A Real-Time Soot Model for Emission Control of a Diesel Engine*

6th IFAC Symposium Advances in Automotive Control Munich, Germany, July 12-14, 2010

A Real-Time Soot Model for Emission Control of a Diesel Engine ⋆ Fr´ ed´ eric Tschanz ∗ Alois Amstutz ∗ Christopher H. Onder ∗ Lino Guzzella ∗ ∗

ETH Z¨ urich, Institute for Dynamic Systems and Control, 8092 Z¨ urich, Switzerland (e-mail: [email protected]) Abstract: Upcoming stringent emissions legislations more and more require feedback control of diesel engines raw emissions. For controller design, control oriented, easily identifiable, and portable models of the plant are needed. This paper presents a novel model for diesel engines particulate matter (PM) emissions that aims to achieve the aforementioned requirements. The PM emissions are modeled as relative deviations of stationary base maps. A polynomial approach is used to estimate the influence of the deviation of each input on the PM emissions. The model is easily extendable and can be refined to the user’s needs. Keywords: Diesel engines, Sensitivity analysis, Control oriented models, System identification, Modelling 1. INTRODUCTION Amongst all prime movers that include combustion, the compression ignition (CI) or diesel engine has the highest thermal efficiency. And despite the facts that modern diesel engines are significantly more expensive than comparable Otto engines and that the lean, diffusion controlled combustion leads to the dissatisfyingly treated problem of NOx and particulate matter (PM) emissions, the high efficiency of diesel engines has lead to widespread use also in light-duty applications. Pfeifer et al. (2003) showed that in order to fulfill the actual and upcoming stringent emission legislations, measures need to be taken not only on the aftertreatment system, but also on the engines raw emissions (i.e. internal measures). One important issue of the internal measures is to treat the influences on the emissions caused by components drift and manufacturing tolerances. Therefore the integration of emission-feedback into the controller structure is needed. Alfieri (2009) showed an emission controlled diesel engine with NOx and air-to-fuel ratio (AFR) feedback. The concept of Stoelting et al. (2008) includes (opacity-based) PM and NOx feedback and is based on two cascaded single input single output loops for NOx and PM control. One important issue of controlling the emissions of diesel engines is to handle the high nonlinearity of the PM emissions and to appropriately take into account the strong multiple input multiple output characteristics of the plant (i.e. the NOx -PM trade-off). Therefore control oriented models of the emissions are a fundamental prerequisite. Schilling et al. (2006) presented a control oriented model for the NOx emissions. This paper is focused on the control-oriented modeling of the PM emissions. A novel model for the PM emissions is ⋆ This work is supported by the FVV (Forschungsvereinigung Verbrennungskraftmaschinen e.V., Frankfurt, Germany), and by the BAFU (Bundesamt f¨ ur Umwelt, Bern, Switzerland).

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presented that attempts to fulfill the above stated requirements and that estimates the PM emissions in real-time and based on signals available in the engines electronic control unit (ECU). The structure of the paper is such that in the following, an overview to PM emission modeling is given. Sections 2, 3, and 4 cover the engine test bench and data acquisition, the model design and identification, and the validation and discussion of the results. 1.1 PM Modeling; An Overview Generally PM models can be classified as phenomenological models and (semi-) empirical models. Phenomenological models exist in various modeling depths from detailed chemical modeling for CFD analysis to mean-value phenomenological modeling based on the conditions in the cylinder at intake valve close (IVC). Due to the high computational burden of phenomenological models their use in real-time applications is not possible yet. Therefore phenomenological models are not further considered here. Interested readers are referred to Hiroyasu and Kadota (1983) and Kirchen (2008). Empirical or semi-empirical models include the black- and grey-box approaches. In these modeling approaches, the physical principles of the PM emissions are not included at all or only in a very general manner. As a consequence, these types of models need a relatively large number of parameters in order to be able to predict the PM emissions with sufficient precision. Additionally, the identified parameters are generally only valid for the engine that was used for identification. Furthermore, extrapolation is problematic or even impossible. The non-phenomenological part of the model structure of the grey- and black-box models can be polynomial on the one hand or it is determined by artificial neural networks on the other hand. Benz et al. (2010) presented a promising control oriented model for the emissions of diesel engines. Their quasi-stationary approach is based on the estima10.3182/20100712-3-DE-2013.00107

AAC 2010 Munich, Germany, July 12-14, 2010

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2. MATERIALS AND METHODS

Table 1. Engine characteristics OM 642

Technical data

3000 cm3 , 6 cylinders 4 valves/cylinder

Max. power

165 kW at 3800 rpm

Max. torque (limited)

400 Nm at 1400 − 3800 rpm

Features

cooled EGR, VTG, IPSO

Injection features

2 pilot, 1 main, 2 post injections 1600 bar max. common-rail pressure

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The measurements used for the identification and validation of the model have been carried out on a production type 6 cylinder 3 liters diesel engine from Daimler AG. The characteristics of the engine are listed in table 1

Name

soot [mg/m ]

6

prail [bar]

tion of the emission deviation relatively to the steadystate value of the specific operating point. The estimate is obtained by an artificially composed relationship between the deviations of the relevant 1 inputs. A polynomial modeling approach for the emissions of a diesel engine is presented in Christen and Vantine (2001) and Hirsch and del Re (2009), where in the latter, the modeling is done for several overlapping regions of operation and linear interpolation between the regions. Models of the logarithmic PM emissions estimated by quadratic equations of the inputs are presented in Hirsch et al. (2008) and Brahma et al. (2009), where in the former, the models are valid for local overlapping regions and interpolation between the regions. In the latter the model performance was optimized in several ways through local and global regression, neural networks, input variation including gradients, history, etc. and a multi model approach where two models were identified for high and low AFR.

Fig. 1. Steps in the rail-pressure at 2200 rpm; 120 Nm and their corresponding influence on the PM emissions (upper plot). of elementary carbon in the continuously sampled and diluted exhaust gas with a small time constant (i.e. it is also suitable for transient measurements). With the known dilution ratio, the concentration of elementary carbon in the exhaust gas can be observed. For identification and validation various measurements have been carried out on the hot engine (cp. table C.1 in the appendix). 3. MODEL DESIGN AND IDENTIFICATION

As stated in the introduction, the aim of the model is its use in control of the emissions of a diesel engine. Due The engine is integrated in a test bench with a station- to the fact that control theory is hardly applicable for ary eddy current brake with a maximum brake power of non-LTI systems, a linearization of the model is needed 130 kW. for controller design. A requirement of the model is its The engine ECU is bypassed via an ES910 rapid proto- easy identifiability. The identification of a model that is typing module from ETAS. Bypass implementation and linear in the parameters is guaranteed to yield optimal data acquisition are done with INTECRIOTM and INCATM , results at very low cost. A polynomial approach with low respectively. With this system, the inputs of the engine order represents a good compromise between the needs for (i.e. boost pressure, exhaust gas recirculation (EGR) rate, controller design, identification and plant characteristics intake port shut-off (IPSO), start of injection (SOI) of and is therefore chosen as model structure. the main injection and of the pilots, rail pressure and governor position) can be varied freely within the bounds The engine-out PM emissions are assumed to be quasistatically influenced by the conditions inside the cylinder of feasibility. Additionally to the standard sensors of the engine, several at IVC and the injection parameters. The former are sensors have been integrated in the engine. The most defined by the CO2 rate, which is coupled to the EGR rate relevant are the AVL micro soot sensor, an intake CO2 and the O2 rate of the exhaust, the gas temperature and sensor, and a Pierburg exhaust gas analyzer for NOx , CO, the boost pressure. Figure 1 illustrates this characteristic HC, CO2 , and O2 . The signals from additional sensors are with steps in the rail pressure and their influence on the collected on two additional CAN bus lines via the ES910. measured PM emissions. The model presented here is similarly structured as the The PM emission are measured with the AVL Micro NOx -model from Schilling et al. (2006). It’s fundamental Soot Sensor which is a photo-acoustic soot sensor (PASS). idea relies on the fact that the engine state in stationary This sensor is capable of measuring the concentration conditions is defined by the engine speed ne and load (i.e. fuel mean effective pressure pm,ϕ ). Accordingly for a first 1 The relevant inputs are found with a combination of expert approximation of the emissions, a stationary map can be knowledge and an input variable selection algorithm, i.e. a genetic used. To take into account the influence of deviations in algorithm which selects the most relevant inputs out of a number of the engine inputs (for example in transient mode) the given inputs. Compression ratio

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δu1

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Fig. 2. Block diagram of the control oriented PM model structure. The inputs to the model are obtained from ECU-data.

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where yˆ, y¯ and δy stand for the estimated, base-map, and relatively deviated PM emissions, respectively. y¯ = y¯ (ne , pm,ϕ ) is a look-up table with the stored operating-point dependent PM emission values. The relative deviation of the emissions δy is modeled as operating point dependent and its complexity is adaptable to the user’s needs. For example, a quadratic approach is shown in equation (2). Note the single use of the absolute input deviation |δu| in the quadratic term to take into account the direction of the deviation. δy = Θl · δu + |δu| · Θq · δu (2)

δu4

normalized deviations need to be integrated. This leads to the following structure of the model: yˆ = y¯ · (1 + δy) (1)

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t [s]

Fig. 3. Trajectories of the model inputs δui representing the measurement data used for identification. The operating point shown here is 2200 rpm, 160 Nm. ∆tpm is taken into account. Thus the model is extended as follows (cp. the PT1 and delay block in figure 2): 1 d yˆs (t) = − · [ˆ ys (t) − yˆ (t − ∆tpm )] (5) dt τfilt

The operating point dependency is required to take into account the high nonlinearity of the PM emissions. In this paper it is considered in the form of look-up tables for the parameter matrices Θ. For each grid-point i, the parameter matrices have the following form (where p is the number of inputs):

The delay ∆tpm is modeled as a combination of a constant part and a exhaust volume-flow proportional part. This approximation takes into account the variable transport delay from the cylinders to the sampling point and the assumed to be constant transport delay from the sampling point to the measurement chamber. Vref (6) ∆tpm = ∆tconst + V˙ eg

h i Θl (ne,i , pm,ϕ,i ) = θpm,1,i · · · θpm,p,i   θpm,11,i · · · θpm,1p,i  . ..  ..  Θq (ne,i , pm,ϕ,i ) =  . .   .. θpm,p1,i · · · θpm,pp,i

where the exhaust volume flow is obtained with the exhaust mass flow under ideal gas assumption. m ˙ eg · Reg · ϑut (7) V˙ eg = put

(3)

The vector of input deviations δu is obtained with the deviations of each input j: uj − u ¯j δuj = (4) u ¯j where u ¯j and uj stand for the base-map and measured value of input j, respectively. Figure 2 shows the structure of the model formulation.

where the index ut refers to upstream of the turbine. The exhaust mass flow is obtained with the cylinder gas and fuel mass mg,cyl , mϕ,cyl (delayed by the induction-toexhaust and the injection-to-exhaust delay, respectively; cp. Guzzella and Onder (2010)), and the engine speed ne : (mg,cyl + mϕ,cyl ) · Z · ne m ˙ eg = (8) 60 · 2 where Z is the number of cylinders. The inputs used for the model are:

Due to the quasi-static modeling of the PM raw emissions, input oscillations result in oscillations of the modeled PM emissions. In the real engine, such oscillations are damped through gas mixing on the way to the PASS. A first order filter with time constant τfilt = 0.25 s is included in the model to take into account this damping. Furthermore, the delay from the cylinder to the PASS measurement chamber 224

• • • • 2

u1 u2 u3 u4

burned-gas ratio 2 in the intake gas xbg,im . inducted cylinder fresh-gas mass mg,cyl . rail pressure prail . start of injection φSOI .

Burned gas refers to exhaust gas obtained from stoichiometric combustion of fuel with air.

AAC 2010 Munich, Germany, July 12-14, 2010

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Fig. 6. Operating point dependent sensitivity of the model on input u3 (i.e. value of the parameter θpm,3 in the operating map).

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The identification has been carried out sequentially on the parameters Θ and the time delay ∆tpm . For identification, the measured data has been modified by removing the dynamic part. This was done by removing the trajectory fraction from the beginning of each reference value step to the settling of the PM value. To take into account the delay ∆tpm , the utilized interval of the PM signal has been shifted relatively to the input signals. Figures 4, 5, 6, 7, and 8 show the operating point dependent sensitivities of the model on the different inputs δui and the coupled term δu1 ·δu2 , respectively. The sensitivity values shown in the maps are the gains from a relative deviation in the corresponding input on the relative deviation of the PM emissions. For example a 10% increase in the inducted cylinder freshgas mass (u2 ) with respect to the base-map value u ¯2 at an operating point of 2000 rpm and 17 bar fuel mean effective pressure results in a decrease of approx. 30% in the PM emissions with respect to the base-map emissions y¯.

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3.1 Identification For the identification procedure, measurements with steps in the engine inputs have been used (i.e. measurement # 2 in table C.1). Figure 3 shows the trajectories of the model inputs δui at one operating point (2200 rpm, 160 Nm) used for identification. The base maps have been identified based on the steady state measurements (i.e. measurement # 1 in table C.1).

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The inducted cylinder fresh-gas mass mg,cyl and the intake burned-gas ratio xbg,im are obtained from engine models and are available on the ECU or can be calculated from ECU-data. Adequate models for these values can be found in Guzzella and Onder (2010) or Heywood (1988) for example. To avoid high sensitivities and sign changes for injection close to top dead center an offset of 10◦ crank angle has been added to the SOI values (φTDC = 0).

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Fig. 5. Operating point dependent sensitivity of the model on input u2 (i.e. value of the parameter θpm,2 in the operating map).

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Fig. 4. Operating point dependent sensitivity of the model on input u1 (i.e. value of the parameter θpm,1 in the operating map).

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Fig. 7. Operating point dependent sensitivity of the model on input u4 (i.e. value of the parameter θpm,4 in the operating map).

AAC 2010 Munich, Germany, July 12-14, 2010

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R2 = 0.796 Av. Rel. Err. = 22.3%

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Fig. 8. Operating point dependent sensitivity of the model coupled inputs u1 · u2 (i.e. value of the parameter θq in the operating map).

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Fig. 9. Measured and modeled PM raw emissions for various transients in speed and load. (cp. measurement #3 in table C.1).

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4. VALIDATION AND RESULTS

The results of the verification shows that the approach of modeling the emission deviations relatively to the engine’s steady-state value and as a polynomial function of the relative input deviations yields practical results for emission control. 226

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Figure 10, 11 and 12 show the measured and modeled PM emissions, the input deviation and the operating point for one of the verification transients, respectively. The shown trajectory is a load step starting at 2500 rpm and 200 Nm.

Fig. 11. Trajectories of the model inputs δui corresponding to the modeled PM emissions shown in figure 10.

ne [rpm]

The model (obtained with equations (1), (5) and (9)) has been validated on measured data that had not been used for the identification. The measurements used for validation are # 3 in table C.1. It contains various steps in the engine speed and load. Figure 9 shows the result of the combined identification of the transport delay ∆tpm and the parameters Θ. Also shown in figure 9 are the relative error δe and the coefficient of determination R2 .

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Fig. 12. Operating point trajectory for the transient verification measurement shown in figures 10.

AAC 2010 Munich, Germany, July 12-14, 2010

The disadvantage of the use of a polynomial approach, compared to Benz et al. (2010), is its diminished extrapolation ability. This is due to the fact that for exceeding deflection of the inputs from their reference values, the sensitivity of the PM emissions might change significantly not only in magnitude but potentially also in sign. This is particularly the case for high intake burned-gas ratios. Furthermore, the number of parameters is relatively high for the presented model. Nevertheless, the advantage of the approach presented here is its easy identifiability, its low computational burden and its use of inputs that are obtainable from the ECU. Also, its employment for control applications is straightforward. ACKNOWLEDGEMENTS The authors gratefully acknowledge the financial support by the FVV and the BAFU. Furthermore, we thank Dr. Josef Steuer, Christian Dengler, and Johan Eldh of Daimler AG for their support on engine issues. REFERENCES Alfieri, E. (2009). Emissions-controlled Diesel Engine. Diss. ETH No. 18214, ETH Z¨ urich. Benz, M., Onder, C.H., and Guzzella, L. (2010). Engine emission modeling using a mixed physics and regression approach. Journal of Engineering for Gas Turbines and Power, Vol. 132(No. 4). Brahma, I., Sharp, M.C., and Frazier, T.R. (2009). Empirical modeling of transient emissions and transient response for transient optimization. SAE Intl. Journal of Engines, (Paper No. 2009-01-1508). Christen, U. and Vantine, K. (2001). Event-based meanvalue modeling of DI diesel engines for controller design. SAE Journal of Engines, (Paper No. 2001-01-1242). Guzzella, L. and Onder, C.H. (2010). Introduction to Modeling and Control of Internal Combustion Engine Systems. Springer-Verlag, Berlin, 2nd edition. Heywood, J.B. (1988). Internal Combustion Engine Fundamentals. McGraw-Hill International Editions. Hiroyasu, H. and Kadota, T. (1983). Development and use of a spray combustion modeling to predict diesel engine efficiency and pollutant emissions (part 1 combustion modeling). JSME, Vol. 26(No. 214). Hirsch, M., Alberer, D., and del Re, L. (2008). Grey-box control oriented emissions models. Proceedings of the 17th World Congress, 8514 – 8519. IFAC. Hirsch, M. and del Re, L. (2009). Adapted D-optimal experimental design for transient emission models of diesel engines. SAE 2009 World Congress, (Paper No. 2009-01-0621). Kirchen, P. (2008). Steady-State and Transient Diesel Soot Emissions. Diss. ETH No. 18088, ETH Z¨ urich. Pfeifer, A., Krueger, M., Gruetering, U., and Tonmazic, D. (2003). U.S. 2007 - which way to go? Possible technical solutions. SAE Journal of Engines, (Paper No. 2003-010770). Schilling, A., Amstutz, A., Onder, C., and Guzzella, L. (2006). A real-time model for the prediction of the NOx emissions in DI diesel engines. IEEE International Conference on Control Applications, 2042–2047. Stoelting, E., Seebode, J., Gratzke, R., and Behnk, K. (2008). Emissionsgef¨ uhrtes Motormanagement f¨ ur Nutzfahrzeuganwendungen. MTZ, 69(2008), 1042–1049. 227

Appendix A. ACRONYMS AND ABBREVIATIONS AFR BG EGR ECU IPSO IVC PASS PM SOI VTG

Air-to-fuel ratio Burned gas Exhaust gas recirculation Electronic control unit Intake port shut-off Intake valve close Photo-acoustic soot sensor Particulate matter Start of injection Variable turbine geometry

Appendix B. SYMBOLS m ˙ eg mg,cyl mϕ,cyl ne pi pm,ϕ ui V˙ eg xbg,im y Z Θ ϑi σst φSOI

Exhaust gas mass flow [kg/s] Cylinder gas mass [kg] Injected fuel mass per cylinder [kg] Engine speed [rpm] Pressure at measurement point i [Pa] Fuel mean effective pressure [Pa] Model input i [.] Exhaust gas mass flow [m3 /s] Intake burned-gas ratio [−] 3 Model/plant output [mg/m ] Number of cylinders [−] Parameter matrix [−] Temperature at measurement point i [K] Stoichiometric air to fuel ratio [−] SOI crank angle [deg] Appendix C. MEASUREMENTS

The following table gives an overview to the measurements carried out for identification and validation of the presented model. Table C.1. Measurements #

Range

Description

1

1600 − 3400 rpm 80 − 320 Nm

Stationary measurements

2

1600 − 3400 rpm 80 − 320 Nm

Measurements with steps in the rail pressure, EGR rate, charge pressure and SOI, respectively

3

1900 − 3100 rpm 100 − 280 Nm

Measurements with transients in both speed and load