbH in Berlin (Germany).
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Olaf Friedrichs is Team Manager, Algorithm D evelopment – Exhaust Gas After treatment Diesel, at IAV GmbH in Berlin (Germany).
Daniel Heß is Head of Department, Software and Algorithm Development – D iesel Passenger Cars, at IAV GmbH in Berlin (Germany).
Dr. Lars Henning is Team Manager, Electronics and Diagnostic Systems – C ommercial Vehicles, at IAV GmbH in Berlin (Germany).
ADVANTAGES OF PHYSICAL MODELS
SCR (Selective Catalytic Reduction) catalysts, hereinafter called SCR, are a key component in modern diesel vehicle exhaust gas aftertreatment for reducing nitrogen oxide emission (NOx). For the SCR reactions to take place, ammonia (NH3) is required which, in volume production applications, is generated in the exhaust system by means of a urea solution (known in Europe as AdBlue). The urea solution is added to the hot exhaust gas and decomposes into NH3 in the course of two intermediate reactions. The resultant NH3 is adsorbed by the catalyst whereupon it is available for the SCR reactions. Achieving high NOx conversion rates, while at the same time preventing NH3 escaping from the catalyst (NH3 slip), demands exact adjustment of the NH3 filling level in the catalyst and the target filling level depends on the operating conditions. The SCR dosing software has the function to accurately estimate the actual filling level and then to compute the AdBlue dosing amount required to obtain the target filling level. Current volume production applications mainly use map-based control systems. Map-based algorithms in general come with the drawback that they are only valid within the selected calibration range and provide either limited or no extrapolation capability at all. For this reason, it is difficult or it requires high effort to calibrate a map structure such that it can be applied to all conceivable boundary conditions possibly occurring in real-world driving (RDE, Real Driving Emissions). In contrast to this, models based on the laws of physics and balance equations can be expected to permit a certain extrapolation capability. This even applies if only the fundamental relationships are modeled, as in the case of the low-dimensional model presented below. With its few physical parameters, the model used by IAV is also fairly easy to calibrate. A further major advantage of the physical model over map-based structures is the ability to use standard algorithms for creating a state estimator that con tinuously compares the model with the MTZ worldwide 02|2017
information measured by the downstream NOx sensor. An extended Kalman filter is used here for this purpose. The result is a closed-loop control of the NH3 filling level with all the known advantages of closed-loop control over openloop control systems. DESCRIPTION OF THE PHYSICAL SCR MODEL
The physical model of the SCR catalyst represents the heart of the dosing software. In creating the model, the aim was to cover all of the key processes in the SCR while also keeping the model so simple that it can run on a standard control unit in real time using only few resources. For this purpose, the catalyst is initially modeled as an ideally mixed stirred-tank reactor, as shown in [1] and [2] for example. This means that the concentrations at output ci, ds equate to those inside the catalyst ci, FIGURE 1. The chemical reactions covered are the adsorption and desorption of ammonia, three reactions for reducing the nitrogen oxides and an oxidation reaction for the adsorbed NH3. The reaction rates r·j of the six reactions are modeled on the basis of a formal kinetic Arrhenius approach, where k0,j is the pre-exponential factor and Ej the activation energy of the reaction. These twelve parameters are also the main parameters for calibrating the model. The equations use a mean temperature TSCR and, for the sorption reactions, the temperature at the output of catalyst Tds. This has proven advantageous in modeling NH3 slip. A mole balance then produces the differential equation system with Eq. 1, 3, 4 and 5 in FIGURE 1. Solving the equations the gas concentrations at the catalyst output and, through cNH3,s, the mass of stored NH3 can be calculated. However, the differential equation system can only be integrated with high computational effort because the equations have widely differing time scales: Eq. 3 to 5 run very quickly, Eq. 1 runs slowly and therefore determine the dynamic of the overall system. To resolve this problem, the left-hand sides of Eq. 3 to 5 are set to zero, i.e. only the steady-state solution is taken into consideration. The concentrations
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of NH3, NO and NO2 at the output of the SCR then follow from an analytical function of the other state variables and inputs. Investigations have shown that the effects of this simplification on model accuracy are negligible. Compared to the above-mentioned publications, a second major difference of the model comes from introducing the correction state finj for the NH3 dosage in Eq. 2. The state is modeled as a constant and initialised with 1. In the closed loop-control, i.e. with active extended Kalman filter, the state can be changed if implausible behaviour is given in relation to the model. For example, it is recognised if the NH3 concentration actually available for the reaction at the catalyst inlet does not equate to what should in theory be produced from the AdBlue dosing amount requested by the software. Examples of this are shown in the results part. This adaptability makes the software highly robust also to other faults, such as drift of the upstream NOx sensor. COMPUTING THE ADBLUE DOSING QUANTIT Y AND CLOSING THE CONTROL LOOP
FIGURE 2 shows a schematic diagram of the dosing software with the input variables on the left-hand side and the mass flow of AdBlue to be dosed as output on the right-hand side. Integrating the model equations constantly provides estimates of the gas concentrations at
Reaction rates r·ads = k0,ads exp (–Eads / (R Tds ))(1 – θ)cNH3 RTaus r·des = k0,des exp (–Edes (1 – Ω θ ) / (RTds )) θ r· = k exp (–E / (R T ))c c
Modeled reactions
r·NOx = k0,NOx exp (–ENOx / (R TSCR ))cNH3,s cNO cNO2 r·NO2 = k0,NO2 exp (–ENO2 / (R TSCR ))cNH3,s cNO2 r· = k exp (–E / (R T ))c
Fast SCR (reduction of NO and NO2)
NO
0,NO
Ox
NO
0,Ox
Ox
θ=
With
SCR
SCR
NH3,s
NO
NH3,s
nNH3,s nNH3,s,max
NH3 adsorption NH3 desorption Standard SCR (reduction of NO) Slow SCR (reduction of NO2) Oxidation of adsorbed NH3
State equations
TSCR = f (Tus ,Tds )
Eq. 1 Eq. 2 ci, ds = ci Eq. 3
ci
ci, us
Eq. 4 Eq. 5
the output of the SCR and of the NH3 filling level. A filling-level controller adjusts the estimated filling level m ˆ NH3,s to a temperature-dependent target filling level. Together with the value measured by the upstream NOx sensor, a feed-forward control quantity is also computed. Below the model, the extended Kalman filter is shown in schematic form. NOx sensors used today in volume-produced vehicles have a cross sensitivity to NH3, making the value measured by the downstream NOx sensor a function of NO, NO2
· m Exh
dxˆ dt
SCR model
cNO,us
cNOx,us
+
∫
cˆ NH3,ds cˆ NO,ds cˆ NO2,ds
xˆ
Map
Tus
m ˆ NH3,s–
Filling level controller
cNOx,us K(y – ˆy) EKF P ∫ Dosing software
=0
dt dcNH3 dt dcNO dt dcNO2 dt
= a3 (f
in j
cNH3,ein – cNH3 ) - r·ads + r·des
= a3 (cNO,us – cNO ) – r·NO – 0.5 r·NOx = a3 (cNO2,us – cNO2 ) – 0.75 r·NO2 – 0.5 r·NOx
CALIBRATION PROCESS
To achieve a high level of accuracy in control of the NH3 filling level,
FIGURE 2 Schematic diagram of the dosing software with physical SCR model, extended Kalman filter (EKF), filling-level controller and feed-forward control (© IAV)
· m AdB,LC +
mNH3,s,set
cˆNO,ds,cˆNO2,ds
cNOx,ds
d finj
= r·ads – r·des – r·NO – r·NOx – r·NO2 – r·Ox
and NH3 concentration which, in the simplest case, can be modeled as the total sum. The Kalman filter constantly compares the information measured by the downstream NOx sensor with the model prediction and, in the event of deviations, takes action to correct the model states. This ensures that the model is never faroff from the SCR’s actual behaviour.
Map
Tds
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xˆ (1) Tus
cNO2,us
dt
FIGURE 1 Modeled reactions and state equations of the low-dimensional SCR model (© IAV)
AdB NH3
cNH3,us
dcNH3,s
dP dt
SCR model with state correction
Feed-forward control
· m AdB,FF
· m AdB
the model must be matched to the target system. To do this, dynamic measurements are conducted on a roller dynamometer or engine test bench and the relevant input and output quantities of SCR are recorded. There is no need to conduct time-consuming pointby-point measurements of steady-state operating points as is it necessary at calibration of maps. Important is the design of the experiments since exact matching is only possible if the SCR is measured in all relevant operating ranges. For instance, the catalyst must also be operated in ranges in which NH3 slip and oxidation occurs in order to determine the kinetic parameters of the corresponding equations. Optimisation routines are available for adjusting the model parameters, FIGURE 3. A weighted sum of the squared deviations between gas concentrations measured at the output of the SCR and model predictions is used as quality functional. Starting from an initial parameter set Par0, the model’s kinetic parameters are changed until the quality functional Fsum, and therefore the deviation between model and measurement, is minimal. RESULTS FROM SIMULATION AND EXPERIMENT
FIGURE 4 shows a schematic diagram of a virtual development environment for the dosing software. The dosing software is set up to adjust the NH3 filling
Par0 Optimiser
Fsum, k
Park
FIGURE 3 Optimum model parameters are found using optimisation routines (© IAV)
Simulation run SCR model FNO = WNO (cN0,ds,measured (t) – cN0,ds (t))2 dt Fsum = FNO + FNO2 + FNH3
level of a high-dimensional SCR model generated with the program Axisuite to a target filling level. For this purpose, the parameters of the low-dimensional model were matched to the behaviour of the high-dimensional model using the above-described optimisation process. To test the robustness of the software to faults in the dosing system, the computed · is multiplied mass flow of AdBlue m AdB by the disturbance factor KD,inj which is unknown to the software. In the case of KD,inj = 0.5 therefore, 50 % less and, in the case of KD,inj = 1.5, 50 % more is dosed than computed by the software. In real-world driving, such faults may occur as a result of diluting the AdBlue medium, dosing valve wear or soiling or by incorrect pressure in the dosing system.
FIGURE 5 shows simulation results for the cold-started WLTC. It presents the Axisuite model’s characteristic variables as well as the correction state finj computed by the dosing software. Integral dosing amount, NH3 load and slip are shown in normalised form. Several cycles were consecutively simulated for each disturbance factor until the curves stopped changing. In other words, the quasi-steady state is shown in each case. The effects of the faults for open-loop control can be seen in the left-hand column of FIGURE 5. Open-loop means that the Kalman filter is not activated in the software and, as a result, the information from the downstream NOx sensor is not used to adjust the model in the software. Correction state finj therefore stays
Model-based dosing software Low-dim. SCR model
m ˆ NH3,s
cˆNH3,ds m ˆ NH3,s
Ref.
cˆNOx,ds
Filling level controller
m ˙ AdB
FIGURE 4 Schematic diagram of a simulation environment for testing the robustness of the dosing software to faults in the dosing system: dosing software (top) and high-dimensional SCR model (bottom) (© IAV)
Model correction at closed loop control
Extended Kalman filter
cNOx,ds cNOx,us
m ˙ AdB, disturbed
X
KD,inj = [0.5, 0.8, 1, 1.2, 1.5]
Axisuite SCR MTZ worldwide 02|2017
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Open loop
1.5
Closed loop
1.0
0.5
0.5
0
0
3
3
2
2
1
1
0
0
1
1
0.5
KD,inj KD,inj KD,inj KD,inj KD,inj
0 9 6
= = = = =
0.5
0.5 0.8 1 1.2 1.5
0 9 6
3
3
0
0 1.5
1
1 0.5 1800
0.5 0
600
Time [s]
1200
at its initial value of 1 and the software behaves in a very similar way to a classic map-based structure. Disturbing factors greater than 1 result in more being dosed than in the
1800
0
600
Time [s]
1200
nominal case (K D,inj = 1.0), an excessive NH3 filling level in the Axisuite SCR model and a significant increase in NH3 slip. Disturbing factors smaller than 1 result in an insufficient dosing quantity,
a reduced NH3 filling level and reduced NOx conversion η. The results from the closed-loop control, i.e. with Kalman filter activated, can be seen in the right-hand column
v [km/h] m· AdB normalised [-]
150 100
1.5
400 300 200 100 0
50 0
1.5 1
1
0.5
0.5
0
0
Integral NOx mass normalised [-]
1
3
KD,inj = 0.5 KD,inj = 1 KD,inj = 1.5 us ds
0.8 0.6
2 1 0 1.5 1.25
0.4
1 0.2
0.75 0.5
0 0
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FIGURE 5 Simulation results in the WLTC: comparison of open- and closed-loop control with various disturbing factors KD,inj (© IAV)
Tus [°C]
finj [-]
1.5
NH3 slip NH3 load DCU normalised [-] normalised [-]
NH3 slip normalised [-]
1.5
1
1000
2000 3000 Time [s]
4000
0
1000
2000 3000 Time [s]
4000
finj [-]
η [-]
NH3 load normalised [-]
Integral dosing amount AdBlue normalised [-]
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FIGURE 6 Experimental results from road tests with various disturbing factors KD,inj (© IAV)
of F IGURE 5. The software has adapted the correction state finj in each case and thus fully compensated for the faults. FIGURE 6 shows results from the closedloop control in experimental testing. For this purpose, the software was installed in a prototype vehicle, c alibrated on a roller dynamometer and then tested in normal road traffic. The vehicle was taken on a round trip involving urban and expressway driving all around IAV’s Berlin development center. As in the case of simulation, the effect of a multiplicative dosing disturbance was examined. For the case without disturbance (KD,inj = 1.0), it can be seen that apart from minor fluctuations, correction state finj remains very close to the initial value of 1. For the case of underdosing (KD,inj = 0.5), the integral curve for downstream NOx mass initially rises somewhat more sharply. However, correction state finj quickly runs towards 0.5, thus compensating for the error and leaving the integrals to run parallel again from 1500 s on. Once again, NOx masses, dosing quantity, NH3 slip and filling level estimated by the software (NH3 load DCU) are shown in normalised form. NH3 slip was measured with an NH3 sensor additionally installed in the vehicle. In the case of overdosing (KD,inj = 1.5), significantly higher values can be seen for NH3 slip, and correction state finj takes a little longer to run to 1.5. However, after 2700 s this error is also fully compensated.
REFERENCES [1] Schar, C. M.; Onder, C. H.; Geering, H. P.; Elsener, M.: Control-oriented model of an SCR catalytic converter system. SAE World Congress 2004, SAE paper 2004-01-0153, 2004 [2] Hsieh, M. F.; Wang, J.: Diesel Engine SCR Systems: Modeling, Measurements, and Control. Springer: New York, 2014, pp. 425-451
SUMMARY
Based on real-time-capable physical models, IAV has developed a closed-loop control for the NH3 filling level of SCR systems and a related partially automated calibration process. A key advantage lies in the software’s high level of robustness to faults on the hardware side. A modular setup also allows it to be used for complex exhaust systems with combinations of Lean NOx Trap (LNT) and SCR, tandem SCR or anti-slip catalysts. Additional sensors, such as the NH3 sensors increasingly being used in heavy-duty commercial vehicles, can be integrated to improve the accuracy of model predictions. Conversely, the high level of robustness also provides the potential for saving on sensors, like the upstream NOx sensor. IAV has already used the software successfully in several customer projects. MTZ worldwide 02|2017
HERMANN APPEL PRIZE The authors are delighted to mention that Benjamin Fietzke’s Master’s degree thesis on “Model-Based Closed-Loop Control for an SCR Catalyst and Implementation in a Near-Control-Unit Environment”, written while the software was being developed, was awarded the 2016 Hermann Appel Prize.
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