SIMPLIFIED MODELS OF ENGINE HCEMISSIONS, EXHAUST TEMPERATURE AND

CATALYST TEMPERATURE FORAUTOMOTIVE COLDSTART

J.Carlos Zavala ∗,1 Pannag R. Sanketi ∗

M.Wilcutts ∗ T.Kaga ∗∗ J. K. Hedrick ∗

∗Vehicle Dynamics Laboratory, Etcheverry Hall,University of California, Berkeley, USA- 94720∗∗ Toyota Technical Center U.S.A., Inc. Berkeley

Laboratory, Tech. Research Dept.

Abstract: The initial 1-2 minutes of operation of an automotive spark-ignitionengine, commonly called as the ”coldstart” period, produces more than 75-80% of the hydrocarbon (HC) emissions in a typical drive cycle. Model-basedcontroller development requires accurate, yet simple, models that can run in real-time. Simple, intuitive models are developed to predict both tailpipe hydrocarbon(HC) emissions and exhaust temperature during coldstart. Each of the models ischosen to be sum of first order linear systems based on the experimental dataand ease of parameter identification. Inputs to these models are AFR, sparktiming and engine crankshaft speed. A reduced order thermodynamic model for thecatalyst temperature is also developed. The parameters are identified using leastsquares technique. The model estimates for the coldstart are compared with theexperimental results with good agreement. Submitted to Fifth IFAC Symposiumon Advances in Automotive Control

Keywords: Coldstart, Engine Thermal Model, Catalyst Model

1. INTRODUCTION

As regulations on emissions for automotive en-gines become more stringent, the reduction ofhydrocarbon (HC) emissions during coldstart con-tinues to pose a relevant challenge for the industry.Developing simple models which can run in real-time is necessary to design controllers using themodel-based paradigm.

A lot of interest has been shown in modeling andanalysis of engine and catalyst subsystems forcoldstart analysis. The initial work on physicallybased dynamic engine models that account for the

1 czavala@me.berkeley.edu

throttle dynamics and intake manifold dynamicscan be traced back to (Powell 1979) and (Dobner1983). It was further modified by (Moskwa andHedrick 1987) and (Cho and Hedrick 1989). Re-cent work on engine subsytems modeling can befound in (Tunestal and Hedrick 2001), (Balluchiet al. 2001),(Shaw and Hedrick 2002),(Zavalaet al. 2006),(Sanketi et al. 2006b). (Shaw andHedrick 2002) and references therein developedmodels for engine-out exhaust gas temperature(Texh) and raw HC (HCraw). In this paper, sim-ple, intuitive models for Texh and HCraw are de-veloped. Each of these is modeled as a sum of firstorder linear systems based on the experimentaldata and ease of parameter identification. Inputsto these models are air to fuel ratio (AFR), spark

timing and engine crankshaft speed (ωe). AFR,spark and changes in ωe are related to the com-bustion stability. (See Sec. 2.1 and 2.2).

Modeling and analysis of catalysts is also impor-tant for coldstart controller design. These rangefrom very complex ones to simplified ones whichare more suitable for closed-loop control. Someof the important contributions are (Ohsawa et al.1998), (Shen et al. 1999), (Chan and Hoang 1999),(Jones et al. 2000), (Brandt et al. 2000),(Fiengoet al. 2002), (Shaw et al. 2002), (Koltsakis andTsinoglou 2003), (Sanketi et al. 2006a) and refer-ences therein. The catalyst model presented hereis an improved version of the model developed in(Sanketi et al. 2006a). A thermodynamic energybalance is used to model the catalyst temperature(Tcat). Further, thermal diffusivity calculation isused to reduce the order of the catalyst tempera-ture model. (See Sec. 2.3).

The contribution of this paper lies in developingnew simplified models for HCraw, Texh and Tcat.Our goal is to develop a simplified model-basedcontroller for coldstart. A MIMO sliding controllerfor coldstart designed using these models is pre-sented in another paper submitted to the samesymposium.

2. MODEL OF PLANT

The model presented here has been developedbased on the influence of the AFR, engine speedand spark timing on Texh and HCraw. AFR andspark timing directly affect the combustion pro-cess. In addition, changes in engine speed affectthe cylinder pressure and hence, the quality ofcombustion. Experiments indicated that the en-gine speed was having a more noticeable influenceon HCraw and Texh as compared to the intakeair flow rate. Also, each of the chosen inputscan be modified easily to observe the effect onTexh, which simplifies the process of modeling.The Texh, HCraw and Tcat submodels have beensimulated together with an engine model pre-sented in (Cho and Hedrick 1989) and (Sanketiet al. 2006b).

2.1 Exhaust Temperature Model

Through experiments, it was observed that Texh

was responding almost like a first order linearsystem to each of the input variables. Hence,the output was modeled as a set of three firstorder linear systems running in parallel that relatethe three variables mentioned before to Texh.The block diagram shown in Fig.1 illustrates theidea. It should be noted that however, the inputshave been offset around certain nominal value

Fig. 1. Block Model for Exhaust temperaturemodel

0 20 40 60 80 1000

100

200

300

400

500

600

Texh

deg C

TIME (s)

Exh

Tem

p C

Case 1Case 2Case 3

Fig. 2. Experiments showing the effect of inputson exhaust temperature- Texh

0 20 40 60 80 100−20

−15

−10

−5

0

5

10Spark after TDC

TIME (s)

∆ A

TD

C

Case 1Case 2Case 3

Fig. 3. Experiments showing the effect of inputson exhaust temperature- Spark

in the model and saturations have been applied,too. Negative actuation has also to be ruled out.Though this model does not follow any physics-based combustion modeling, it is intuitive; and itis simple and suitable for engine controller design.

Figures 2 through 5 illustrate the effect of inputson Texh. Retarding the spark, increasing the en-gine speed and a richer AFR lead to an increasein Texh. Texh is slower in response to AFR and en-gine speed as compared to the spark timing. Also,the effect of spark timing was found to be moreprominent than that of others. The parameters ofthe model were obtained for the coldstart periodusing least squares.

0 20 40 60 80 1000

500

1000

1500

2000

2500

3000Engine Speed RPM

TIME (s)

ωe R

PM

Case 1Case 2Case 3

Fig. 4. Experiments showing the effect of inputson exhaust temperature- RPM

0 20 40 60 80 1007

8

9

10

11

12

13

14

15

16

17AFR

TIME (s)

AF

R

Case 1Case 2Case 3

Fig. 5. Experiments showing the effect of inputson exhaust temperature- AFR

0 20 40 60 80 1000

200

400

600

Time [s]

Tex

h

Texh measuredTexh from model

0 100 200 300 400 500 6000

200

400

600

Texh model

Tex

h ex

p.

Fig. 6. Comparison between measured and com-puted exhaust temperature for a coldstartrun

Fig.6 shows the comparison of the model versusexperimental data for an engine coldstart run.The second part of the figure shows an error ofabout 50C, however, the first part of the figureillustrates that it is due to a small delay in thetransient rise of the temperature. This will nothave a significant effect on the catalyst efficiencyprofile. Fig.7 shows the comparison between themodel and the experimental values for exhausttemperature over several coldstart experiments.Errors of about 50-60 C are consistently foundin the transient part of the temperature profile. Asteady state error of about 80 C is also found inone of the data sets. Overall, the mean error was

0 100 200 300 400 500 6000

100

200

300

400

500

600

Texh

model

Tex

h exp

erim

ents

Fig. 7. Comparison between measured and com-puted exhaust temperature for several cold-start runs

Fig. 8. Block Model for hydrocarbon emissionsmodel

4.9414 C with a standard deviation of 34.8981 C.

2.2 Hydrocarbon Emissions Model

The raw hydrocarbon emissions HCraw was alsomodeled as a sum of first-order linear systems,very similar in concept to that of Texh. It makessense since both HCraw and Texh are productsof the same process. As in the case of Texh,three linear subsystems describe the interactionbetween AFR, engine speed and spark timingwith the hydrocarbon emissions. However, theinput offsets are different than those used for theTexh model. Fig.8 illustrates the concept of themodel.

Figures 9 through 12 illustrate the effect of inputson HCraw. Retarding the spark above certainvalue, decreasing the engine speed and a richerAFR lead to an increase in HCraw. HCraw ismuch faster in response to AFR as compared tothe engine speed and the spark timing. Also, theeffect of AFR was found to be more prominentthan others. The parameters of the model were ob-tained for the coldstart period using least squares.

Fig.13 shows the comparison between the modeland the experimental hydrocarbon emissions fora coldstart run and Fig.14 shows the compari-son of the model and experimental hydrocarbon

0 20 40 60 80 100 1200

2000

4000

6000

8000

10000

12000

14000HC raw ppm

TIME (s)

HC

raw

ppm

Case 1Case 2Case 3

Fig. 9. Experiments showing the effect of inputson raw emissions- HCraw

0 20 40 60 80 100 1208

10

12

14

16

18

20

22AFR

TIME (s)

AF

R

Case 1Case 2Case 3

Fig. 10. Experiments showing the effect of inputson raw emissions- AFR

0 20 40 60 80 100 1200

500

1000

1500

2000

2500Engine Speed RPM

TIME (s)

ωe R

PM

Case 1Case 2Case 3

Fig. 11. Experiments showing the effect of inputson raw emissions- RPM

0 20 40 60 80 100 120−25

−20

−15

−10

−5

0

5

10

15

20Spark after TDC

TIME (s)

∆ A

TD

C

Case 1Case 2Case 3

Fig. 12. Experiments showing the effect of inputson raw emissions- Spark

0 20 40 60 80 1000

5000

10000

15000

Time [s]

HC

HC measuredHC from model

0 2000 4000 6000 8000 10000 120000

5000

10000

15000

HCs model

HC

s ex

p.

Fig. 13. Comparison between measured and com-puted hydrocarbon for one coldstart run

0 2000 4000 6000 8000 10000 12000 140000

2000

4000

6000

8000

10000

12000

14000

HCs model

HC

s ex

perim

ents

Fig. 14. Comparison between measured and com-puted hydrocarbon for several coldstart runs

emissions in ppm over several experiments. Thelargest errors occur during the transients closeto the peak of the emissions which is the periodwhen the signal changes more rapidly, whereas theerrors are lower at steady state. Overall, the meanerror was 388.7233 ppm with a standard deviationof 959.3685 ppm.

2.3 Catalyst Model

This part describes the physics that governs thecatalyst warm up including the water condensa-tion and evaporation effect. The simplified cat-alyst model has a structure similar to that de-scribed in (Sanketi et al. 2006a). Here, a thermaldiffusivity calculation is used to show that the gascomes in equilibrium with the solid before it leavesthe catalyst, thus making unnecessary the use ofdifferent states for the catalyst solid temperatureand the gas temperature.

A single cell of the catalytic converter is analyzed.The time scale required for the gas and the hon-eycomb mass to come in equilibrium is given by

tdiff =d2

α(1)

where, the characteristic length d for diffusion isequal to half the cell side length and α is thermaldiffusivity of the gas. This was compared with

the time required for the gas to travel throughthe catalyst, which was calculated using the av-erage exhaust gas flow rate in a typical coldstart.The calculations were performed at three differenttemperatures spanning the coldstart. The resultsare shown in Table 1.

Table 1. Time for travel and diffusiontime scale

No. Gas Temp. Time Travel Diffusion Time(K) (s) Scale (s)

1 350 0.1114 0.05592 550 0.0709 0.02693 700 0.0557 0.0183

From table 1, it can be seen that the time takenby the gas to travel through the catalyst is two tothree times the time scale for the gas to come intoequilibrium with the catalyst solid mass. Hence,for our analysis, we can assume that the gas andthe solid mass of the catalyst are at the sametemperature and modeling the catalyst requiresonly one temperature state instead of two.

2.4 Model Equations

The catalyst temperature depends on the heat ob-tained from the feedgas flowing into the catalyst,the amount of heat generated due to oxidation ofpollutants from the feedgas (Qgen) and the heattransfer to the surroundings (Qout) . In additionto these heat transfers, heat is lost due to evapo-ration of the moisture in the catalyst (Qev). Thismoisture is accumulated in the initial few secondsof operation due to condensation of vapor on thecold surface of the catalytic converter. When thetemperature reaches the saturation temperatureof the condensed vapor, the vapor starts evapo-rating. Due to the heavy heat loss in evaporation,the catalyst temperature remains almost constantor increases at a very low rate. Thus, there is aplateau in the temperature profile. The catalysttemperature dynamics can be summarized as fol-lows.

During the plateau:

Tcat =1

mgasCv + MC[mexhCp(Texh − Ttp)

−Qout + Qgen − Qev] (2)

otherwise

Tcat =1

mgasCv + MC[mexhCp(Texh − Ttp)

−Qout + Qgen] (3)

Qev = mev∆hev (4)

0 10 20 30 40 50 60 700

100

200

300

400

Time [s]

Tca

t C

Tcat

measured

Tcat

from model

0 50 100 150 200 250 300 350 4000

100

200

300

400

Tcat

model C

Tca

t exp

. C

Fig. 15. Comparison between measured and com-puted Tcat for several coldstart runs

0 50 100 150 200 250 300 350 400 4500

50

100

150

200

250

300

350

400

450

Tcat

model C

Tca

t exp

. C

Fig. 16. Comparison between measured and com-puted Tcat for several coldstart runs

where, mexh is the exhaust gas flow rate, M isthe solid mass of the catalyst, mgas is the massof the gas inside the catalyst, mev is the massrate of evaporation and ∆hev is the enthalpyof evaporation at the corresponding saturationtemperature. It is not straightforward to find Qev

directly. Hence, it is calculated implicitly using amethod that is similar to that used in (Sanketiet al. 2006a). It employs a parameter adaptationalgorithm that uses the Tcat measurement to findQev through Qout. Readers are encouraged to read(Sanketi et al. 2006a) for details.

Fig.15 shows the comparison of the model versusexperimental data for an engine coldstart run.Fig.16 shows the comparison between the modeland the experimental values for exhaust temper-ature over several coldstart experiments. Overall,the mean error was 10.4227 C with a standarddeviation of 22.2439 C.

3. CONCLUSIONS

Simplified control-oriented models of engine-outhydrocarbon emissions (HCraw), exhaust temper-ature (Texh), and catalyst temperature (Tcat) werepresented. HCraw was modeled as a sum of firstorder linear systems with three different inputsnamely, air-fuel ratio AFR, spark timing and en-gine speed ωe. Such a model structure was based

on the experimental data and ease of parameteridentification. The structure of the Texh modelwas chosen similar to that of HCraw. A reducedorder thermodynamic model for the catalyst tem-perature was developed using thermal diffusivityanalysis. The parameters were identified usingleast squares methodology. The model estimatesduring the warm-up agreed well with the exper-imental results. A MIMO sliding controller forcoldstart designed using these models is presentedin another paper submitted to the same sympo-sium.

4. ACKNOWLEDGEMENTS

Authors acknowledge the financial support pro-vided by CONACYT (Consejo Nacional de Cien-cia y Tecnologıa de Mexico) and by the Cen-ter for Hybrid and Embedded Software Systems(CHESS) at UC Berkeley, which receives sup-port from the National Science Foundation (NSFaward #CCR-0225610), the State of CaliforniaMicro Program, and the following companies: Ag-ilent, Bosch, DGIST, General Motors, HewlettPackard, Infineon, Microsoft, National Instru-ments, and Toyota.

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