An Extended Kalman Filter for NO x Sensor Ammonia Cross- Sensitivity Elimination in Selective Catalytic Reduction Applications

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1 21 American Control Conference Marriott Waterfront, Baltimore, MD, USA June 3-July 2, 21 ThA19.6 An Extended Kalman Filter for NO x Sensor Ammonia Cross- Sensitivity Elimination in Selective Catalytic Reduction Applications Ming Feng Hsieh and Junmin Wang * Department of Mechanical Engineering Ohio State University, Columbus, OH 4321 Abstract Vehicle NO x emission regulations are becoming more and more stringent worldwide. A selective catalytic reduction (SCR) system which uses ammonia as the reductant to reduce tailpipe NO x emissions is widely adopted by Diesel engine applications. For SCR control, a NO x sensor is commonly used to monitor the emissions, however it has been discovered that NO x sensors typically are cross-sensitive to the presence of ammonia. Such a feature becomes a critical problem as ammonia slip can be present downstream of a SCR catalyst where the NO x sensor is located. To address this issue, an extended Kalman filter (EKF) is designed in this paper to estimate the actual exhaust gas NO x concentration and the cross-sensitive factor such that the cross-sensitivity error can be eliminated. W I. INTRODUCTION ITH the increasing concerns on energy consumption and environment, including the greenhouse gas emissions, worldwide, Diesel engines have attracted much attention in recent years due to their better fuel efficiency and lower CO 2 emission compared to their gasoline counterparts. However, Diesel engines also feature higher NO x emissions which have been tightly restricted by emission regulations worldwide in recent years. It has been studied that the stringent NO x emissions regulations in the near future cannot be satisfied by pure engine control alone [21]-[25]. An aftertreatment system is necessary to further reduce tailpipe NO x emissions. Among a variety of options, selective catalytic reduction (SCR) is one of the most promising technologies for Diesel engine vehicle applications. SCR utilizes ammonia as the reductant to convert the NO x emission to diatomic nitrogen. Several SCR controllers have been proposed in recent years to control the SCR catalyst ammonia concentration such that the tailpipe NO x emission can be minimized [3]-[6]. Among the controllers surveyed in the study of [7], it is widely considered that feedback control is necessary to reduce the NO x emissions to an acceptable level and to prevent undesired ammonia slip. Feedback control of SCR requires measurements of tailpipe NO x and ammonia concentrations. NO x sensors have been available in production for a few years and ammonia sensors for aftertreatment application were recently available from suppliers such as Delphi [8]. An important issue is that many studies have pointed out that NO x sensors have significant cross-sensitivity to ammonia [7]-[1]. The M. F. Hsieh is with the Ohio State University, Columbus, OH 4321 USA (phone: ; hsieh.122@osu.edu). * Corresponding author. Junmin Wang is with the Ohio State University, Columbus, OH 4321 USA ( wang.1381@osu.edu). ammonia cross-sensitivity can cause overrated tailpipe NO x emissions and the closed loop system becomes potentially unstable. Even though the problem is critical for SCR control, not many effective solutions can be found in literature. Most applications adopt the straightforward manner of utilizing a factory provided cross-sensitivity constant to compensate the error based on the sensor model [1]. However, this may not be sufficient especially as the vehicle emission regulations are stringent enough to where consistent and precise measurement of NO x concentration is essential. The cross-sensitivity factor can be different between sensors and also can change with time due to sensor aging and environmental variations. By these effects, the conventional correction approach may not work as well as expected. In this paper, with the recently available ammonia sensors, we propose an approach of using an extended Kalman filter (EKF) [1][2][2] to estimate the actual NO x concentration and ammonia cross-sensitivity factor such that the NO x sensor cross-sensitivity error can be well handled. The rest of this paper is organized as follows. A brief introduction of the SCR model is presented in the second section. After that, an EKF for the ammonia crosssensitivity error elimination is designed. Then simulations based on an experimentally-validated full-vehicle simulator are introduced to verify the proposed approach. At the end of the paper, conclusive remarks and future work are summarized. II. SELECTIVE CATALYTIC REDUCTION (SCR) A. SCR Operation Principles The SCR NO x reduction mainly includes three processes. In the first process, ammonia is injected upstream of the SCR catalyst as the reductant. In the second process the ammonia inside the catalyst is partially adsorbed on the catalyst surface. And then the adsorbed ammonia can react with NO x and convert it to nitrogen molecule and water. A schematic view of SCR operations is shown in Fig. 1. The dominant chemical reactions and the corresponding reaction rates are briefly introduced below. 1) NH 3 Adsorption/Desorption The NH 3 inside the SCR catalyst can be adsorbed on the SCR substrate. The adsorbed NH 3 can also be desorbed from the substrate as shown in the following reaction equation. NH 3 + θ NH 3, (1) where θ is the free catalyst site. The rate of the NH 3 adsorption/desorption can be expressed by the following equations [11] /1/$ AACC 333

2 RR aaaaaa = kk aaaaaa eeeeee EE aaaaaa RRRR CC NNNN 3 1 θθ NNNN3, (2) RR dddddd = kk dddddd eeeeee EE dddddd RRRR θθ NNNN 3, (3) where RR xx represent the chemical reaction rates, TT is temperature, EE, kk, and RR are constants, CC xx represented concentration of species xx, and θθ NNNN3 is the ammonia surface coverage ratio define by: θθ NNNN3 = MM NNNN 3 ΘΘ. (4) MM NNNN3 is the mass of ammonia stored in the SCR substrate and ΘΘ is the ammonia storage capacity. 2) NO x Oxidation Also, at a temperature higher than 45 deg C, the adsorbed NH 3 can be oxidized to NO by the following reaction. NH O 2 NO + 1.5H 2 O, (5) RR oooooo = kk oooooo eeeeee EE oooooo RRRR θθ NNNN 3. (6) 3) NO x Reduction The adsorbed NH 3 can then catalytically react with NO x to become nitrogen by the following reactions. 4NH 3 + 4NO + O 2 4N 2 + 6H 2 O, (7) 2NH 3 + NO + NO 2 2N 2 + 3H 2 O, (8) 4NH 3 + 3NO 2 3.5N 2 + 6H 2 O. (9) Because more than 9% of the Diesel engine-out exhaust NO x is usually composed of NO [12]. Assuming there is no DOC/DPF presented upstream of the SCR catalyst, reaction in Eq. (7) is considered the dominant one in NO x reductions. The reaction rate is described below [6]: RR rrrrrr = kk rrrrrr eeeeee EE rrrrrr RRRR CC NNNNθθ NNNN3. (1) In case a DOC/DPF is used upstream of the SCR catalyst, fraction of NO 2 inside NO x can be increased significantly. With this situation the reaction of Eq. (8), which is much faster than the reaction in Eq. (7), should be considered. CC NNNN = ΘΘ(RR oooooo RR rrrrrr ), (11) θθ NNNN 3 = RR aaaaaa RR dddddd RR rrrrrr RR oooooo, (12) CC NNNN 3 = ΘΘ(RR dddddd RR aaaaaa ). (13) Such dynamic equations can be used to develop a SCR model using the continuous stirred tank reactor (CSTR) approach and mass conservation law. Different SCR models for vehicle applications have been proposed in the literature [11]-[14]. In this paper we adopted the model presented in [11]. The nonlinear model in state-space form is shown in Eq. (14). CC NNNN θθ NNNN 3 = CC NNNN 3 CC NNNN ΘΘrr rreeee θθ NNNN3 + FF + rr VV NNNN 3,oooooo ΘΘθθ NNNN3 θθ NNNN3 rr aaaaaa CC NNNN3 + rr,dddddd + rr rrrrrr CC NNNN + rr oooooo + rr aaaaaa CC NNNN3 + CC NNNN3 ΘΘrr aaaaaa 1 θθ NNNN3 + FF + ΘΘrr VV dddddd θθ NNNN3 FF VV CC FF NNNN3,iiii + CC NNNN,iiii, VV (14) where rr xx = kk xx ee EE xx RRRR ; xx = aaaaaa, dddddd, oooooo, rrrrrr; CC NNNN and CC NNNN3 are the tailpipe NO x and ammonia concentrations; CC NNNN3,iiii is the pre-scr ammonia concentration controlled by the SCR controller; and CC NNNN,iiii is the engine exhaust NO x concentration. III. EXTENDED KALMAN FILTER FOR NO X SENSOR AMMONIA-SENSITIVITY ESTIMATION A. NO x Sensor Cross-Sensitivity against Ammonia A typical setup of the SCR and the corresponding sensors is shown in the figure below. Figure 2. Architecture of SCR and the corresponding sensors. It has been known that NO x sensors are cross-sensitive against the presence of ammonia. The measurement CC NNNN,ssssss from the NO x sensor can be modeled by the superposition of NO x on ammonia concentration as below [3]. CC NNNN,ssssss = CC NNNN + KK cccc CC NNNN3, (15) Figure 1. Schematic presentation of SCR reactions. B. SCR Model Based on the molar balance, the main SCR dynamics can be described by the following equations [11]: where KK cccc is the cross-sensitivity factor, CC NNNN is the actual NO x concentration, and CC NNNN3 is the (actual) ammonia concentration in the exhaust gas. It can be seen from Figure 2 that the pre-scr NO x sensor is not affected by the ammonia cross-sensitivity since it is placed upstream of the urea injector. However, the post- SCR NO x sensor is subjected to ammonia slip and measurement error caused by the ammonia-sensitivity, 334

3 KK cccc CC NNNN3. This not only hampers the effectiveness of the NO x sensor, but also makes the SCR controller potentially unstable and can induce unnecessary urea cost. With the cross-sensitivity, it is possible that the more ammonia injected, the higher the NO x reading from the post-scr NO x sensor, because of the higher ammonia slip. A common approach to address this problem is to predict the actual NO x concentration using the sensor model in Eq. (15) and the corresponding ammonia measurement and a factory provided cross-sensitivity factor KK cccc. However, it is believed that the cross-sensitivity factor has variance between sensors, and slowly time-varying bias can be expected as the environment changes and the sensor ages. An inaccurate cross-sensitivity factor can cause serious NO x concentration measurement error and an observer must be designed to estimate the actual value. As the cross-sensitivity factor changes slowly with time, it is not easy to develop a model to predict this variation, and a conventional model-based observer is hard to be designed to estimate this value. To better address this problem, we propose the idea of using an extended Kalman filter (EKF) to estimate the value based on an approximated model and the stochastic process calculation. B. EKF Design for NO x Cross-Sensitivity Elimination 1) Extended Kalman Filter (EKF) Kalman filter is well-known as an efficient recursive filter that can optimally estimate the state of a linear dynamic system from a series of noisy measurement [2]. For nonlinear systems, extended Kalman filter [1][2] has been developed and validated by many studies to be effective in real applications [15]-[17] and [24]. Unlike model-based observers which heavily rely upon plant models and measurements, a specific feature of a Kalman filter is that it finds the stochastic relations between model predictions and sensor measurements, and then estimates system states in an optimal approach. By utilizing this feature of the Kalman filter, a slowly time-varying state can be modeled as a constant and then be estimated by comparing the model prediction and measurements in a stochastic manner. A well studied example of such applications is the GPS/INS sensor fusion, where EKFs were used to predict the sensor biases from gyroscopes and accelerometers. In this study, the cross-sensitivity factor KK cccc in Eq. (15) is also a slowly timevarying state. A general formulation of EKF is presented below. The nonlinear system to be dealt with by an EKF is generally expressed in the following form. xx(kk) = ff xx(kk 1), uu(kk) + ww(kk), (16) zz(kk) = h xx(kk) + vv(kk), (17) where ww(kk) and vv(kk) are the process and observation noises with zero-mean multivariate Gaussian noise with covariance of QQ(kk) and R(kk). By the model described in Eq. (16) and Eq. (17), an EKF estimates the states by two steps: prediction and update. In the prediction step, the state vector xx and the error covariance matrix PP are predicted as follows: xx(kk kk 1) = ff xx(kk 1 kk 1), uu(kk), (18) PP(kk kk 1) = FF(KK)PP(kk 1 kk 1)FF(KK) TT (19) + QQ(kk), where FF is the Jacobian matrix of the state function ff. Then in the update step, the predicted system states xx(kk kk 1) and error covariance matrix PP(kk kk 1) are updated by comparing them to the measurement zz(kk). Based on the assumption that the noises are zero-mean Gaussian distribution, the optimal Kalman gain KK(kk) and the estimated value xx(kk) can be calculated by the following equations: yy(kk) = zz(kk) h xx(kk kk 1), (2) SS(kk) = HH(kk)PP(kk kk 1)HH(kk) TT + RR(kk), (21) KK(kk) = PP(kk kk 1)HH(kk) TT SS(kk) 1, (22) x(k k) = x(k k 1) + KK(kk)yy(kk) (23) PP(kk kk) = II KK(kk)HH(kk) PP(kk kk 1) (24) where HH is the Jacobian matrix of the output function h. 2) EKF for Cross-Sensitivity Factor and NO x Concentration Estimations Because the cross-sensitivity factor KK cccc in Eq. (15) is assumed to be a slowly time-varying variable, it can be modeled by the following equation. KK cccc =. (25) And based on the SCR model in Eq. (14), the NO x concentration is modeled by the following equation: CC NNNN = CC NNNN ΘΘrr rrrrrr θθ NNNN3 + FF VV + rr oooooo ΘΘθθ NNNN3 + FF VV CC NNNN,ssssss,iiii. (26) where CC NNNN,ssssss,iiii is measured by the upstream NO x sensor which is not affected by the ammonia cross-sensitivity under the assumption CC NNNN,ssssss,iiii = CC NNNN,iiii, VV is a constant, FF, rr NNNN3,oooooo, and rr rrrrrr are available from measurements and corresponding models, ΘΘ is assumed to be a known and temperature-dependent variable, and θθ NNNN3 is the ammonia surface coverage ratio which is estimated by the observer developed in [18]. By the above models, the prediction equation in discrete form is obtained bellow. xx(kk kk 1) = KK cccc (kk kk 1) CC NNNN (kk kk 1) (27) KK cccc (kk 1 kk 1) = CC NNNN (kk 1 kk 1) + ttcc NNNN (kk 1 kk 1), where tt is the EKF updating period. The EKF measurement is the post-scr NO x sensor reading CC NNNN,ssssss which can be modeled as: zz(k) = CC NNNN,ssssss (kk) = CC NNNN (k k 1) + KK cccc (k k (28) 1)CC NNNN3 (kk), 335

4 where CC NNNN3 is the ammonia concentration reading from the post-scr ammonia sensor which is assumed to be accurate enough. Based on the prediction and measurement equations of Eq. (27) and Eq. (28), the extended Kalman filter for the estimations of post-scr NO x concentration, CC NNNN, and the sensor cross-sensitivity factor, KK cccc, can be constructed according to Eq. (18) to Eq. (24). IV. SIMULATION RESULTS Simulations of the proposed EKF NO x concentration estimator were done using an experimentally-validated full vehicle simulator cx-emission developed by the Center for Automotive Research at the Ohio State University [19]. Normally (Gaussian) distributed noises with zero mean values were imposed to all the sensor measurements. The simulations were based on the FTP75 test cycle. Vehicle speed, pre-scr NO x concentration, exhaust flow rate, and the exhaust temperature during the cycle are presented in Figure 3. Notice that to feature the presence of NO x sensor ammonia cross-sensitivity, more-than-normal amount of urea was injected during the simulation to have extra high tailpipe ammonia slip, also higher load was imposed to the simulated vehicle in order to have more NO x emissions. Two cases are presented in the following simulation results. The first case assumes the cross-sensitivity factor to be a constant during the test cycle, and the EKF estimates this value with an initial value of zero which is different from the value in the model. The second case imposed a slowly time-varying cross-sensitivity factor. The estimation also started from an initial value of zero, different from the model value. Practically, considering sensor aging, the timevarying effect is unnoticeable from a single FTP75 cycle which is the situation in the first case. On the other hand, for some sensors, the cross-sensitivity factor can change with environment. In this case, noticeable variation could be observed during the time period of a test cycle, which is imitated in the second case. Flow Rate (m 3 /sec) Velocity (m/sec) Temperature (deg C) Exhaust Flow Rate Exhaust Temp/1 4 Exhaust NOx Ammonia Injection Vehicle Velocity/ Figure 3. Considered factors during the FTP75 test cycle simulation. A. Case 1: Constant Cross-Sensitivity Factor during a Cycle Figure 4 shows the comparisons of model predicted post- SCR ammonia concentration, post-scr NO x sensor reading, model predicted NO x concentration, EKF estimated NO x concentration, model predicted cross-sensitivity factor, and estimated cross-sensitivity factor. The cross-sensitivity factor was selected to be.5 as a constant during the test cycle. As seen in Figure 4, the post-scr NO x sensor reading is always higher than the actual NO x concentration due to the presence of ammonia Model Cross-Sen. Fac./25 Estimated Cross-Sen. Fac./ Figure 4. Comparisons of ammonia concentration, NO x measurement, model predicted NO x concentration, and estimated NO x concentration calculated by EKF Model Cross-Sen. Fac./25 Estimated Cross-Sen. Fac./ Figure 5. Zoom-in on beginning porting of the Figure 4. Figure 5 shows the first 2 seconds of the test cycle which offers a better presentation. It can be seen that the predicted NO x concentration converged to the true value as the estimated cross-sensitivity factor approached its true value. It is clear that the NO x estimation is robust to the presence of ammonia NOx Error after EKF NOx Error before EKF NH 3 Concentration Figure 6. Comparisons of errors of post-scr sensor measurement and estimated NO x concentration and the corresponding ammonia concentration. Figure 6 shows the comparisons of errors between the actual NO x concentration and the NO x sensor reading and NO x concentration after the EKF-based correction. The 336

5 cross-sensitivity of the NO x sensor against ammonia can be clearly seen. Also we can see that the EKF significantly reduced the cross-sensitivity error. Figure 7 shows the comparison between the true crosssensitivity factor in the model and the predicted value. It can be seen that the estimated value converged to the actual value fairly well. Cross-Sensitivity Factor Model Value Estimated Value Figure 7. Comparison of estimated cross-sensitivity factor and the actual value (from model). There exist some deviations at the time regions around the 2th second and the 17th second which also caused higher NO x estimation error as can be observed in Figure 6. These are due to the fact that the vehicle was quickly accelerated to high speeds as can be seen in the speed profile in Figure 3. At these moments, the temperature, exhaust gas flow rate, and NO x emissions, together with ammonia injection, were increased significantly such that the system was hardly approximated by the linearized models in the EKF, i.e. Eq. (18), Eq. (21), and Eq. (24). Since the model cannot capture the real dynamics very well, higher estimation errors were presented. However, the errors caused by these variations are still acceptable. The situation can be improved by increasing the EKF updating rate, i.e. decrease t in Eq. (27), if computation capability is allowed. B. Case 2: Slowly Time-Varying Cross-Sensitivity Factor In this case the cross-sensitivity factor is modeled as a time-varying variable during the cycle as shown in Figure 8 and Figure 1. In Figure 8 we can see, because of the timevarying cross-sensitivity factor, the post-scr NO x sensor reading not only changed with NO x concentration and ammonia concentration but was also affected by the factor variation. However, as expected, the estimated NO x concentration can still track the actual value very well. Concentrations (mol/m 3 ) Model Cross-Sens. Fac./5 Estimated Cross-Sens. Fac./ Figure 8. Comparisons of ammonia concentration, time-varying cross sensitive factor, NO x measurement, actual NO x concentration (from model), and estimated NO x concentration calculated by EKF. The following figure shows the time region of the first 2 seconds of the FTP cycle. As can be seen the estimated NO x concentration was not close to the actual value initially, however as the estimated cross-sensitivity factor approaches the actual value, as shown in Figure 1, the NO x concentration calculated by the EKF converged to the actual value. The estimated NO x concentration is almost the same as the actual value after the 9 seconds. For the time period between 115 seconds and 165 seconds the ammonia concentration was reduced to zero, allowing the post-scr NO x sensor reading and estimated NO x concentration to become identical. This happens because there is no ammonia present. After the 165 th second, the NO x sensor reading diverged again because of the presence of the increased ammonia concentration, but the EKF still estimated the actual NO x concentration very well. Concentrations (mol/m 3 ) Figure 9. Zoom in at the beginning of the FTP 75 testing cycle of the simulation in Figure 8. Cross-Sensitivity Factor Model Cross-Sens. Fac./5 Estimated Cross-Sens. Fac./5 Model Value Estimated Value Figure 1. Comparison of estimated cross-sensitivity factor and the actual value (from model) with the cross-sensitivity factor changes with time. Figure 1 shows the convergence of the estimated crosssensitivity factor to the actual time-varying value. The estimated one converged to the desired value very well and the estimation errors were in acceptable ranges. As before, there exist some deviations at the regions where the vehicle accelerated hard and the SCR dynamics was hardly captured by the EKF linearized models. V. CONCLUSIONS AND FUTURE WORK The NO x sensor ammonia cross-sensitivity problem was 337

6 addressed in this paper. It has been studied that the crosssensitivity of NO x sensor can raise a serious issue for Diesel engine SCR system control because ammonia is used as the reductant and the presence of tailpipe ammonia slip can induce significant measurement error on the post-scr NO x sensor. This problem was generally handled by an experimental model to predict the cross-sensitive value in an open-loop fashion which is not a reliable manner when NO x emissions have to be monitored precisely. An extended Kalman filter-based estimation approach was proposed in this paper. The method utilized the stochastic character of EKF and an approximate cross-sensitivity factor model to estimate the actual NO x concentration and cross-sensitivity factor. Simulation results based on the FTP75 test cycle verified the approach of being able to accurately eliminate the cross-sensitivity error caused by the presence of ammonia and to well predict the NO x concentration and cross-sensitivity factor. SCR plant model mismatch and ammonia sensor dynamics were not considered in this paper and they will be part of the future work. ACKNOWLEDGMENT The authors would like to thank the partial financial support provided to this research by the members of The Ohio State University Center for Automotive Research (OSU-CAR) Industrial Consortium. REFERENCES [1] S. J. Julier and J. K. Uhlmann, A New Extension of the Kalman Filter to Nonlinear System, Int. Symp. Aerospace/Defense Sensing, Simulation, and Control, [2] EA Wan, R Van Der Merwe, The Unscented Kalman Filter for Nonlinear Estimation, IEEE 2 Adaptive Systems for Signal Processing, Communication, and Control Symposium, 2. [3] Q. Song and G. 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