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Research Papers

Determining Model Accuracy Requirements for Automotive Engine Coldstart Hydrocarbon Emissions Control

[+] Author and Article Information

Department of Systems Design Engineering,  University of Waterloo, Waterloo, ON, N2L 3G1, Canadanlashgar@uwaterloo.ca

Pannag R. Sanketi

Google, Inc, Mountain View, CA 94043pannag@gmail.com

J. Karl Hedrick

Vehicle Dynamics and Control Lab, Etcheverry Hall,  University of California, Berkeley, CA 94720khedrick@me.berkeley.edu

J. Dyn. Sys., Meas., Control 134(5), 051002 (Jun 05, 2012) (11 pages) doi:10.1115/1.4006217 History: Received March 09, 2010; Revised January 30, 2012; Published June 05, 2012; Online June 05, 2012

Abstract

In this work, a systematic method is introduced to determine the required accuracy of an automotive engine model used for real-time optimal control of coldstart hydrocarbon ($HC$) emissions. The engine model structure and development are briefly explained and the model predictions versus experimental results are presented. The control design problem is represented with a dynamic optimization formulation on the basis of the engine model and solved using the Pontryagin’s minimum principle (PMP). To relate the level of plant/model mismatch and the control performance degradation in practice, a sensitivity analysis using a computationally efficient method is employed. In this way, the sensitivities or the effects of small parameter variations on the optimal solution, which is the minimum of cumulative tailpipe $HC$ emissions over the coldstart period, are calculated. There is a good agreement between the sensitivity analysis results and the experimental data. The sensitivities indicate the directions of the subsequent parameter estimation and model improvement tasks to enhance the control-relevant accuracy, and thus, the control performance. Furthermore, they provide some insights to simplify the engine model, which is critical for real-time implementation of the coldstart optimal control system.

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Figures

Figure 5

Typical engine speed curves during coldstart period (known external inputs)

Figure 4

Comparison between the measured and computed Texh for several coldstart runs

Figure 3

Comparison between the measured and computed HCraw-c for a coldstart run

Figure 2

Comparison between the measured and computed Texh for a coldstart run

Figure 1

Block diagram models for Texh and HCraw-c

Figure 19

ϖe for a coldstart run

Figure 9

The engine-out HC emissions rate for the optimum solution

Figure 10

The profile of air/fuel ratio for the optimum solution

Figure 6

The minimum value of the objective function in different iterations

Figure 7

The optimal exhaust temperature trajectory

Figure 8

The catalyst efficiency for the optimum solution

Figure 13

Δ for a coldstart experiment

Figure 14

AFR for a coldstart experiment

Figure 15

ϖe for a coldstart experiment

Figure 16

HCraw-c for a coldstart run

Figure 17

Δ for a coldstart run

Figure 18

AFR for a coldstart run

Figure 11

The profile of spark timing for the optimum solution

Figure 12

Texh for a coldstart experiment

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